Abstract:
A method of forming a dispersed message for embedding in an image, includes the steps of: providing a random phase carrier; defining a set of ordered bit locations; assigning a polarity to each bit location corresponding to a bit of the message; cyclically shifting the random phase carrier in accordance with each bit location and weighting the cyclically shifted carriers by the polarity of the corresponding bit; and forming a sum of the cyclically shifted weighted carriers to form the dispersed message.

Description:
The Federal Government shall have a nonexclusive, non-transferable, irrevocable, paid-up license to practice or have practiced for or on behalf of the United States the subject invention throughout the world. Invention made under Government Agreement No. F30602-99-2-0541. 
    
    
     FIELD OF THE INVENTION 
     The invention relates generally to the field of embedding and extracting hidden messages in source data. This field is also referred to as data hiding, information hiding, watermarking and also steganography. More specifically the invention relates to the generation of a dispersed message for embedding in a digital image in a camera or printer. 
     BACKGROUND OF THE INVENTION 
     U.S. Pat. No. 6,044,156 issued Mar. 28, 2000 to Honsinger et al. entitled Method For Generating An Improved Carrier For Use In An Image Data Embedding Application, discloses a technique for embedding messages in digital image data. This method for embedding a hidden message into a digitized image includes the steps of: forming a digitized version of the desired message; generating a random phase carrier; convolving the digitized version of the desired message and the random phase carrier to form a dispersed message; and combining the dispersed message with the digitized image to form an embedded hidden message image. Hidden messages may be embedded in photographic images recorded on film and paper using conventional photographic printing techniques, or they may be embedded in images produced on printers such as ink jet and thermal dye transfer printers, by combining the dispersed message with a digital image using digital image processing techniques. 
     The hidden messages are recovered from the embedded hidden message image by cross correlating the embedded hidden message image containing the dispersed message with a decoding carrier to recover the embedded dispersed message; and extracting the digital message data from the recovered dispersed message. 
     One problem with the above described techniques is that when a digital image is formed in an apparatus such as a camera or a printer, the complex computer processing capability needed for forming the dispersed message is not present in the apparatus although the apparatus will generally include a simple computer suitable for basic digital image processing and machine control. There is a need therefore for a simpler method of forming the dispersed message. 
     SUMMARY OF THE INVENTION 
     The need is met according to the present invention by providing a method for forming a dispersed message for embedding in an image, that includes the steps of: providing a random phase carrier; defining a set of ordered bit locations; assigning a polarity to each bit location corresponding to a bit of the message; cyclically shifting the random phase carrier in accordance with each bit location and weighting the cyclically shifted carriers by the polarity of the corresponding bit; and forming a sum of the cyclically shifted weighted carriers to form the dispersed message. 
     The method of the present invention has the advantage of requiring very little image processing capability for implementation, and is therefore suitable for use in apparatus such a digital camera or printer. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 is a block diagram showing a typical digital camera configuration useful for practicing the method of the present invention; 
     FIG. 2 is a flow chart showing the steps of the method of the present invention; and 
     FIG. 3 is a table showing a 64×64 pixel carrier according to the present invention. 
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     Referring to FIG. 1 a digital camera useful for practice of the present invention includes a lens  10  for forming an image a subject  12  onto a solid state image sensor  14 . The image sensor  14  may include a color filter array  16 . The image signals produced by the image sensor  14  are processed in process and control electronics  18 , which is generally embodied as a microprocessor having limited memory storage and data processing capability. Image processing carried out by the process and control electronics  18  includes data formatting, color interpolation, image enhancement and data compression. The processed digital image can be displayed on a display screen  20 , or stored in a digital image memory  22 , such as a magnetic storage device, or solid state memory chip. 
     An operator interface  24  includes camera controls, and data input means such as a physical keyboard, or a virtual keyboard provided via a touch sensitive screen over the display screen  20  whereby the operator can enter a message that will be embedded in the image data recorded by the camera. Alternatively, a message, such as a current date, can be generated by the process and control electronics  18 . The camera may include sensors such as a global position sensor for generating message data. 
     Referring to FIG. 2, the message is generated according to the present invention by defining ( 26 ) a list of ordered bit locations, an example of which is shown in Table 1 
     
       
         
               
             
               
               
               
             
               
               
               
             
           
               
                 TABLE 1 
               
             
             
               
                   
               
               
                 32 place X,Y ordered bit location table 
               
             
          
           
               
                 BIT NUMBER 
                 XLOC 
                 YLOC 
               
               
                   
               
             
          
           
               
                 0 
                 43 
                 4 
               
               
                 1 
                 4 
                 7 
               
               
                 2 
                 15 
                 7 
               
               
                 3 
                 28 
                 9 
               
               
                 4 
                 9 
                 12 
               
               
                 5 
                 55 
                 12 
               
               
                 6 
                 15 
                 16 
               
               
                 7 
                 37 
                 17 
               
               
                 8 
                 5 
                 18 
               
               
                 9 
                 44 
                 21 
               
               
                 10 
                 11 
                 22 
               
               
                 11 
                 35 
                 24 
               
               
                 12 
                 27 
                 25 
               
               
                 13 
                 55 
                 28 
               
               
                 14 
                 9 
                 29 
               
               
                 15 
                 31 
                 31 
               
               
                 16 
                 48 
                 34 
               
               
                 17 
                 9 
                 37 
               
               
                 18 
                 17 
                 38 
               
               
                 19 
                 2 
                 40 
               
               
                 20 
                 34 
                 41 
               
               
                 21 
                 12 
                 44 
               
               
                 22 
                 41 
                 46 
               
               
                 23 
                 5 
                 47 
               
               
                 24 
                 34 
                 48 
               
               
                 25 
                 16 
                 49 
               
               
                 26 
                 44 
                 53 
               
               
                 27 
                 22 
                 53 
               
               
                 28 
                 29 
                 56 
               
               
                 29 
                 15 
                 58 
               
               
                 30 
                 7 
                 60 
               
               
                 31 
                 43 
                 61 
               
               
                   
               
             
          
         
       
     
     In a preferred embodiment, the ordered bit locations are generated in such a way that the autocorrelation of the bit locations in an image is highly peaked. An example of how to generate such a list of bit locations is disclosed in U.S. patent application Ser. No. 09/453,160 filed Dec. 2, 1999 by Honsinger et al. entitled Method And Computer Program For Embedding And Extracting An Embedded Message From A Digital Image. 
     The message, which may have been input by the camera user, or generated by the process and control electronics is digitized ( 28 ), if required, and each bit of the digital message is assigned ( 30 ) as a polarity (+ or −) with ones being assigned a plus polarity and zeros a minus polarity, to one of the ordered bit locations. Next, a random carrier  32  is cyclically shifted ( 34 ) according to the corresponding bit location and the shifted carriers are weighted by the corresponding polarity assigned to the bit location. If the polarity is +, no change is made to the shifted carrier, however if the polarity is −, all of the values of the carrier are reversed in sign. The carrier is a random array of values, for example from +10 to −10 that is preferably generated according to the disclosure in U.S. Pat. No. 6,044,156, referenced above. The carrier preferably has a random phase and a flat Fourier spectrum. An example of a 64 pixel by 64 line carrier generated according to the method described by Honsinger et al. is shown in FIG.  3  and Table 3A-3D. 
     The cyclic shifting operation ( 34 ) can be simply implemented in the process and control computer by use of a look up table that defines the new locations for the shifted data from the carrier based on the bit location data. The new data values are defined as follows 
       C ′( x,y )= C (LUT( x+Δx ), LUT( y+Δy )), 
     where C′(x,y) is the cyclically shifted carrier, x and y are the coordinate locations of the values in both the original and shifted carriers, and Δx and Δy are the bit locations from Table 1. The LUT is a 128 place table that starts with 0 and goes up to 63 and then repeats. The effect of the table is to implement the mathematical process of cyclically shifting and eliminates the need for the use of the C language runtime library Modulus function when the program is implemented in the C programming language. 
     Finally the weighted, cyclically shifted carriers are summed ( 36 ) to produce the dispersed message. 
     Assuming that the digital image is much larger than the dispersed message, the dispersed message is preferably added to the digital image in a tile wise fashion as is known in the prior art. The image containing the hidden message is then stored in the memory  22 . If the digital image is compressed, for example by using JPEG compression, the hidden message is can be added to the image prior to compression to minimize the amount of redesign from current practice that is required. 
     The present invention may be implemented in existing cameras by addition of a computer program to the computer in the process and control electronics. Similarly, the invention can be implemented in a digital printer such as an ink jet printer or thermal resistive printer, a display device such as an Liquid Crystal Display or Organic Light Emitting Diode Display, or a scanner such as a flatbed or handheld scanner. Hidden message, such as a copyright notice, to an image can be added respectively before printing, displaying, or after scanning an image. 
     Appendix A contains a computer program written in the C language for generating an embedded message according to the present invention. The computer program can be distributed to camera users for example by delivering the software on a PCMCIA memory card or a CompactFlash card available from the SanDisc corporation that is plugged into the camera and accessed by the process and control electronics. 
     The hidden messages are recovered from the image by cross correlating the image containing the dispersed message with the carrier to produce a recovered message image that appears as a digital image having negative or positive peaks located at the same bit locations that are noted in Table 1 above. The digital message data is then reconstructed by detecting the polarity of the peaks and assigning corresponding bit values (i.e. a 1 for positive peaks and a 0 for negative peaks). 
     The invention has been described in detail with particular reference to certain preferred embodiments thereof, but it will be understood that variations and modifications can be effected within the spirit and scope of the invention. 
     PARTS LIST 
       10  lens 
       12  subject 
       14  image sensor 
       16  filter array 
       18  process and control electronics 
       20  display screen 
       22  memory 
       24  operator interface 
       26  generate message step 
       28  digitize message step 
       30  assign bit polarity step 
       32  carrier 
       34  cyclically shift carrier step 
       36  sum weighted carrier step 
     
       
         
               
             
               
               
             
               
             
               
               
             
               
             
               
               
             
               
             
               
               
             
               
             
               
               
             
               
             
               
               
             
               
             
               
               
             
               
             
               
               
             
               
             
               
               
             
               
             
               
               
             
               
             
               
               
             
               
             
               
               
             
               
             
               
               
             
               
             
               
               
             
               
             
               
               
             
               
             
               
               
             
               
             
               
               
             
               
             
               
               
             
               
             
               
               
             
               
             
               
               
             
               
             
               
               
             
               
             
               
               
             
               
             
               
               
             
               
             
               
               
             
               
             
               
               
             
               
             
               
               
             
               
             
               
               
             
               
             
               
               
             
               
             
               
               
             
               
             
               
               
             
               
             
               
               
             
               
             
               
               
             
               
             
               
               
             
               
             
               
               
             
               
             
               
               
             
               
             
               
               
             
               
             
               
               
             
               
             
               
               
             
               
             
               
               
             
               
             
               
               
             
               
             
               
               
             
               
             
               
               
             
               
               
             
               
               
             
               
             
               
               
             
               
             
               
               
             
               
             
               
               
             
               
             
               
               
             
               
             
               
               
             
               
             
               
               
             
               
             
               
               
             
               
             
               
               
             
               
             
               
               
             
               
             
               
               
             
               
             
               
               
             
               
             
               
               
             
               
             
               
               
             
               
             
               
               
             
               
             
               
               
             
               
             
               
               
             
               
             
               
               
             
               
             
           
               
                 APPENDIX A 
               
               
                   
               
             
             
               
                 Program Source Code 
               
               
                 #include &lt;stdio.h&gt; 
               
               
                 #include &lt;stdlib.h&gt; 
               
               
                 #include &lt;sys/param.h&gt; 
               
               
                 #include &lt;curses.h&gt; 
               
               
                 #define BOOL unsigned char 
               
               
                 #define UCHAR unsigned char 
               
               
                 #define ULONG unsigned long 
               
               
                 #define USHORT unsigned short 
               
               
                 #define CLIP(X) (((X) &lt; 0) ? 0:(((X) &gt; 255) ? 255:(X))) 
               
               
                 #define SIZE 128 
               
               
                 #define NUM_BITS 64 
               
               
                 #define II 0x4949 
               
               
                 #define MM 0x4D4D 
               
               
                 #define BIG_ENDIAN 0x01020304 
               
               
                 #define LITTLE_ENDIAN 0x04030201 
               
               
                 #define IMAGE_WIDTH_TAG 256 
               
               
                 #define IMAGE_LENGTH_TAG 257 
               
               
                 #define STRIP_OFFSETS_TAG 273 
               
               
                 #define SAMPLES_PER_PIXEL_TAG 277 
               
               
                 #define STRIP_BYTE_COUNTS_TAG 279 
               
               
                 typedef struct 
               
               
                 { 
               
               
                 USHORT byteOrder; 
               
               
                 USHORT version; 
               
               
                 ULONG firstIFDoffset; 
               
               
                 } TIFF_HEADER; 
               
               
                 typedef struct 
               
               
                 { 
               
               
                 USHORT tag; 
               
               
                 USHORT type; 
               
               
                 ULONG count; 
               
               
                 ULONG value; 
               
               
                 } IFD_ENTRY; 
               
               
                 void process (UCHAR *data, int msgCarrier[SIZE][SIZE], ULONG 
               
               
                  numBytes, ULONG width, ULONG height, ULONG samples); 
               
               
                 ULONG getEndianess(void); 
               
               
                 ULONG swapULong(ULONG value); 
               
               
                 USHORT swapUShort(USHORT value); 
               
               
                 void getIFD(IFD_ENTRY *ifdCopy, IFD_ENTRY *ifd, BOOL 
               
               
                  swapBytes); 
               
               
                 ULONG getULong(ULONG *value, BOOL swapBytes); 
               
               
                 USHORT getUShort(USHORT *value, BOOL swapBytes); 
               
               
                 unsigned char coords[NUM_BITS][2] = { 
               
               
                 /* Bit xloc yloc */ 
               
               
                 /* --- ---- ---- */ 
               
             
          
           
               
                 /* 0 
                 */ 42, 7, 
               
               
                 /* 1 
                 */ 86, 7, 
               
               
                 /* 2 
                 */ 115, 8, 
               
               
                 /* 3 
                 */ 8, 13, 
               
               
                 /* 4 
                 */ 99, 13, 
               
               
                 /* 5 
                 */ 29, 14, 
               
               
                 /* 6 
                 */ 70, 17, 
               
               
                 /* 7 
                 */ 55, 18, 
               
               
                 /* 8 
                 */ 84, 22, 
               
               
                 /* 9 
                 */ 18, 23, 
               
               
                 /* 10 
                 */ 41, 23, 
               
               
                 /* 11 
                 */ 110, 23, 
               
               
                 /* 12 
                 */ 96, 30, 
               
               
                 /* 13 
                 */ 30, 32, 
               
               
                 /* 14 
                 */ 60, 32, 
               
               
                 /* 15 
                 */ 74, 33, 
               
               
                 /* 16 
                 */ 118, 35, 
               
               
                 /* 17 
                 */ 10, 36, 
               
               
                 /* 18 
                 */ 46, 37, 
               
               
                 /* 19 
                 */ 87, 41, 
               
               
                 /* 20 
                 */ 105, 41, 
               
               
                 /* 21 
                 */ 22, 44, 
               
               
                 /* 22 
                 */ 36, 47, 
               
               
                 /* 23 
                 */ 69, 47, 
               
               
                 /* 24 
                 */ 4, 49, 
               
               
                 /* 25 
                 */ 53, 49, 
               
               
                 /* 26 
                 */ 94, 53, 
               
               
                 /* 27 
                 */ 110, 55, 
               
               
                 /* 28 
                 */ 81, 57, 
               
               
                 /* 29 
                 */ 17, 58, 
               
               
                 /* 30 
                 */ 32, 61, 
               
               
                 /* 31 
                 */ 61, 62, 
               
               
                 /* 32 
                 */ 46, 63, 
               
               
                 /* 33 
                 */ 96, 67, 
               
               
                 /* 34 
                 */ 111, 70, 
               
               
                 /* 35 
                 */ 18, 73, 
               
               
                 /* 36 
                 */ 80, 73, 
               
               
                 /* 37 
                 */ 34, 75, 
               
               
                 /* 38 
                 */ 52, 78, 
               
               
                 /* 39 
                 */ 4, 79, 
               
               
                 /* 40 
                 */ 92, 81, 
               
               
                 /* 41 
                 */ 67, 82, 
               
               
                 /* 42 
                 */ 106, 84, 
               
               
                 /* 43 
                 */ 23, 87, 
               
               
                 /* 44 
                 */ 41, 87, 
               
               
                 /* 45 
                 */ 82, 91, 
               
               
                 /* 46 
                 */ 118, 92, 
               
               
                 /* 47 
                 */ 10, 93, 
               
               
                 /* 48 
                 */ 54, 95, 
               
               
                 /* 49 
                 */ 68, 96, 
               
               
                 /* 50 
                 */ 98, 96, 
               
               
                 /* 51 
                 */ 32, 98, 
               
               
                 /* 52 
                 */ 18, 105, 
               
               
                 /* 53 
                 */ 87, 105, 
               
               
                 /* 54 
                 */ 110, 105, 
               
               
                 /* 55 
                 */ 44, 106, 
               
               
                 /* 56 
                 */ 73, 110, 
               
               
                 /* 57 
                 */ 58, 111, 
               
               
                 /* 58 
                 */ 99, 114, 
               
               
                 /* 59 
                 */ 29, 115, 
               
               
                 /* 60 
                 */ 120, 115, 
               
               
                 /* 61 
                 */ 13, 120, 
               
               
                 /* 62 
                 */ 42, 121, 
               
               
                 /* 63 
                 */ 86, 121}; 
               
             
          
           
               
                 main(int argc, char *argv[ ]) 
               
               
                 { 
               
               
                 int carrier[SIZE][SIZE]; 
               
               
                 int msgCarrier[SIZE][SIZE]; 
               
               
                 unsigned char tmp, tmp2; 
               
               
                 int x,y; 
               
               
                 int ix,iy; 
               
               
                 int max; 
               
               
                 char msg[80]; 
               
               
                 char inputFilePath[MAXPATHLEN]; 
               
               
                 char outputFilePath[MAXPATHLEN]; 
               
               
                 FILE *inFile, *outFile; 
               
               
                 UCHAR *file; 
               
               
                 USHORT version; 
               
               
                 USHORT numEntries; 
               
               
                 ULONG fileLength; 
               
               
                 ULONG ifdPtr; 
               
               
                 ULONG i,j; 
               
               
                 ULONG stripOffset; 
               
               
                 ULONG stripByteCount; 
               
               
                 ULONG endianess; 
               
               
                 ULONG imageWidth; 
               
               
                 ULONG imageLength; 
               
               
                 ULONG samplesPerPixel; 
               
               
                 TIFF[—HEADER *header; 
               
               
                 IFD_ENTRY *ifd; 
               
               
                 IFD_ENTRY ifdCopy; 
               
               
                 float scaleFactor; 
               
               
                 BOOL swapBytes; 
               
               
                 if (argc == 1) 
               
               
                 { 
               
             
          
           
               
                   
                 strcpy(msg, “DC290WMC”); 
               
             
          
           
               
                 } 
               
               
                 else 
               
               
                 { 
               
             
          
           
               
                   
                 strcpy(msg, argv[1]); 
               
             
          
           
               
                 } 
               
               
                 if ((inFile = fopen(“carrier.dat”, “rb”)) == NULL) 
               
               
                 { 
               
             
          
           
               
                   
                 perror(“fopen”); 
               
               
                   
                 return(−1); 
               
             
          
           
               
                 } 
               
               
                 if (fread(carrier, SIZE*SIZE*sizeof(int), 1, inFile) != 1) 
               
               
                 { 
               
             
          
           
               
                   
                 perror(“fread”); 
               
               
                   
                 return(−1); 
               
             
          
           
               
                 } 
               
               
                 if (fclose(inFile) != 0) 
               
               
                 { 
               
             
          
           
               
                   
                 perror(“fclose”); 
               
               
                   
                 return(−1); 
               
             
          
           
               
                 } 
               
               
                 for (y=0; y&lt;SIZE; y++) 
               
               
                 { 
               
             
          
           
               
                   
                 for (x=0; x&lt;SIZE; x++) 
               
               
                   
                 { 
               
             
          
           
               
                 carrier[y][x] = (int)swapULong((ULONG)carrier[y][x]); 
               
             
          
           
               
                   
                 } 
               
             
          
           
               
                 } 
               
               
                 for (y=0; y&lt;SIZE; y++) 
               
               
                 { 
               
             
          
           
               
                   
                 for (x=0; x&lt;SIZE; x++) 
               
               
                   
                 { 
               
             
          
           
               
                 msgCarrier[y][x] = 0; 
               
             
          
           
               
                   
                 } 
               
             
          
           
               
                 } 
               
               
                 printf(“Message to embed is %s\n\n”, msg); 
               
               
                 printf(“Bit Xloc Yloc Val\n”); 
               
               
                 printf(“--- ---- ---- ---\n”); 
               
               
                 for (i=0; i&lt;NUM_BITS, i++) 
               
               
                 { 
               
             
          
           
               
                   
                 tmp = msg[i/8]; 
               
               
                   
                 /* tmp2 cal below works ok, but you end up with numbers &gt; 1 
               
               
                   
                 tmp2 = tmp &amp; (1 &lt;&lt; (i % 8)); */ 
               
               
                   
                 tmp2 = (tmp &amp; (1 &lt;&lt; (i % 8))) &gt;&gt; (i % 8); 
               
               
                   
                 printf(“ %2d %3d %3d %d\n”, i, coords[i][0], coords[i][1], tmp2); 
               
               
                   
                 if (tmp2) 
               
               
                   
                 { 
               
             
          
           
               
                 for (iy=0, y=coords[i][1]; iy&lt;SIZE; iy++, y++) 
               
               
                 { 
               
             
          
           
               
                   
                 for (ix=0, x=coords[i][0]; ix&lt;SIZE; ix++, x++) 
               
               
                   
                 { 
               
             
          
           
               
                 msgCarrier[iy][ix] += carrier[y % SIZE][x % SIZE]; 
               
             
          
           
               
                   
                 } 
               
             
          
           
               
                 } 
               
             
          
           
               
                   
                 } 
               
               
                   
                 else 
               
               
                   
                 { 
               
             
          
           
               
                 for (iy=0, y=coords[i][1]; iy&lt;SIZE; iy++, y++) 
               
               
                 { 
               
             
          
           
               
                   
                 for (ix=0, x=coords[i][0]; ix&lt;SIZE; ix++, x++) 
               
               
                   
                 { 
               
             
          
           
               
                 msgCarrier[iy][ix] −= carrier[y % SIZE][x % SIZE]; 
               
             
          
           
               
                   
                 } 
               
             
          
           
               
                 } 
               
             
          
           
               
                   
                 } 
               
             
          
           
               
                 } 
               
               
                 max = 0; 
               
               
                 for (y=0; y&lt;SIZE; y++) 
               
               
                 { 
               
             
          
           
               
                   
                 for (x=0; x&lt;SIZE; x++) 
               
               
                   
                 { 
               
             
          
           
               
                 if (abs(msgCarrier[y][x]) &gt; max) 
               
               
                 { 
               
             
          
           
               
                   
                 max = abs(msgCarrier[y][x]); 
               
             
          
           
               
                 } 
               
             
          
           
               
                   
                 } 
               
             
          
           
               
                 } 
               
               
                 printf(“\nAbsolute Maximum value is %d\n”, max); 
               
               
                 /* Scale the message carrier to 16 max. */ 
               
               
                 scaleFactor = 16.0 / (float)max; 
               
               
                 for (y=0; y&lt;SIZE; y++) 
               
               
                 { 
               
             
          
           
               
                   
                 for (x=0; x&lt;SIZE; x++) 
               
               
                   
                 { 
               
             
          
           
               
                 msgCarrier[y][x] = nint((float)msgCarrier[y][x] * scaleFactor); 
               
             
          
           
               
                   
                 } 
               
             
          
           
               
                 } 
               
               
                 strcpy(inputFilePath, “barney.tif”); 
               
               
                 strcpy(outputFilePath, “barney1.tif”); 
               
               
                 if ((inFile = fopen(inputFilePath, “r”)) == NULL) 
               
               
                 { 
               
             
          
           
               
                   
                 perror(“Unable to open input file”); 
               
               
                   
                 return(−1); 
               
             
          
           
               
                 } 
               
               
                 if(fseek(inFile, 0L, SEEK_END) &lt; 0) 
               
               
                 { 
               
             
          
           
               
                   
                 perror(“Unable to seek to end of input file”); 
               
               
                   
                 return(−1); 
               
             
          
           
               
                 } 
               
               
                 fileLength = ftell(inFile); 
               
               
                 if (fseek(inFile, 0L, SEEK_SET) &lt; 0) 
               
               
                 { 
               
             
          
           
               
                   
                 perror(“Unable to seek to start of input file”); 
               
               
                   
                 return(−1); 
               
             
          
           
               
                 } 
               
               
                 printf(“%s is %u bytes in length.\n”, inputFilePath, fileLength); 
               
               
                 if((file = malloc(fileLength)) == NULL) 
               
               
                 { 
               
             
          
           
               
                   
                 perror(“Unable allocate memory for the input file”); 
               
               
                   
                 return(−1); 
               
             
          
           
               
                 } 
               
               
                 if (fread(file, fileLength, 1, inFile) == 0) 
               
               
                 { 
               
             
          
           
               
                   
                 perror(“Unable to read input file”); 
               
               
                   
                 return(−1); 
               
             
          
           
               
                 } 
               
               
                 printf(“%s file read in\n”, inputFilePath); 
               
               
                 header = (TIFF_HEADER*)&amp;file[0]; 
               
               
                 if (header−&gt;byteOrder != MM &amp;&amp; header−&gt;byteOrder != II) 
               
               
                 { 
               
             
          
           
               
                   
                 printf(“This is not a valid TIFF Image File.\n”); 
               
               
                   
                 return(−1); 
               
             
          
           
               
                 } 
               
               
                 endianess = getEndianess( ); 
               
               
                 if (header−&gt;byteOrder == MM &amp;&amp; endianess == LITTLE_ENDIAN || 
               
             
          
           
               
                   
                 header−&gt;byteOrder == II &amp;&amp; endianess == BIG_ENDIAN) 
               
             
          
           
               
                 { 
               
             
          
           
               
                   
                 swapBytes = TRUE; 
               
             
          
           
               
                 } 
               
               
                 else 
               
               
                 { 
               
             
          
           
               
                   
                 swapBytes = FALSE; 
               
             
          
           
               
                 } 
               
               
                 version = getUShort(&amp;header−&gt;version, swapBytes); 
               
               
                 if (version &lt; 42) 
               
               
                 { 
               
             
          
           
               
                   
                 printf(“This is not a valid TIFF Image File (Version &lt; 42).\n”); 
               
               
                   
                 return(−1); 
               
             
          
           
               
                 } 
               
               
                 ifdPtr = getuLong(&amp;header−&gt;firstIFDoffset, swapBytes); 
               
               
                 ifd = &amp;ifdCopy; 
               
               
                 printf(“\n”); 
               
               
                 while(ifdPtr) 
               
               
                 { 
               
             
          
           
               
                   
                 numEntries = getUShort((USHORT*)&amp;file[ifdptr], swapBytes); 
               
               
                   
                 printf(“IFD at 0x%08x has %u entries:\n”, ifdPtr, numEntries); 
               
               
                   
                 stripOffset = 0; 
               
               
                   
                 stripByteCount = 0; 
               
               
                   
                 for (i=0; i&lt;numEntries; i++) 
               
               
                   
                 { 
               
             
          
           
               
                 getIFD(&amp;ifdCopy,(IFD_ENTRY*)&amp;file[ifdPtr+2+i*sizeof(IFD_EN- 
               
               
                  TRY)], swapBytes); 
               
               
                 printf(“%2u) Tag:%5u, Type:%2u, Count:%4u, Value:%1Ou%08x\n”, 
               
               
                  i+1, ifd−&gt;tag, ifd−&gt;type, ifd−&gt;count, ifd−&gt;value, 
               
               
                  ifd−&gt;value); 
               
               
                 if (ifd−&gt;tag == STRIP_OFFSETS_TAG) 
               
               
                 { 
               
             
          
           
               
                   
                 if (ifd−&gt;count &gt; 1) 
               
               
                   
                 { 
               
             
          
           
               
                 printf(“Only one strip offset is supported.\n”); 
               
               
                 return(−1); 
               
             
          
           
               
                   
                 } 
               
               
                   
                 stripOffset = ifd−&gt;value; 
               
             
          
           
               
                 } 
               
               
                 if (ifd−&gt;tag == STRIP_BYTE_COUNTS_TAG) 
               
               
                 { 
               
             
          
           
               
                   
                 if (ifd−&gt;count &gt; 1) 
               
               
                   
                 { 
               
             
          
           
               
                 printf(“Only one strip byte count is supported.\n”); 
               
               
                 return(−1); 
               
             
          
           
               
                   
                 } 
               
               
                   
                 stripByteCount = ifd−&gt;value; 
               
             
          
           
               
                 } 
               
               
                 if (ifd−&gt;tag == IMAGE_WIDTH_TAG) 
               
               
                 { 
               
             
          
           
               
                   
                 imageWidth = ifd−&gt;value; 
               
             
          
           
               
                 } 
               
               
                 if (ifd−&gt;tag == IMAGE_LENGTH_TAG) 
               
               
                 { 
               
             
          
           
               
                   
                 imageLength = ifd−&gt;value; 
               
             
          
           
               
                 } 
               
               
                 if (ifd−&gt;tag == SAMPLES_PER_PIXEL_TAG) 
               
               
                 { 
               
             
          
           
               
                   
                 samplesPerPixel = ifd−&gt;value; 
               
             
          
           
               
                 } 
               
             
          
           
               
                   
                 } 
               
               
                   
                 if (stripOffset != 0 &amp;&amp; stripByteCount != 0) 
               
               
                   
                 { 
               
             
          
           
               
                 printf(“\nEncoding strip at 0x%08x of %u bytes\n”, 
               
               
                  stripOffset, stripByteCount); 
               
               
                 process(&amp;file[stripOffset], msgCarrier, stripByteCount, 
               
               
                  imageWidth, imageLength, samplesPerPixel); 
               
             
          
           
               
                   
                 } 
               
               
                   
                 ifdPtr = getULong((ULONG*)&amp;file[ifdPrt+2+i*sizeof(IF_ENTRY)], 
               
             
          
           
               
                   
                 swapBytes); 
               
             
          
           
               
                   
                 print(“\n”); 
               
             
          
           
               
                 } 
               
               
                 if ((outFile = fopen(outputFilePath, “w”)) == NULL) 
               
               
                 { 
               
             
          
           
               
                   
                 perror(“Unable to open output file”); 
               
               
                   
                 return(−1); 
               
             
          
           
               
                 } 
               
               
                 if (fwrite(file, fileLength, 1, outFile) == 0) 
               
               
                 { 
               
             
          
           
               
                   
                 perror(“Unable to write output file”); 
               
               
                   
                 return(−1); 
               
             
          
           
               
                 } 
               
               
                 free(file); 
               
               
                 fclose(outFile); 
               
               
                 print(“%s file written out\n”, outputFilePath); 
               
               
                 fclose(inFile); 
               
               
                 return(0); 
               
               
                 } 
               
               
                 void process (UCHAR *data, int msgCarrier[SIZE][SIZE], ULONG 
               
               
                  numBytes, ULONG width, ULONG height, ULONG sample) 
               
               
                 { 
               
               
                 ULONG, x,y; 
               
               
                 int tmp; 
               
               
                 if (samples == 3) 
               
               
                 { 
               
             
          
           
               
                   
                 for (y=0; y&lt;height; y++) 
               
               
                   
                 { 
               
             
          
           
               
                  for (x=0; x&lt;width; x++) 
               
               
                  { 
               
             
          
           
               
                   
                 data[(y*width+x)*3] = CLIP( 
               
             
          
           
               
                  data[(y*width+x)*3] + msgCarrier[y % SIZE][x % SIZE]); 
               
             
          
           
               
                   
                 data[(y*width+x)*3+1] = CLIP( 
               
             
          
           
               
                  data[(y*width+x)*3+1] + msgCarrier[y % SIZE][x % SIZE]); 
               
             
          
           
               
                   
                 data[(y*width+x)*3+2] = CLIP( 
               
             
          
           
               
                  data[(y*width+x)*3+2] + msgCarrier[y % SIZE][x % SIZE]); 
               
               
                  } 
               
             
          
           
               
                   
                 } 
               
             
          
           
               
                 } 
               
               
                 else if (samples == 1) 
               
               
                 { 
               
             
          
           
               
                   
                 for (y=0; y&lt;height; y++) 
               
               
                   
                 { 
               
             
          
           
               
                  for (x=0; x&lt;width; x++) 
               
               
                  { 
               
             
          
           
               
                   
                 data[y*width+x] = CLIP( 
               
             
          
           
               
                  data[y*width+x] + msgCarrier[y % SIZE][x % SIZE]); 
               
               
                  } 
               
             
          
           
               
                   
                 } 
               
             
          
           
               
                  } 
               
               
                 } 
               
               
                 ULONG getEndianess(void) 
               
               
                 { 
               
               
                 UCHAR buf[4]; 
               
               
                 int i; 
               
               
                 ULONG value; 
               
               
                 for (i=0; i&lt;4; i++) 
               
               
                 { 
               
             
          
           
               
                   
                 buf[i] = i+1; 
               
             
          
           
               
                 } 
               
               
                 value = *((ULONG*)buf); 
               
               
                 return(value); 
               
               
                 } 
               
               
                 ULONG swapULong(ULONG value) 
               
               
                 { 
               
               
                 UCHAR *ptr; 
               
               
                 UCHAR tmp; 
               
               
                 ptr = (UCHAR*)&amp;value; 
               
               
                 tmp = ptr[0]; 
               
               
                 ptr[0] = ptr[3]; 
               
               
                 ptr[3] = tmp; 
               
               
                 tmp = ptr[1]; 
               
               
                 ptr[1] = ptr[2]; 
               
               
                 ptr[2] = tmp; 
               
               
                 return (value); 
               
               
                 } 
               
               
                 USHORT swapUShort(USHORT value) 
               
               
                 { 
               
               
                 UCHAR *ptr; 
               
               
                 UCHAR tmp; 
               
               
                 ptr = (UCHAR*)&amp;value; 
               
               
                 tmp = ptr[0]; 
               
               
                 ptr[0] = ptr[1]; 
               
               
                 ptr[1] = tmp; 
               
               
                 return (value); 
               
               
                 } 
               
               
                 void getIFD(IFD_ENTRY *ifdCopy, IFD_ENTRY *ifd, BOOL 
               
               
                  swapBytes) 
               
               
                 { 
               
               
                 /* Copy the IFD to another buffer to take care of 
               
               
                  the 4 byte boundary problems. */ 
               
               
                 memcpy(ifdCopy, ifd, sizeof(IFD_ENTRY)); 
               
               
                 if (swapBytes) 
               
               
                 { 
               
             
          
           
               
                   
                 ifdCopy−&gt;tag = swapUShort(ifdCopy−&gt;tag); 
               
               
                   
                 ifdCopy−&gt;type = swapUShort(ifdCopy−&gt;type); 
               
               
                   
                 ifdCopy−&gt;count = swapULong(ifdCopy−&gt;count); 
               
               
                   
                 if (ifdCopy−&gt;type == 3 &amp;&amp; ifdCopy−&gt;count == 1) /* 1 Short */ 
               
               
                   
                 { 
               
             
          
           
               
                  ifdCopy−&gt;value = swapUShort((USHORT)(ifdCopy−&gt;value &gt;&gt; 16)); 
               
             
          
           
               
                   
                 } 
               
               
                   
                 else 
               
               
                   
                 { 
               
             
          
           
               
                  ifdCopy−&gt;value = swapULong(ifdCopy−&gt;value); 
               
             
          
           
               
                   
                 } 
               
             
          
           
               
                  } 
               
               
                  else if (ifdCopy−&gt;type == 3 &amp;&amp; ifdCopy−&gt;count == 1) 
               
               
                  { 
               
             
          
           
               
                   
                 ifdCopy−&gt;value = ifdCopy−&gt;value &gt;&gt; 16; 
               
             
          
           
               
                  } 
               
               
                 } 
               
               
                 ULONG getULong(ULONG *value, BOOL swapBytes) 
               
               
                 { 
               
               
                 ULONG tmp; 
               
               
                 /* Copy the value to another buffer to take care of 
               
               
                  the 4 byte boundary problems. */ 
               
               
                 memcpy(&amp;tmp, value, sizeof(ULONG)); 
               
               
                 if (swapBytes) 
               
               
                 { 
               
             
          
           
               
                   
                 tmp = swapULong(tmp); 
               
             
          
           
               
                 } 
               
               
                 return(tmp); 
               
               
                 } 
               
               
                 USHORT getUShort(USHORT *value, BOOL swapBytes) 
               
               
                 { 
               
               
                 USHORT tmp; 
               
               
                 /* Copy the value to another buffer to take care of 
               
               
                  the 2 byte boundary problems. */ 
               
               
                 memcpy(&amp;tmp, value, sizeof(USHORT)); 
               
               
                 if (swapBytes) 
               
               
                 { 
               
             
          
           
               
                   
                 tmp = swapUShort(tmp); 
               
             
          
           
               
                 } 
               
               
                 return(tmp); 
               
               
                 } 
               
               
                   
               
             
          
         
       
     
     
       
         
               
             
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 3A 
               
               
                   
               
               
                 Upper Left = 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 1 
                 66 
                 −7 
                 0 
                 37 
                 23 
                 −41 
                 −7 
                 23 
                 29 
                 20 
                 −29 
                 39 
                 −29 
                 19 
                 −22 
                 2 
                 6 
                 −31 
                 5 
                 39 
                 −61 
                 −4 
                 −52 
                 7 
                 19 
                 23 
                 −27 
                 19 
                 9 
                 −26 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 7 
               
               
                 −19 
                 18 
                 −33 
                 18 
                 −9 
                 31 
                 40 
                 5 
                 −14 
                 −13 
                 −17 
                 12 
                 25 
                 −33 
                 9 
                 −29 
                 32 
                 −37 
                 56 
                 18 
                 −6 
                 4 
                 24 
                 9 
                 −27 
                 5 
                 9 
                 −9 
                 1 
                 −4 
                 5 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 0 
               
               
                 2 
                 43 
                 −72 
                 4 
                 −4 
                 18 
                 −53 
                 6 
                 −15 
                 19 
                 −19 
                 −1 
                 −3 
                 −5 
                 −36 
                 15 
                 −5 
                 −21 
                 15 
                 −50 
                 48 
                 −3 
                 −13 
                 29 
                 −25 
                 −11 
                 −19 
                 44 
                 −12 
                 −7 
                 15 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 45 
               
               
                 22 
                 18 
                 12 
                 4 
                 2 
                 13 
                 60 
                 −5 
                 −50 
                 27 
                 44 
                 23 
                 −34 
                 0 
                 26 
                 10 
                 12 
                 41 
                 −24 
                 −8 
                 17 
                 −41 
                 11 
                 −10 
                 30 
                 37 
                 31 
                 −56 
                 52 
                 −2 
                 −59 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 46 
               
               
                 5 
                 −3 
                 −62 
                 16 
                 5 
                 −10 
                 30 
                 −23 
                 −22 
                 14 
                 5 
                 0 
                 0 
                 28 
                 21 
                 43 
                 −39 
                 −36 
                 16 
                 −3 
                 −11 
                 15 
                 −3 
                 22 
                 −33 
                 4 
                 15 
                 −68 
                 15 
                 −7 
                 5 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 −38 
               
               
                 −2 
                 −18 
                 21 
                 41 
                 28 
                 −74 
                 −27 
                 41 
                 41 
                 −23 
                 −5 
                 −7 
                 −23 
                 −20 
                 −27 
                 −16 
                 16 
                 9 
                 41 
                 43 
                 2 
                 9 
                 −31 
                 28 
                 20 
                 −41 
                 40 
                 −19 
                 38 
                 −2 
                 7 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 35 
               
               
                 53 
                 24 
                 −39 
                 −7 
                 −8 
                 −35 
                 −6 
                 9 
                 6 
                 −12 
                 1 
                 6 
                 −43 
                 12 
                 31 
                 −36 
                 27 
                 −46 
                 −14 
                 −55 
                 −22 
                 5 
                 −32 
                 −44 
                 −47 
                 11 
                 6 
                 64 
                 −20 
                 −43 
                 −3 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 22 
               
               
                 6 
                 15 
                 −14 
                 1 
                 4 
                 34 
                 27 
                 26 
                 −18 
                 −40 
                 −8 
                 18 
                 17 
                 −8 
                 19 
                 −4 
                 3 
                 −10 
                 29 
                 −74 
                 54 
                 47 
                 −5 
                 21 
                 23 
                 −29 
                 17 
                 −49 
                 −45 
                 25 
                 7 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 −38 
               
               
                 −48 
                 −23 
                 4 
                 −77 
                 −9 
                 −3 
                 −74 
                 6 
                 −33 
                 −12 
                 31 
                 37 
                 7 
                 −17 
                 −20 
                 33 
                 −47 
                 −17 
                 41 
                 16 
                 −28 
                 −7 
                 −10 
                 16 
                 24 
                 26 
                 −16 
                 4 
                 42 
                 24 
                 −29 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 −17 
               
               
                 6 
                 −4 
                 33 
                 19 
                 −15 
                 14 
                 10 
                 36 
                 10 
                 4 
                 18 
                 54 
                 −37 
                 −50 
                 36 
                 −2 
                 24 
                 42 
                 −56 
                 −20 
                 −39 
                 32 
                 28 
                 −65 
                 17 
                 1 
                 −21 
                 −46 
                 1 
                 23 
                 22 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 −4 
               
               
                 −17 
                 17 
                 −34 
                 −42 
                 5 
                 0 
                 0 
                 −2 
                 22 
                 11 
                 −42 
                 −17 
                 −57 
                 16 
                 12 
                 −11 
                 −6 
                 22 
                 −14 
                 1 
                 −28 
                 4 
                 16 
                 23 
                 −23 
                 40 
                 −9 
                 −24 
                 −24 
                 −14 
                 −11 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 49 
               
               
                 25 
                 −2 
                 −11 
                 26 
                 −4 
                 41 
                 −57 
                 −6 
                 −12 
                 13 
                 −39 
                 39 
                 78 
                 2 
                 −67 
                 42 
                 −32 
                 −5 
                 20 
                 −6 
                 11 
                 4 
                 −19 
                 −3 
                 −23 
                 −38 
                 16 
                 25 
                 −6 
                 12 
                 −51 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 −5 
               
               
                 35 
                 −21 
                 58 
                 25 
                 4 
                 −7 
                 30 
                 −46 
                 0 
                 17 
                 −49 
                 −8 
                 27 
                 −18 
                 −1 
                 10 
                 −29 
                 37 
                 29 
                 −5 
                 −31 
                 63 
                 −11 
                 −15 
                 44 
                 −7 
                 26 
                 73 
                 10 
                 −5 
                 −8 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 32 
               
               
                 9 
                 −35 
                 −42 
                 14 
                 −20 
                 35 
                 21 
                 −15 
                 −7 
                 36 
                 −3 
                 −38 
                 −36 
                 42 
                 −17 
                 −8 
                 −24 
                 69 
                 −44 
                 4 
                 −16 
                 −3 
                 −1 
                 −28 
                 −16 
                 27 
                 12 
                 −4 
                 −22 
                 0 
                 6 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 36 
               
               
                 −45 
                 −6 
                 7 
                 9 
                 4 
                 −30 
                 2 
                 12 
                 −11 
                 7 
                 26 
                 23 
                 −6 
                 5 
                 −51 
                 27 
                 25 
                 48 
                 15 
                 −1 
                 18 
                 −9 
                 −7 
                 33 
                 17 
                 −23 
                 −31 
                 −44 
                 −7 
                 −58 
                 22 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 −13 
               
               
                 12 
                 −16 
                 35 
                 −1 
                 −3 
                 −31 
                 −39 
                 24 
                 25 
                 18 
                 27 
                 −1 
                 35 
                 −14 
                 −17 
                 −40 
                 4 
                 −19 
                 −43 
                 −64 
                 28 
                 0 
                 −13 
                 28 
                 −12 
                 −12 
                 41 
                 24 
                 0 
                 22 
                 12 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 −38 
               
               
                 0 
                 −1 
                 −9 
                 8 
                 21 
                 36 
                 −53 
                 36 
                 −48 
                 16 
                 2 
                 −20 
                 −3 
                 −3 
                 42 
                 −22 
                 63 
                 −38 
                 42 
                 50 
                 50 
                 −36 
                 −5 
                 −18 
                 9 
                 −1 
                 0 
                 −20 
                 6 
                 20 
                 −15 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 35 
               
               
                 −39 
                 −26 
                 −8 
                 −44 
                 18 
                 24 
                 10 
                 −11 
                 −41 
                 −2 
                 −36 
                 8 
                 1 
                 29 
                 −36 
                 53 
                 11 
                 −29 
                 −1 
                 −33 
                 −5 
                 25 
                 −49 
                 3 
                 0 
                 18 
                 −17 
                 −12 
                 22 
                 5 
                 −18 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 5 
               
               
                 63 
                 19 
                 59 
                 −13 
                 −58 
                 3 
                 1 
                 18 
                 −8 
                 36 
                 5 
                 −23 
                 29 
                 −66 
                 −3 
                 −34 
                 −13 
                 1 
                 −12 
                 −38 
                 −30 
                 29 
                 75 
                 −46 
                 −2 
                 6 
                 −20 
                 28 
                 −15 
                 39 
                 10 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 0 
               
               
                 −59 
                 −3 
                 0 
                 64 
                 −2 
                 3 
                 12 
                 −30 
                 32 
                 −34 
                 15 
                 27 
                 −21 
                 31 
                 0 
                 −28 
                 47 
                 −66 
                 −2 
                 18 
                 47 
                 −39 
                 38 
                 −35 
                 6 
                 5 
                 2 
                 −42 
                 −2 
                 43 
                 −78 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 −22 
               
               
                 −14 
                 −36 
                 −14 
                 1 
                 −41 
                 −14 
                 15 
                 −8 
                 −35 
                 21 
                 22 
                 −34 
                 73 
                 −21 
                 29 
                 3 
                 57 
                 −5 
                 27 
                 53 
                 21 
                 −17 
                 −44 
                 26 
                 9 
                 0 
                 20 
                 −38 
                 −11 
                 40 
                 −9 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 46 
               
               
                 −1 
                 19 
                 −18 
                 11 
                 51 
                 14 
                 22 
                 23 
                 −52 
                 −2 
                 −2 
                 10 
                 −30 
                 −1 
                 −5 
                 −36 
                 −72 
                 −26 
                 −38 
                 −29 
                 −6 
                 −41 
                 29 
                 20 
                 −19 
                 49 
                 −30 
                 5 
                 3 
                 −14 
                 31 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 40 
               
               
                 −15 
                 45 
                 −26 
                 −35 
                 −47 
                 −20 
                 60 
                 −3 
                 −9 
                 −3 
                 −7 
                 17 
                 22 
                 −33 
                 −11 
                 40 
                 5 
                 30 
                 27 
                 4 
                 7 
                 21 
                 −8 
                 9 
                 −36 
                 37 
                 −21 
                 −27 
                 25 
                 −18 
                 19 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 −37 
               
               
                 0 
                 −5 
                 18 
                 −3 
                 13 
                 2 
                 −29 
                 −31 
                 58 
                 −27 
                 −17 
                 14 
                 41 
                 −6 
                 −53 
                 25 
                 3 
                 79 
                 11 
                 −1 
                 −26 
                 12 
                 −1 
                 11 
                 −5 
                 4 
                 7 
                 6 
                 −15 
                 −25 
                 26 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 −51 
               
               
                 56 
                 −37 
                 −5 
                 0 
                 35 
                 34 
                 −18 
                 −26 
                 4 
                 20 
                 −5 
                 16 
                 24 
                 23 
                 0 
                 19 
                 −10 
                 −17 
                 −25 
                 −7 
                 9 
                 7 
                 −19 
                 4 
                 −1 
                 −11 
                 −42 
                 57 
                 27 
                 −1 
                 −8 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 −31 
               
               
                 15 
                 28 
                 −33 
                 −1 
                 −17 
                 10 
                 −17 
                 0 
                 3 
                 −1 
                 −4 
                 −18 
                 −4 
                 −34 
                 27 
                 −13 
                 −55 
                 45 
                 −27 
                 7 
                 −33 
                 8 
                 −5 
                 36 
                 −3 
                 1 
                 0 
                 −23 
                 −30 
                 24 
                 12 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 68 
               
               
                 13 
                 −14 
                 −46 
                 32 
                 7 
                 −2 
                 −21 
                 10 
                 33 
                 −16 
                 1 
                 −29 
                 −12 
                 −32 
                 17 
                 −12 
                 15 
                 13 
                 −32 
                 1 
                 2 
                 −11 
                 34 
                 −12 
                 21 
                 −21 
                 −17 
                 17 
                 3 
                 −49 
                 −33 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 1 
               
               
                 53 
                 16 
                 −2 
                 −2 
                 58 
                 11 
                 −26 
                 −6 
                 −1 
                 15 
                 6 
                 10 
                 22 
                 32 
                 5 
                 −11 
                 −8 
                 −24 
                 1 
                 20 
                 −16 
                 −25 
                 7 
                 44 
                 −2 
                 −41 
                 46 
                 −25 
                 38 
                 −35 
                 −30 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 49 
               
               
                 0 
                 −37 
                 28 
                 12 
                 −14 
                 −29 
                 26 
                 −7 
                 5 
                 −14 
                 −23 
                 33 
                 −31 
                 −9 
                 31 
                 10 
                 6 
                 −9 
                 14 
                 53 
                 −29 
                 37 
                 −42 
                 −28 
                 −28 
                 23 
                 19 
                 −20 
                 69 
                 0 
                 23 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 63 
               
               
                 −38 
                 11 
                 −32 
                 5 
                 −5 
                 −5 
                 12 
                 4 
                 −9 
                 7 
                 21 
                 −49 
                 48 
                 −19 
                 −19 
                 −8 
                 −28 
                 −20 
                 −17 
                 7 
                 47 
                 −6 
                 6 
                 −20 
                 57 
                 −19 
                 −7 
                 −20 
                 7 
                 −10 
                 −5 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 2 
               
               
                 21 
                 −6 
                 14 
                 −27 
                 7 
                 34 
                 −27 
                 −31 
                 33 
                 −25 
                 13 
                 37 
                 −51 
                 −16 
                 64 
                 −36 
                 28 
                 36 
                 10 
                 −26 
                 −15 
                 −23 
                 0 
                 −16 
                 −15 
                 43 
                 −29 
                 −36 
                 −27 
                 −8 
                 −2 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 17 
               
               
                 7 
                 18 
                 −32 
                 −8 
                 −26 
                 −13 
                 32 
                 −33 
                 −13 
                 22 
                 47 
                 18 
                 −4 
                 −21 
                 34 
                 −27 
                 −2 
                 −11 
                 14 
                 15 
                 26 
                 5 
                 5 
                 63 
                 −52 
                 14 
                 −18 
                 3 
                 −11 
                 13 
                 4 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 −8 
               
               
                   
               
             
          
         
       
     
     
       
         
               
             
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 3B 
               
               
                   
               
               
                 Upper Right = 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 −30 
                 0 
                 −2 
                 −13 
                 56 
                 −47 
                 −27 
                 −26 
                 17 
                 −7 
                 20 
                 21 
                 −22 
                 23 
                 −7 
                 −71 
                 26 
                 −24 
                 −8 
                 30 
                 −3 
                 −52 
                 −15 
                 −32 
                 −73 
                 84 
                 27 
                 29 
                 −34 
                 −7 
                 −15 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 39 
               
               
                 7 
                 10 
                 −24 
                 25 
                 −24 
                 36 
                 6 
                 20 
                 35 
                 −20 
                 −53 
                 −21 
                 25 
                 42 
                 35 
                 −37 
                 −10 
                 −2 
                 2 
                 −23 
                 1 
                 13 
                 46 
                 21 
                 −23 
                 −15 
                 11 
                 5 
                 −16 
                 37 
                 −1 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 0 
               
               
                 23 
                 13 
                 −37 
                 17 
                 −11 
                 −4 
                 −4 
                 29 
                 −31 
                 4 
                 6 
                 24 
                 −9 
                 −27 
                 7 
                 40 
                 −10 
                 31 
                 16 
                 −8 
                 2 
                 −13 
                 1 
                 6 
                 47 
                 −33 
                 37 
                 −46 
                 −36 
                 20 
                 −10 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 −45 
               
               
                 −50 
                 16 
                 −31 
                 5 
                 −39 
                 5 
                 −2 
                 −45 
                 42 
                 21 
                 0 
                 −18 
                 −35 
                 8 
                 −28 
                 37 
                 18 
                 −33 
                 −7 
                 8 
                 −46 
                 9 
                 −13 
                 −15 
                 21 
                 3 
                 −50 
                 32 
                 48 
                 −51 
                 2 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 34 
               
               
                 17 
                 −62 
                 69 
                 −3 
                 11 
                 5 
                 −12 
                 −9 
                 5 
                 12 
                 0 
                 −8 
                 36 
                 27 
                 −4 
                 7 
                 −5 
                 −19 
                 41 
                 1 
                 51 
                 −25 
                 65 
                 −2 
                 −1 
                 16 
                 1 
                 0 
                 17 
                 16 
                 −24 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 8 
               
               
                 25 
                 49 
                 −17 
                 0 
                 34 
                 2 
                 −3 
                 10 
                 42 
                 −17 
                 6 
                 −51 
                 −7 
                 28 
                 −36 
                 −28 
                 −5 
                 5 
                 27 
                 −35 
                 −6 
                 2 
                 −26 
                 −19 
                 2 
                 −12 
                 14 
                 19 
                 −34 
                 56 
                 −83 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 −28 
               
               
                 35 
                 −47 
                 15 
                 −18 
                 2 
                 −2 
                 −11 
                 21 
                 −29 
                 −11 
                 −5 
                 24 
                 9 
                 9 
                 −54 
                 6 
                 −25 
                 −77 
                 4 
                 30 
                 −38 
                 −30 
                 −3 
                 15 
                 5 
                 −53 
                 −12 
                 3 
                 4 
                 17 
                 41 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 −13 
               
               
                 −40 
                 −1 
                 −4 
                 43 
                 −20 
                 13 
                 −22 
                 −55 
                 17 
                 −56 
                 59 
                 −10 
                 17 
                 −10 
                 −2 
                 94 
                 −34 
                 −16 
                 1 
                 −19 
                 0 
                 29 
                 −28 
                 31 
                 −10 
                 45 
                 −28 
                 3 
                 27 
                 −48 
                 −19 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 −2 
               
               
                 44 
                 3 
                 −19 
                 −46 
                 9 
                 −24 
                 25 
                 24 
                 35 
                 −26 
                 5 
                 −2 
                 −28 
                 −23 
                 11 
                 10 
                 7 
                 −10 
                 −4 
                 17 
                 28 
                 −6 
                 −38 
                 −4 
                 35 
                 −50 
                 −6 
                 −2 
                 −11 
                 51 
                 1 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 −20 
               
               
                 10 
                 −38 
                 −2 
                 −7 
                 26 
                 37 
                 6 
                 27 
                 7 
                 −19 
                 17 
                 57 
                 −9 
                 45 
                 18 
                 −1 
                 −10 
                 −1 
                 −1 
                 −15 
                 26 
                 21 
                 60 
                 −4 
                 −38 
                 47 
                 −10 
                 −39 
                 5 
                 −30 
                 8 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 −43 
               
               
                 15 
                 15 
                 50 
                 −8 
                 3 
                 −3 
                 2 
                 −46 
                 −27 
                 −32 
                 4 
                 −30 
                 −6 
                 −62 
                 14 
                 −1 
                 −31 
                 20 
                 −22 
                 −9 
                 16 
                 −44 
                 −9 
                 0 
                 −4 
                 31 
                 36 
                 −16 
                 3 
                 41 
                 18 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 10 
               
               
                 22 
                 −20 
                 −21 
                 −34 
                 13 
                 −37 
                 −42 
                 4 
                 29 
                 29 
                 −18 
                 0 
                 54 
                 −7 
                 0 
                 37 
                 −3 
                 8 
                 28 
                 27 
                 −33 
                 −12 
                 14 
                 −34 
                 −30 
                 −27 
                 86 
                 −14 
                 37 
                 −46 
                 −5 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 1 
               
               
                 −29 
                 23 
                 −12 
                 41 
                 31 
                 36 
                 19 
                 −27 
                 −37 
                 −6 
                 −39 
                 −6 
                 10 
                 −16 
                 8 
                 −35 
                 −2 
                 18 
                 −23 
                 −10 
                 −17 
                 12 
                 42 
                 34 
                 −35 
                 −26 
                 13 
                 −3 
                 0 
                 −18 
                 −3 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 4 
               
               
                 −6 
                 −31 
                 −33 
                 −12 
                 −51 
                 −9 
                 4 
                 −19 
                 35 
                 −2 
                 25 
                 37 
                 36 
                 23 
                 −7 
                 28 
                 −8 
                 −44 
                 −39 
                 34 
                 46 
                 3 
                 21 
                 11 
                 2 
                 2 
                 9 
                 −44 
                 34 
                 10 
                 −6 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 −32 
               
               
                 −26 
                 26 
                 25 
                 28 
                 −6 
                 34 
                 7 
                 −18 
                 13 
                 36 
                 −24 
                 3 
                 −24 
                 −40 
                 12 
                 14 
                 −6 
                 −1 
                 5 
                 23 
                 −26 
                 −37 
                 27 
                 −72 
                 23 
                 −4 
                 −3 
                 −14 
                 5 
                 18 
                 0 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 15 
               
               
                 −14 
                 −2 
                 −18 
                 −15 
                 3 
                 22 
                 54 
                 −78 
                 −2 
                 15 
                 −15 
                 −22 
                 10 
                 −45 
                 36 
                 15 
                 −3 
                 −20 
                 −12 
                 7 
                 −18 
                 −3 
                 −16 
                 63 
                 −51 
                 44 
                 18 
                 −7 
                 1 
                 53 
                 9 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 −1 
               
               
                 −25 
                 43 
                 −28 
                 −35 
                 42 
                 −26 
                 0 
                 5 
                 25 
                 35 
                 −27 
                 18 
                 20 
                 −14 
                 25 
                 −14 
                 28 
                 26 
                 −7 
                 −37 
                 7 
                 35 
                 −6 
                 −22 
                 −23 
                 9 
                 −54 
                 −19 
                 −17 
                 9 
                 −51 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 −15 
               
               
                 0 
                 26 
                 22 
                 14 
                 −14 
                 26 
                 38 
                 −34 
                 0 
                 −42 
                 −37 
                 3 
                 12 
                 −47 
                 −1 
                 −42 
                 7 
                 17 
                 14 
                 −21 
                 −40 
                 −12 
                 0 
                 −2 
                 12 
                 36 
                 41 
                 0 
                 2 
                 15 
                 −6 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 −7 
               
               
                 12 
                 4 
                 9 
                 28 
                 −55 
                 −27 
                 1 
                 −25 
                 23 
                 14 
                 −59 
                 54 
                 −3 
                 47 
                 34 
                 −2 
                 −39 
                 16 
                 30 
                 −9 
                 29 
                 53 
                 7 
                 −6 
                 15 
                 −22 
                 6 
                 −2 
                 11 
                 −11 
                 29 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 −23 
               
               
                 −5 
                 5 
                 −22 
                 −33 
                 −7 
                 31 
                 −27 
                 57 
                 −3 
                 5 
                 16 
                 12 
                 0 
                 −3 
                 6 
                 −26 
                 11 
                 10 
                 −48 
                 −3 
                 38 
                 21 
                 −64 
                 38 
                 −4 
                 −28 
                 33 
                 −50 
                 −26 
                 −6 
                 −6 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 12 
               
               
                 −17 
                 11 
                 27 
                 30 
                 −47 
                 3 
                 23 
                 −19 
                 −5 
                 −4 
                 −53 
                 3 
                 26 
                 −47 
                 31 
                 65 
                 −18 
                 −38 
                 22 
                 −10 
                 −22 
                 10 
                 18 
                 −20 
                 −5 
                 −11 
                 −18 
                 8 
                 −37 
                 −15 
                 36 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 12 
               
               
                 −4 
                 −48 
                 −7 
                 −9 
                 62 
                 −15 
                 −10 
                 −35 
                 18 
                 46 
                 18 
                 0 
                 7 
                 −21 
                 −38 
                 −32 
                 25 
                 −10 
                 −23 
                 26 
                 −8 
                 −1 
                 −13 
                 −3 
                 3 
                 39 
                 48 
                 32 
                 6 
                 21 
                 −50 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 11 
               
               
                 31 
                 −10 
                 −27 
                 43 
                 13 
                 −3 
                 2 
                 2 
                 −22 
                 21 
                 7 
                 −29 
                 −20 
                 −38 
                 −9 
                 −14 
                 29 
                 −44 
                 56 
                 6 
                 −35 
                 46 
                 −77 
                 −23 
                 59 
                 −13 
                 −32 
                 28 
                 −34 
                 76 
                 16 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 −1 
               
               
                 12 
                 12 
                 5 
                 5 
                 −47 
                 3 
                 20 
                 −35 
                 −9 
                 18 
                 −46 
                 0 
                 40 
                 27 
                 35 
                 1 
                 1 
                 26 
                 14 
                 6 
                 14 
                 4 
                 −11 
                 19 
                 −9 
                 0 
                 −25 
                 −16 
                 −17 
                 −39 
                 −4 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 16 
               
               
                 6 
                 −18 
                 29 
                 −23 
                 −54 
                 −7 
                 48 
                 7 
                 −34 
                 37 
                 59 
                 15 
                 0 
                 24 
                 1 
                 30 
                 8 
                 −49 
                 −27 
                 37 
                 −30 
                 6 
                 19 
                 −19 
                 45 
                 1 
                 −29 
                 38 
                 −6 
                 3 
                 −16 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 37 
               
               
                 10 
                 −28 
                 41 
                 0 
                 50 
                 −22 
                 11 
                 34 
                 −3 
                 −41 
                 −47 
                 −60 
                 9 
                 −52 
                 24 
                 18 
                 −24 
                 −14 
                 12 
                 −12 
                 0 
                 −23 
                 −19 
                 −28 
                 26 
                 −37 
                 23 
                 −4 
                 1 
                 −5 
                 22 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 20 
               
               
                 −14 
                 −25 
                 13 
                 −24 
                 −6 
                 41 
                 −26 
                 −22 
                 10 
                 26 
                 27 
                 −13 
                 −11 
                 34 
                 11 
                 −4 
                 −37 
                 7 
                 −8 
                 45 
                 −16 
                 43 
                 4 
                 53 
                 −1 
                 7 
                 22 
                 9 
                 11 
                 −6 
                 14 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 44 
               
               
                 28 
                 −28 
                 −50 
                 −9 
                 15 
                 26 
                 −17 
                 18 
                 −1 
                 36 
                 34 
                 −18 
                 −23 
                 19 
                 −29 
                 27 
                 −36 
                 29 
                 4 
                 −9 
                 −24 
                 32 
                 −32 
                 −28 
                 71 
                 −10 
                 −44 
                 −95 
                 −27 
                 5 
                 −26 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 −22 
               
               
                 −7 
                 0 
                 −37 
                 60 
                 2 
                 −24 
                 −6 
                 −18 
                 −15 
                 −49 
                 −33 
                 −27 
                 −18 
                 8 
                 5 
                 0 
                 −32 
                 54 
                 −1 
                 −19 
                 −7 
                 22 
                 −20 
                 27 
                 −45 
                 −10 
                 22 
                 57 
                 26 
                 −2 
                 −11 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 −23 
               
               
                 −57 
                 15 
                 44 
                 −46 
                 −22 
                 24 
                 −24 
                 32 
                 18 
                 37 
                 30 
                 56 
                 26 
                 18 
                 −31 
                 19 
                 −23 
                 6 
                 14 
                 −21 
                 −20 
                 −38 
                 54 
                 11 
                 −34 
                 −18 
                 4 
                 30 
                 −8 
                 −1 
                 2 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 −21 
               
               
                 8 
                 −15 
                 47 
                 −13 
                 −2 
                 4 
                 37 
                 4 
                 −21 
                 −33 
                 −30 
                 −5 
                 −23 
                 42 
                 −56 
                 −1 
                 6 
                 −12 
                 −25 
                 0 
                 20 
                 12 
                 −45 
                 3 
                 −43 
                 19 
                 33 
                 −60 
                 16 
                 23 
                 23 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 11 
               
               
                 −3 
                 −21 
                 −15 
                 22 
                 −2 
                 6 
                 −10 
                 −33 
                 21 
                 −5 
                 6 
                 −13 
                 −23 
                 4 
                 9 
                 35 
                 −3 
                 −10 
                 −6 
                 42 
                 28 
                 22 
                 −1 
                 0 
                 23 
                 39 
                 5 
                 −9 
                 18 
                 −74 
                 9 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 −3 
               
               
                   
               
             
          
         
       
     
     
       
         
               
             
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 3C 
               
               
                   
               
               
                 Lower Left = 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 −21 
                 −25 
                 20 
                 42 
                 30 
                 −4 
                 5 
                 −43 
                 6 
                 −27 
                 16 
                 −7 
                 −24 
                 −7 
                 −6 
                 −13 
                 41 
                 −11 
                 −6 
                 21 
                 −22 
                 −42 
                 14 
                 5 
                 20 
                 41 
                 −1 
                 4 
                 23 
                 20 
                 −21 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 −43 
               
               
                 4 
                 88 
                 −10 
                 −57 
                 1 
                 −8 
                 0 
                 −6 
                 33 
                 −14 
                 −11 
                 −24 
                 22 
                 −23 
                 −11 
                 32 
                 −48 
                 −52 
                 26 
                 −3 
                 0 
                 −13 
                 −2 
                 −27 
                 −41 
                 12 
                 −13 
                 −5 
                 39 
                 30 
                 4 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 −28 
               
               
                 −68 
                 4 
                 −3 
                 5 
                 6 
                 46 
                 30 
                 5 
                 8 
                 −32 
                 11 
                 −7 
                 38 
                 65 
                 −23 
                 −26 
                 22 
                 56 
                 −8 
                 56 
                 −19 
                 −12 
                 14 
                 7 
                 24 
                 −40 
                 −43 
                 61 
                 6 
                 6 
                 9 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 −7 
               
               
                 20 
                 −46 
                 −8 
                 −26 
                 10 
                 −38 
                 −11 
                 3 
                 56 
                 −53 
                 21 
                 −17 
                 −27 
                 18 
                 −28 
                 32 
                 20 
                 −7 
                 −43 
                 −32 
                 7 
                 −4 
                 29 
                 −45 
                 −7 
                 −3 
                 −43 
                 34 
                 −30 
                 −56 
                 5 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 15 
               
               
                 −22 
                 −28 
                 19 
                 26 
                 −8 
                 −20 
                 −9 
                 31 
                 30 
                 −14 
                 15 
                 27 
                 −10 
                 −40 
                 −8 
                 −43 
                 −41 
                 54 
                 −52 
                 26 
                 33 
                 12 
                 4 
                 4 
                 26 
                 28 
                 −2 
                 7 
                 −14 
                 −9 
                 33 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 −51 
               
               
                 −8 
                 22 
                 11 
                 30 
                 9 
                 1 
                 1 
                 −13 
                 −4 
                 −29 
                 −10 
                 20 
                 46 
                 19 
                 −22 
                 51 
                 8 
                 −12 
                 −1 
                 −7 
                 −14 
                 −8 
                 −17 
                 31 
                 9 
                 −8 
                 37 
                 6 
                 −4 
                 48 
                 6 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 2 
               
               
                 −11 
                 16 
                 −37 
                 20 
                 −45 
                 5 
                 −15 
                 0 
                 28 
                 13 
                 −11 
                 −52 
                 22 
                 14 
                 −1 
                 −45 
                 40 
                 17 
                 −23 
                 51 
                 −14 
                 −16 
                 39 
                 35 
                 −26 
                 −48 
                 35 
                 1 
                 28 
                 −40 
                 −24 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 8 
               
               
                 5 
                 −7 
                 9 
                 −44 
                 34 
                 69 
                 −5 
                 −99 
                 23 
                 −11 
                 −27 
                 −6 
                 −18 
                 0 
                 25 
                 6 
                 −20 
                 −33 
                 75 
                 −11 
                 −26 
                 −28 
                 −6 
                 −5 
                 −27 
                 −41 
                 −14 
                 −12 
                 10 
                 −10 
                 24 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 −18 
               
               
                 3 
                 38 
                 −7 
                 −23 
                 21 
                 5 
                 −33 
                 −21 
                 15 
                 20 
                 33 
                 −2 
                 42 
                 −22 
                 −33 
                 −5 
                 44 
                 −23 
                 −20 
                 −23 
                 22 
                 46 
                 −40 
                 66 
                 −39 
                 −2 
                 −14 
                 23 
                 −16 
                 0 
                 −11 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 30 
               
               
                 −25 
                 1 
                 13 
                 −3 
                 −31 
                 0 
                 −7 
                 58 
                 −9 
                 27 
                 0 
                 3 
                 9 
                 −24 
                 21 
                 −21 
                 −1 
                 17 
                 1 
                 4 
                 7 
                 −41 
                 −18 
                 11 
                 −33 
                 14 
                 16 
                 28 
                 −16 
                 16 
                 7 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 −21 
               
               
                 24 
                 30 
                 21 
                 −57 
                 −23 
                 7 
                 −17 
                 52 
                 34 
                 −7 
                 −52 
                 58 
                 4 
                 −31 
                 −5 
                 7 
                 23 
                 −16 
                 26 
                 −3 
                 53 
                 −16 
                 54 
                 40 
                 −4 
                 11 
                 −33 
                 37 
                 −23 
                 53 
                 −9 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 26 
               
               
                 −32 
                 −6 
                 3 
                 11 
                 44 
                 31 
                 −36 
                 5 
                 −77 
                 −11 
                 −21 
                 −23 
                 −12 
                 −7 
                 12 
                 −15 
                 −5 
                 −1 
                 −21 
                 −22 
                 −54 
                 −19 
                 18 
                 8 
                 −16 
                 22 
                 12 
                 12 
                 −65 
                 33 
                 4 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 −41 
               
               
                 28 
                 −2 
                 19 
                 −45 
                 27 
                 −20 
                 −40 
                 10 
                 −7 
                 67 
                 −57 
                 22 
                 50 
                 15 
                 −23 
                 40 
                 6 
                 −9 
                 −3 
                 −20 
                 −15 
                 −4 
                 −4 
                 −24 
                 −15 
                 35 
                 −40 
                 −6 
                 −37 
                 −31 
                 −8 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 4 
               
               
                 9 
                 −17 
                 −16 
                 −60 
                 29 
                 19 
                 30 
                 34 
                 −34 
                 7 
                 −6 
                 13 
                 11 
                 −28 
                 19 
                 25 
                 −16 
                 24 
                 −21 
                 47 
                 4 
                 53 
                 −27 
                 −43 
                 −47 
                 66 
                 7 
                 0 
                 −27 
                 1 
                 43 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 −28 
               
               
                 −4 
                 42 
                 0 
                 −17 
                 30 
                 −24 
                 −4 
                 22 
                 −17 
                 15 
                 52 
                 −7 
                 −55 
                 −2 
                 15 
                 −21 
                 −44 
                 −21 
                 −10 
                 −53 
                 41 
                 14 
                 67 
                 −10 
                 −31 
                 1 
                 −38 
                 34 
                 38 
                 44 
                 −8 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 2 
               
               
                 −38 
                 −21 
                 25 
                 15 
                 24 
                 −4 
                 −45 
                 −22 
                 −18 
                 −17 
                 1 
                 −1 
                 7 
                 21 
                 −41 
                 10 
                 36 
                 41 
                 42 
                 1 
                 −43 
                 −17 
                 24 
                 27 
                 47 
                 30 
                 21 
                 30 
                 −90 
                 24 
                 11 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 −10 
               
               
                 −36 
                 −36 
                 45 
                 27 
                 −10 
                 47 
                 4 
                 15 
                 17 
                 −30 
                 20 
                 −28 
                 −14 
                 24 
                 22 
                 −5 
                 1 
                 −30 
                 −15 
                 −13 
                 −13 
                 14 
                 −5 
                 −61 
                 −48 
                 −46 
                 8 
                 −77 
                 4 
                 17 
                 2 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 −5 
               
               
                 35 
                 −3 
                 −49 
                 −30 
                 −31 
                 25 
                 −19 
                 42 
                 −11 
                 21 
                 5 
                 −29 
                 −1 
                 1 
                 −36 
                 −13 
                 2 
                 28 
                 4 
                 −1 
                 13 
                 −16 
                 10 
                 2 
                 2 
                 14 
                 −29 
                 −1 
                 27 
                 17 
                 −21 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 −20 
               
               
                 −3 
                 −21 
                 39 
                 13 
                 −1 
                 −31 
                 12 
                 9 
                 4 
                 −38 
                 −22 
                 44 
                 36 
                 9 
                 −4 
                 2 
                 −5 
                 11 
                 22 
                 21 
                 10 
                 −3 
                 25 
                 33 
                 14 
                 −7 
                 19 
                 11 
                 9 
                 4 
                 −16 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 −8 
               
               
                 3 
                 −33 
                 −2 
                 45 
                 −6 
                 −19 
                 5 
                 −2 
                 25 
                 31 
                 −63 
                 40 
                 −17 
                 53 
                 9 
                 −34 
                 4 
                 −17 
                 0 
                 3 
                 −45 
                 −17 
                 −16 
                 0 
                 2 
                 36 
                 −42 
                 −33 
                 −33 
                 10 
                 5 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 −5 
               
               
                 −17 
                 −20 
                 57 
                 −19 
                 0 
                 −30 
                 6 
                 0 
                 4 
                 −1 
                 −8 
                 −5 
                 −52 
                 −19 
                 35 
                 −53 
                 −1 
                 −1 
                 −37 
                 29 
                 −16 
                 −18 
                 4 
                 −34 
                 7 
                 −28 
                 34 
                 12 
                 −22 
                 −6 
                 28 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 −13 
               
               
                 −28 
                 −27 
                 −8 
                 24 
                 5 
                 −28 
                 8 
                 −28 
                 22 
                 −46 
                 40 
                 24 
                 −1 
                 19 
                 7 
                 24 
                 22 
                 9 
                 −14 
                 16 
                 31 
                 39 
                 44 
                 −11 
                 28 
                 −22 
                 −47 
                 31 
                 11 
                 0 
                 34 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 −45 
               
               
                 42 
                 5 
                 −34 
                 −32 
                 58 
                 0 
                 −5 
                 2 
                 24 
                 9 
                 −3 
                 −10 
                 −27 
                 −20 
                 −16 
                 8 
                 14 
                 14 
                 29 
                 −61 
                 19 
                 −14 
                 11 
                 −15 
                 −5 
                 8 
                 −15 
                 26 
                 −3 
                 16 
                 −25 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 −20 
               
               
                 47 
                 21 
                 4 
                 −49 
                 32 
                 9 
                 −41 
                 17 
                 58 
                 −33 
                 0 
                 −22 
                 26 
                 13 
                 19 
                 19 
                 0 
                 −14 
                 −27 
                 8 
                 −29 
                 24 
                 −16 
                 −41 
                 8 
                 −12 
                 10 
                 33 
                 −33 
                 21 
                 −37 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 −11 
               
               
                 −3 
                 24 
                 9 
                 −27 
                 −10 
                 2 
                 25 
                 −18 
                 −71 
                 31 
                 22 
                 −16 
                 25 
                 −2 
                 −65 
                 39 
                 −34 
                 53 
                 15 
                 −2 
                 −22 
                 4 
                 14 
                 14 
                 38 
                 −16 
                 14 
                 −14 
                 1 
                 15 
                 19 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 13 
               
               
                 −5 
                 12 
                 −41 
                 11 
                 −1 
                 24 
                 −31 
                 10 
                 1 
                 −18 
                 −16 
                 −5 
                 10 
                 16 
                 −17 
                 −27 
                 2 
                 −29 
                 12 
                 −12 
                 52 
                 −10 
                 0 
                 −3 
                 −4 
                 35 
                 −69 
                 26 
                 8 
                 −41 
                 29 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 −38 
               
               
                 3 
                 −28 
                 −16 
                 21 
                 33 
                 20 
                 14 
                 −53 
                 42 
                 −4 
                 −17 
                 76 
                 −29 
                 0 
                 −9 
                 −3 
                 44 
                 14 
                 −17 
                 −9 
                 −13 
                 −42 
                 16 
                 −5 
                 43 
                 −46 
                 2 
                 11 
                 −37 
                 40 
                 −8 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 −51 
               
               
                 4 
                 −6 
                 14 
                 22 
                 −35 
                 14 
                 −8 
                 10 
                 36 
                 16 
                 −12 
                 −51 
                 −14 
                 15 
                 −9 
                 −69 
                 26 
                 −2 
                 4 
                 −51 
                 0 
                 21 
                 21 
                 −2 
                 26 
                 14 
                 −27 
                 −8 
                 11 
                 11 
                 −24 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 16 
               
               
                 14 
                 12 
                 −16 
                 −49 
                 −39 
                 −16 
                 32 
                 16 
                 −17 
                 −5 
                 8 
                 −34 
                 30 
                 50 
                 −7 
                 −41 
                 11 
                 21 
                 27 
                 64 
                 −25 
                 0 
                 −9 
                 −46 
                 −38 
                 8 
                 −3 
                 39 
                 14 
                 1 
                 27 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 −15 
               
               
                 −4 
                 −29 
                 28 
                 12 
                 73 
                 −21 
                 −21 
                 −17 
                 −1 
                 25 
                 7 
                 28 
                 −31 
                 23 
                 −38 
                 30 
                 −7 
                 −32 
                 −27 
                 −19 
                 24 
                 19 
                 22 
                 −1 
                 49 
                 5 
                 −23 
                 2 
                 10 
                 13 
                 −22 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 40 
               
               
                 −8 
                 −3 
                 −34 
                 8 
                 14 
                 20 
                 −4 
                 −7 
                 −6 
                 17 
                 −21 
                 −60 
                 −33 
                 64 
                 −18 
                 12 
                 −11 
                 34 
                 −39 
                 −14 
                 −12 
                 −14 
                 7 
                 29 
                 −30 
                 −12 
                 8 
                 30 
                 −37 
                 −33 
                 −40 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 −5 
               
               
                 −13 
                 42 
                 9 
                 27 
                 −17 
                 −5 
                 −43 
                 0 
                 27 
                 −4 
                 39 
                 −42 
                 65 
                 −1 
                 −9 
                 14 
                 35 
                 19 
                 7 
                 −18 
                 6 
                 26 
                 −45 
                 6 
                 −16 
                 −5 
                 3 
                 8 
                 17 
                 50 
                 17 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 33 
               
               
                   
               
             
          
         
       
     
     
       
         
               
             
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 3D 
               
               
                   
               
               
                 Lower Right = 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 −3 
                 10 
                 21 
                 −8 
                 −11 
                 2 
                 −7 
                 −32 
                 −1 
                 24 
                 6 
                 16 
                 11 
                 35 
                 −27 
                 28 
                 −14 
                 −33 
                 22 
                 28 
                 −1 
                 −14 
                 −11 
                 16 
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