Abstract:
For a gradation displaying operation for an electro-optical device, a gradation display system which can be controlled by a digital signal and is hard to be affected by variation in characteristics between respective elements and which can achieve high gradation, is provided. In the active matrix type electro-optical device, by the digital control of time and amplitude of a voltage pulse applied to each picture element electrode, composite pulses having plural voltage values and pulse widths are formed for one frame of an image so that an average effective voltage of the one frame of the image is made an arbitrary value, thereby finally displaying an intermediate color tone on liquid crystal.

Description:
BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     This invention relates to a display method for a high-gradation displaying operation in an electro-optical display device constructed by plural picture elements which are arranged in a matrix form and have driving switch elements, such as a liquid crystal display, a plasma display, a vacuum microelectronics display and the like. 
     2. Description of Related Art 
     The recent miniaturization of various office automation equipments has caused a conventional cathode ray tube (CRT) to be replaced by a thin-type display (flat panel display) such as a plasma display, a liquid crystal display and the like. In addition, there has been also researched a vacuum microelectronics display in which micro vacuum tubes each comprising a field emission cathode and a grid are arranged in a matrix array and an image is displayed by irradiating an electron beam emitted from the matrix array onto fluorescent material. In all the display devices as described above, an image display operation is performed by controlling a voltage to be applied to intersections of the matrix array. 
     That is, a transmitted-light amount or a scattered-light amount is varied by an electric field in a display of liquid crystal material, an electric discharge is induced between electrodes by an electric field in a plasma display, and electrons are emitted from a cathode by field emission effect in a vacuum microelectronics display. 
     The simplest one of these matrix types is a display including a pair of substrates which are confronted to each other, and striped wirings which are arranged longitudinally and laterally on the respective substrates, a voltage being generated in a gap between any intersected longitudinal and lateral wirings by applying a voltage therebetween. This type is called as a simple matrix-structure. This type of display can be produced easily and at low cost because of its simple structure. However, in this type of display, there has been frequently occurs a phenomena called as crosstalk in which an image is blurred due to unintentional signal flow into undesired parts in a driving operation of the display. In order to avoid the crosstalk, material whose optical characteristic varies sharply with a voltage above a predetermined threshold voltage is required. For example, a plasma electric discharge display is a favorable display for such a simple-matrix system because it has a distinct threshold value as described above. 
     When such an optical material as described above is used, however, the display must be driven such that a voltage for each picture element (that is, a crossing between matrix wirings) is extremely near to the threshold voltage. Therefore, when the simple matrix system is adopted, an optical ON/OFF-switching operation can be carried out, but it is difficult to obtain an intermediate brightness or color tone because material which can. vary its brightness in an intermediate variable range in accordance with an applied voltage can not be used as an optical material for the display. 
     This problem is caused by placing the switching function on an optical material (liquid crystal or electric discharge gas). Therefore, an attempt of installing a switching element to the matrix independently of the optical material was tried. This type of device is called as an active matrix display and has one or more switching elements at each picture element. A PIN diode, an MIM diode or a thin film transistor or the like is used as a switching element. 
     However, even though an active matrix system is adopted, it is difficult to achieve a display operation with high gradation as realized in CRT. 
     FIG.  1 (A) shows a conventional gradation display system. In FIG.  1 (A), the ordinate represents the amplitude of a voltage applied to a specified picture element and the abscissa represent a time, and this figure represents the variation of the voltage applied to a picture element of a liquid crystal display. The voltage is applied in the form of an alternative current pulse because the liquid crystal would be deteriorated due to its electrolysis if it is applied with a direct current for a long time. 
     In this figure, the voltage is applied so as to display brightness of “8” in first two periods, “4” in next one period and “6” in last one period. Actually, the liquid crystal material varies in its optical characteristic sharply at a particular threshold value, but it is assumed here that the optical characteristic varies linearly in accordance with the applied voltage. This approximation is a very close approximation for the liquid crystal material such as dispersion type liquid crystal material for example. Thus, in order to achieve the display operation with 16-step gradation for example, it is required to control a voltage at 16 steps and then apply it to a picture element. 
     In a usual liquid crystal material, its optical characteristic is saturated when applied with a voltage over 5 volts, and hardly varies even if a voltage above 5 volts is applied. In order to implement 16-step gradation displaying operation for example, a voltage must be applied with precision of 300 mV which is obtained by dividing 5 volts by 16. It is reasonable that the implementation of a higher-gradation display operation requires a more minute voltage to be applied to the picture element. However, it is not easy to generate a voltage with a resolution of 300 mV or less, and such a minute voltage is attenuated by various factors until it reaches the picture element. These factors contain resistance of wirings, resistance of thin film transistors, reduction of potential of a picture element due to a parasitic capacitance of the thin film transistors and the like. Since these parameters causing the voltage variation or fluctuation are different in accordance with an active element of each picture element, the fluctuation of the voltage of the picture element can be actually suppressed in a range of plus and minus 0.2 V at maximum over the whole panel. 
     On the other hand, there is another method of implementing a gradation displaying operation by controlling a time length (retention time) of a voltage pulse to be applied to each picture element. For example, display methods as disclosed in Japanese patent application Nos. 3-169306, 3-169307, 3-209869, etc. which have been invented by the same inventors as this application are cited as examples of the above method. FIG.  1 (B) shows this example. First two periods are used for brightness of “8”, next one period is used for brightness of “4” and last one period is used for brightness of “6”, as well as the method of FIG.  1 (A). 
     It is known that the liquid crystal material visually functions to display color tone and brightness in accordance with, not an instantaneous voltage, but an average effective voltage. Namely, assuming an effective voltage of first two periods as 1, the next one period is considered as 0.5 though it has the same peak voltage as that of the first two periods, and the last period is considered as 0.75. 
     Further, a response speed of the plasma electric discharge is a high speed of 1 micro second, but a human naked eye cannot follow such a high speed, and can sense only an average brightness, so that a visual brightness is finally determined by an average effective voltage. 
     That is, the gradation displaying system as described above requires the switching speed to be remarkably increased particularly in order to implement a high-gradation displaying operation. 
     FIG. 2 shows a special case of FIG.  1 (B), and an example of FIG. 2 can achieve 64-step (64-level) gradation displaying, operation. Numbers at the left side represent degree of brightness of picture elements. In this example, the optical characteristic varies from “1” to “54” in this order. In FIG. 2, (A) and (B) are not different essentially, and only the order of plural pulses is altered therebetween. The details of this example are described in Japanese patent application No. 3-209869 which has been invented by the same inventors as this application and thus the description thereof is eliminated. 
     For example, in a part marked as “17”, a pulse whose length is 1 and a pulse whose length is 16 appear once in a period of s respectively, and it represents an average brightness of “17”. Further, in a part marked “37”, a pulse whose length is 1, a pulse whose length is 4 and a pulse whose length is 32 appear once in a period of s, and it represents an average brightness of “37”. By this way, 64-step gradation display from “0” to “64” can be achieved. 
     It is apparent from FIG. 2 that the minimum pulse length is required to be one 64th of a voltage repetitive period of s. In a case where a switching operation is actually carried out using a thin film transistor or the like, a pulse whose width is shortened in accordance with the number of lines of matrix is applied to the thin film transistor. For example, when the matrix has 480 lines, a pulse whose width is one 480th of the minimum pulse length is applied to the thin film transistor. Since s is usually 30 msec, the minimum pulse width becomes 500 micro sec. Thus, 1 micro sec is required for a driving signal for the thin film transistor or the like. This value may be considered as a large value, but it is very rapid signal for the thin film transistor. Therefore, in order to achieve higher gradation displaying operation, more rapid pulses must be applied, and by this, electromagnetic wave is radiated from the display. 
     SUMMARY OF THE PRESENT INVENTION 
     This invention has been implemented to solve the problems described above in a conventional gradation displaying system, and is a new type of gradation displaying system which adopts advantages of both of a gradation displaying system which is completely dependent on a voltage as shown in FIG.  1 (A) and a gradation displaying system which is completely dependent on a pulse width as shown in FIG.  1 (B). In addition, in this system, both of the remarkably minute voltage control and the remarkably short-speed pulse as pointed out above are not required. 
     A method of driving an electro-optical device of an active matrix structure in accordance with the present invention comprises applying a voltage comprising pulses of a plurality of pulse heights and a plurality of pulse widths to a pixel of the electro-optical device. 
     In order to distinguish this invention from the conventional system clearly, an embodiment of this invention is shown in FIG.  1 (C). First two periods are used for brightness of “8”, next one period is used for brightness of “4” and last one period is used for brightness of “6”, like the systems as shown in FIG.  1 (A) and FIG.  1 (B). 
     In this invention, the gradation displaying operation is also achieved by utilizing an average effective voltage as well as the system as shown in FIG. 2, however, in this invention, a degree of freedom is increased by varying not only a pulse width, but also a pulse height to solve the above problems. 
     First, in FIG.  1 (C), first two periods are the same as others, and assuming a voltage at these periods as 1 volt, of course, an average effective voltage of the first two periods becomes 1. An average effective voltage at a next one period is 0.5 because in the next one period a pulse height is a half of that at the first two periods. In a last one period, complicated pulses are combined. However, a pulse having pulse height of 1 first appears, and subsequently a pulse having pulse height of 0.5 appears. Since these two pulses are retentive for the same time, an average effective voltage becomes 0.75. As described above, by controlling not only the pulse width but also the pulse height, a load imposed on pulse length (high-speed pulsation) can be reduced by the pulse height. 
     In FIG. 2, the 64-step (64-level) gradation displaying operation is achieved by combination of total 6 pulses whose width is 1, 2, 4, 8, 16 and 32. On the other hand, in this invention, the pulse height is sectioned into five steps (levels) of 0, 1, 2, 3 and 4, and only four pulses having pulse width of 1, 2, 4 and 8 are used to implement the 61-step gradation displaying operation. Of course, a small number of kinds of pulses means that the minimum pulse width is large. 
     FIG. 3 shows an example. FIGS.  3 (A) and (B) are essentially identical to each other except that the pulse order is altered. In the example of FIG. 3, “1” can be represented by a pulse whose height is 1 and whose width is 1 (minimum pulse). “2”can be represented by a pulse whose height is 1 and whose width is 2. “4” can be represented by a pulse whose height is 1 and whose width is 4. “8” can be represented by a pulse whose height is 1 and whose width is 8. “16” can be represented by a pulse whose height is 2 and whose width is 8. “32” can be represented by a pulse whose height is 4 and whose width is 8. These pulses can be represented by combination of pulses having another pulse height and pulse width. As shown in the FIG. 3, all numbers from “0”, “1” to “60” can be represented by a combination of these pulses. It is apparent from this figure that the minimum pulse width becomes longer than that of the conventional system. In the example of FIG. 3, the minimum pulse width is four times of that of FIG.  2 . That is, increase of power consumption due to a high-speed operation and a load imposed on the device can be remarkably reduced. 
     For example, dividing the pulse height into five steps (levels) of 0, 1, 2, 3, 4 and using three kinds of pulses having pulse widths of 1, 2, 4, the maximum number which can be represented by the above pulses is “28”, which is obtained by adding a pulse whose width is 1 and whose height is 4, a pulse whose width is 2 and whose height is 4 and a pulse whose width is 4 and whose height is 4, and all numbers from “0” to “28” can be represented by combination of these three pulses. 
     Assuming a number to be represented as “N”, this problem is a problem to find out combinations of figures (KLM) where 
     
       
         N=1×K+2×L+4×M 
       
     
     (where K, L, M represents any one of 0, 1, 2, 3, 4) Solutions of this problem are shown in Table 1. 
     When this problem is generalized, this problem turns out to be a proof of the following theorem; 
     [Theorem] 
     in an equation; 
     
       
         N=n 0 +2n 1 +2 2 n 2 + . . . +2 k n k   
       
     
     
       
          (n 0 , n 1 , n 2 , . . . , n k  0, 1, 2, . . . , I),  (1) 
       
     
     N may be (can represent) any integer below the following maximum value; 
     
       
         N max =(1+2+2 2 + . . . +2 k )I  (2). 
       
     
     An example shown in Table 1 corresponds to a case of this theorem where k=2 and I=4, and an example shown in FIG. 3 corresponds to a part of a case where k=3 and I=4. In cases where k=4 and I=4 (125 gradations) and where k=5 and I=4 (253 gradations), however, trueness of this theorem is unknown. The trueness of the theorem is unclear for a higher-gradation displaying operation. Therefore, the proof therefor is required. 
     This proof will be made as follows. First of all, considering the theorem as described above for I=1, the theorem is proved to be true. Namely, 
     By the following equation: 
     
       
         N=n 0 +2n 1 +2 2 n 2 + . . . +2 k n k   
       
     
     
       
          (n 0 , n 1 , n 2 , . . . , n k  0, 1) 
       
     
     where k is an arbitrary positive integer, all from 0 to (1+2+2 2 + . . . +2 k ) can be represented (sub theorem 1). Since the proof for this theorem is very easy, it is omitted here. 
     Next, the theorem is assumed to be true for I=i (i represents an arbitrary positive integer)(assumption 1). Under the above assumption, it is examined whether the theorem is true or not for I=i+1. 
     The maximum value of N for I=i is represented by Nmax (represented by the equation (2)), and the maximum value of N for I=i+1 is represented by N′max. 
     
       
         N′max=(1+2+2 2 + . . . +2 k )(i+1)  (3). 
       
     
     Now, it is true that all integers from 0 to Nmax can be represented by the following series: 
     
       
         N=n 0 +2n 1 +2 2 n 2 + . . . +2 k n k   
       
     
     
       
          (n 0 , n 1 , n 2 , . . . , n k  0, 1, 2, . . . , i, i+1)  (4). 
       
     
     Because, from the assumption 1, it supposed to be true that all integers from 0 to Nmax can be represented by the series (4) which uses only number of n 0 , n 1 , n 2 , . . . , n k  0, 1, 2, . . . , i (i+1 is not used). 
     Next, it will be examined whether any integer from Nmax+1 to N′max can be represented or not. An arbitrary integer N′ contained in this region is represented by 
     
       
         N′=Nmax+m=(1+2+2 2 + . . . +2 k )i+m  (5). 
       
     
     Where m represents a figure from 1 to (1+2+2 2 + . . . +2 k ), and by the sub theorem 1 as mentioned above, m is represented by; 
     
       
         equation m=1 0 +21 1 +2 2 1 2 + . . . +2 k 1 k   
       
     
     
       
          (1 0 , 1 1 , 1 2 , . . . 1 k  0, 1). 
       
     
     Thus, the equation (5) is; 
     
       
         N′=(1+2+2 2 + . . . +2 k )i 
       
     
     
       
          +1 0+21   1 +2 2 1 2 + . . . +2 k 1 k   
       
     
     
       
          (1 0 , 1 1 , 1 2 , . . . 1 k  0, 1)  (5)′. 
       
     
     A polynomial equation (5)′ is transformed to the second power series: 
     
       
         N′=n 0 +2n 1 +2 2 n 2 + . . . +2 k n k   
       
     
     
       
          (n 0 , n 1 , n 2 , . . . , n k  i, i+1)  (6). 
       
     
     Thus, it is proved that this theorem is also true for I=i+1. Therefore, by the mathematical inductive method, it is proved that the theorem as mentioned above is true for an arbitrary positive integer k and I. 
     As described above, greatly multiple steps of average voltages can be represented by combinations of pulses whose width and height are different from one another. In this invention, a pulse voltage must be set to plural values above 2 steps (levels), for example, 5 steps (levels). However, setting a threshold voltage of liquid crystal to 5V, these levels are set to 0V, 1.25V, 2.5V, 3.75V and 5V, and using these voltage levels, 61-step gradation displaying operation can be achieved in the case as shown in FIG.  3 . On the other hand, in the conventional system as shown in FIG.  1 (A) where a voltage must be minutely divided (sectioned), in order to achieve the 61-step gradation displaying operation, an input voltage must be stepwisely divided by 80 mV and this is impossible to be carried out. The above is an essential part of this invention, and actually, a signal input to each display device is more complicated. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 shows gradation displaying method of this invention and the prior art; 
     FIG. 2 shows an example of the conventional gradation displaying method; 
     FIG. 3 shows an example of the gradation displaying method of this invention; 
     FIG. 4 shows an embodiment of an image display device to which this invention is applied; and 
     FIG. 5 shows an applied signal, etc. in the embodiment of the image display device to which this invention is applied. 
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT 
     FIG. 4 is a schematic diagram of a display device for implementing this invention. In the device shown here, only indispensable parts to explain this invention are described, and other various equipments may be required to actually operate the device. This device is assumed to carry out the 61-step gradation displaying operation. 
     First of all, a video signal is input from an input terminal of this device. Here, the input video signal is assumed to be a signal for a picture element on an n-th column and an m-th row of an image, whose brightness is represented with “212” when the maximum value of brightness is assumed as 256. Of course, other signals are input into this device continually. 
     After input into the device, this signal is converted to a binary digital signal by an A/D converter. “212” corresponds to “11010100” in binary expression. In this invention, however, only this digital signal cannot be used directly. Accordingly, this digital signal is converted to a signal which is suitable for this invention by a signal processor at next stage. 
     In this device, six kinds of pulses whose pulse widths are T 0 , 2T 0 , 4T 0 , 8T 0 , 16T 0 , 32T 0  are used, and the pulse height thereof is divided into 5 levels (0, 1, 2, 3, 4). 
     In this device, a digital signal “11010100” is converted to “434110”. This signal converting operation may be carried out one by one, but output signals which correspond to input signals are preferably memorized beforehand in a memory device inside of a signal processing device and outputted in correspondence to the input signals in consideration of limitation of signal processing speed. Such data are shown in Table 2, for example. In this Table, N is represented by decimal notation, but in a practical processing step, it has been converted to a binary number. This conversion process has no problem because this process is carried out in one-to-one correspondence. “Signal” represents an output signal. 
     Signals output from the signal processing device are not output continuously like “434100”. Namely, since other picture element data must be output simultaneously, these signals are outputted intermittently like “ . . . 4 . . . 3 . . . 4 . . . 1 . . . 0 . . . 0 . . . ”. A clock pulse is also output simultaneously. 
     As described above the signals output from the signal processing device are transmitted to a shift resistor on the periphery of a screen. Here, each signal is transmitted to a corresponding signal line (Y line) and stored in capacitor or the like and held there until it is outputted. When a driver turns on, a signal voltage is discharged to each Y line. On the other hand, the clock pulse is transmitted to a shift resistor of a gate line (X line) and the signal is successively transmitted to each gate line. 
     This device adopts a mechanism in which the voltage value of 4 or 3 is generated by the signal processing device and held in the capacitor. However, a signal output from signal processing device may be converted to a digital signal corresponding to the voltage value “4” or “3” (for example “100” or “011”), and then a circuit for generating these signals may be connected to each Y line. In a case of using a capacitor, a pulse voltage is not a rectangular wave, but varies greatly with time lapse, and a voltage held in the picture element varies greatly with only a slight shift of a switching timing. The switching timing is dependent on performance of each thin film transistor and it is difficult to produce transistors under precise control of such an analog characteristic of each transistor using the present technology, and thus it is a factor in reducing the yield of the device. 
     Though this invention requires no fine control of a voltage in comparison with the conventional active matrix system of pure analog drive, 10% fluctuation of the voltage is enough to deteriorate the gradation by one order. 
     Thus, the analog method using the capacitor as described above is not favorable for this invention. In this point, in a case of using a system in which the voltage pulse is supplied directly from the voltage generation circuit, a pulse to be applied to the Y line has an excellent rectangular wave, and thus a voltage held in any picture element is substantially constant, so that it is favorable for the high-gradation displaying operation (64-step gradation or 256-step gradation, for example) at which this invention aims. 
     FIG. 5 shows a voltage of a picture element Z n, m  on the n-th column and the m-th row and a voltage between a gate line X n  and a signal line Y m  (which is also called drain line) which is applied to the picture element. In the figure showing the voltage of the picture element pixel Z n,m , a broken line represents an actual signal and a solid line represents an ideal signal. A voltage applied to the picture element does not have an ideal rectangular wave due to various factors. That is, the main factors are a voltage drop due to a so-called diving voltage which is caused by overlap of the gate electrode and the source region, a voltage drop caused by natural discharge from a picture element electrode, and a delay of ON/OFF switching operation of the thin film transistor. Although the analog type voltage supply means is not adopted, the disorder of the signal waveform as described above due to the analog factors in the active matrix is not favorable for this invention as described above. Thus, these factor must be considered fully for a practical circuit design. 
     As shown in FIG. 5, in a picture element, a highest-voltage state (4-voltage state) first continues for 32T 0 , subsequently the zero-voltage state is kept for T 0 , subsequently a 3-voltage state continues for 16T 0 , subsequently the voltage is kept to zero for 2T 0 , and subsequently a 4-voltage state continues for 8T 0 , and a 1-voltage state continues for a last 4T 0 . Through this operation, an average voltage of 212/63 per time T 0  can be obtained. 
     The voltage of the picture element Z n,m  at this time is an assembly of rectangular pulses as shown in a lower part of FIG.  4 . Assuming a period of 1 frame as 17 msec, T 0 =270 micro seconds, and the width of pulses applied to a gate electrode is 300 nsec when total number of X lines is 480. The minimum width of the pulse signal applied to the Y line is also 600 nsec. These numbers correspond to several MHz frequency. 
     On the other hand, in the conventional system (FIG.  2 ), a gate pulse of 75 nsec which is about one fourth of the above value is required. This corresponds to 13 MHz frequency, and in order to achieve such a high-speed operation, for example, it has been required to produce an active element in CMOS form. Further, an electromagnetic wave which is radiated from a display due to the high-frequency driving as described above has induced a problem. However, such a problem rarely occurs in this invention. Of course, the active element produced in the CMOS form can be also available for this invention. 
     According to this invention, an image having remarkably high gradation can be obtained. This invention is particularly suitable for the liquid crystal display, however, it is applicable to other display systems such as a plasma display, a vacuum microelectro display, etc. Optical material which has not only an ON/OFF switching function, but also an intermediate optical characteristic in accordance with an applied voltage is particularly favorable to this invention. 
     Therefore, this invention can be implemented particularly using any material whose optical characteristic varies in accordance with an applied voltage, and which develops the intermediate state with the applied voltage. 
     
       
         
               
             
               
               
             
               
               
             
           
               
                 TABLE 1 
               
             
             
               
                   
               
               
                 *N* = 1 + 2m + 4n 
               
             
          
           
               
                 N 
                 (1 mn) 
               
               
                   
               
             
          
           
               
                 0 
                 (000) 
               
               
                 1 
                 (100) 
               
               
                 2 
                 (200), (010) 
               
               
                 3 
                 (110), (300), 
               
               
                 4 
                 (210), (400), (001), (020) 
               
               
                 5 
                 (120), (101), (310), 
               
               
                 6 
                 (201), (220), (410), (011), (030) 
               
               
                 7 
                 (130), (111), (301), (320) 
               
               
                 8 
                 (211), (230), (401), (420), (002), (021), (040) 
               
               
                 9 
                 (140), (102), (121), (311), (330) 
               
               
                 10 
                 (202), (221), (240), (411), (430), (012), (031) 
               
               
                 11 
                 (112), (131), (302), (321), (340) 
               
               
                 12 
                 (212), (231), (402), (421), (440), (003), (022), (041) 
               
               
                 13 
                 (103), (122), (141), (312), (331) 
               
               
                 14 
                 (203), (222), (241), (412), (431), (013), (032) 
               
               
                 15 
                 (113), (132), (303), (322), (341) 
               
               
                 16 
                 (213), (232), (403), (422), (441), (004), (023), (042) 
               
               
                 17 
                 (104), (123), (142), (313), (332) 
               
               
                 18 
                 (204), (223), (242), (413), (432), (014), (033) 
               
               
                 19 
                 (114), (133), (304), (323), (342) 
               
               
                 20 
                 (214), (233), (404), (423), (442), (024), (043) 
               
               
                 21 
                 (124), (143), (314), (333) 
               
               
                 22 
                 (224), (243), (414), (433), (034) 
               
               
                 23 
                 (134), (324), (343) 
               
               
                 24 
                 (234), (424), (443), (044) 
               
               
                 25 
                 (144), (334) 
               
               
                 26 
                 (244), (434) 
               
               
                 27 
                 (344) 
               
               
                 28 
                 (444) 
               
               
                   
               
             
          
         
       
     
     
       
         
               
               
               
             
           
               
                   
                 TABLE 2 
               
               
                   
                   
               
               
                   
                 N 
                 Signal 
               
               
                   
                   
               
             
             
               
                   
                 001 
                 000001 
               
               
                   
                 002 
                 000010 
               
               
                   
                 003 
                 000003 
               
               
                   
                 004 
                 000100 
               
               
                   
                 005 
                 000101 
               
               
                   
                 006 
                 000030 
               
               
                   
                 007 
                 000103 
               
               
                   
                 008 
                 001000 
               
               
                   
                 009 
                 001001 
               
               
                   
                 010 
                 001010 
               
               
                   
                 011 
                 001003 
               
               
                   
                 012 
                 000300 
               
               
                   
                 013 
                 000301 
               
               
                   
                 014 
                 000310 
               
               
                   
                 015 
                 000303 
               
               
                   
                 016 
                 010000 
               
               
                   
                 017 
                 010001 
               
               
                   
                 018 
                 010010 
               
               
                   
                 019 
                 010003 
               
               
                   
                 020 
                 010100 
               
               
                   
                 021 
                 010101 
               
               
                   
                 022 
                 010110 
               
               
                   
                 023 
                 010103 
               
               
                   
                 024 
                 003000 
               
               
                   
                 025 
                 003001 
               
               
                   
                 026 
                 003010 
               
               
                   
                 027 
                 003003 
               
               
                   
                 028 
                 003100 
               
               
                   
                 029 
                 003101 
               
               
                   
                 030 
                 003110 
               
               
                   
                 031 
                 003103 
               
               
                   
                 032 
                 100000 
               
               
                   
                 033 
                 100001 
               
               
                   
                 034 
                 100010 
               
               
                   
                 035 
                 100003 
               
               
                   
                 036 
                 100100 
               
               
                   
                 037 
                 100101 
               
               
                   
                 038 
                 100030 
               
               
                   
                 039 
                 100103 
               
               
                   
                 040 
                 101000 
               
               
                   
                 041 
                 101001 
               
               
                   
                 042 
                 103000 
               
               
                   
                 043 
                 103001 
               
               
                   
                 044 
                 103010 
               
               
                   
                 045 
                 103003 
               
               
                   
                 046 
                 103100 
               
               
                   
                 047 
                 103101 
               
               
                   
                 048 
                 030000 
               
               
                   
                 049 
                 030001 
               
               
                   
                 050 
                 030010 
               
               
                   
                 051 
                 030003 
               
               
                   
                 052 
                 030100 
               
               
                   
                 053 
                 030101 
               
               
                   
                 054 
                 030030 
               
               
                   
                 055 
                 030103 
               
               
                   
                 056 
                 031000 
               
               
                   
                 057 
                 031001 
               
               
                   
                 058 
                 030130 
               
               
                   
                 059 
                 031003 
               
               
                   
                 060 
                 030300 
               
               
                   
                 061 
                 030301 
               
               
                   
                 062 
                 030310 
               
               
                   
                 063 
                 030303 
               
               
                   
                 064 
                 200000 
               
               
                   
                 065 
                 200001 
               
               
                   
                 066 
                 200010 
               
               
                   
                 067 
                 200003 
               
               
                   
                 068 
                 200100 
               
               
                   
                 069 
                 200101 
               
               
                   
                 070 
                 200030 
               
               
                   
                 071 
                 200103 
               
               
                   
                 072 
                 033000 
               
               
                   
                 073 
                 033001 
               
               
                   
                 074 
                 033010 
               
               
                   
                 075 
                 033003 
               
               
                   
                 076 
                 200300 
               
               
                   
                 077 
                 200301 
               
               
                   
                 078 
                 200310 
               
               
                   
                 079 
                 200303 
               
               
                   
                 080 
                 130000 
               
               
                   
                 081 
                 130001 
               
               
                   
                 082 
                 130010 
               
               
                   
                 083 
                 130003 
               
               
                   
                 084 
                 130100 
               
               
                   
                 085 
                 130101 
               
               
                   
                 086 
                 130030 
               
               
                   
                 087 
                 130031 
               
               
                   
                 088 
                 203000 
               
               
                   
                 089 
                 203001 
               
               
                   
                 090 
                 203010 
               
               
                   
                 091 
                 203003 
               
               
                   
                 092 
                 203100 
               
               
                   
                 093 
                 203101 
               
               
                   
                 094 
                 203030 
               
               
                   
                 095 
                 203031 
               
               
                   
                 096 
                 300000 
               
               
                   
                 097 
                 300001 
               
               
                   
                 098 
                 300010 
               
               
                   
                 099 
                 300003 
               
               
                   
                 100 
                 300100 
               
               
                   
                 101 
                 300101 
               
               
                   
                 102 
                 300030 
               
               
                   
                 103 
                 300031 
               
               
                   
                 104 
                 301000 
               
               
                   
                 105 
                 301001 
               
               
                   
                 106 
                 301010 
               
               
                   
                 107 
                 301003 
               
               
                   
                 108 
                 300300 
               
               
                   
                 109 
                 300301 
               
               
                   
                 110 
                 300310 
               
               
                   
                 111 
                 300303 
               
               
                   
                 112 
                 230000 
               
               
                   
                 113 
                 230001 
               
               
                   
                 114 
                 230010 
               
               
                   
                 115 
                 230003 
               
               
                   
                 116 
                 230100 
               
               
                   
                 117 
                 230101 
               
               
                   
                 118 
                 230030 
               
               
                   
                 119 
                 230031 
               
               
                   
                 120 
                 303000 
               
               
                   
                 121 
                 303001 
               
               
                   
                 122 
                 303010 
               
               
                   
                 123 
                 303003 
               
               
                   
                 124 
                 303100 
               
               
                   
                 125 
                 303101 
               
               
                   
                 126 
                 303030 
               
               
                   
                 127 
                 303031 
               
               
                   
                 128 
                 400000 
               
               
                   
                 129 
                 400001 
               
               
                   
                 130 
                 400010 
               
               
                   
                 131 
                 400003 
               
               
                   
                 132 
                 400100 
               
               
                   
                 133 
                 400101 
               
               
                   
                 134 
                 400030 
               
               
                   
                 135 
                 400031 
               
               
                   
                 136 
                 401000 
               
               
                   
                 137 
                 401001 
               
               
                   
                 138 
                 401010 
               
               
                   
                 139 
                 401003 
               
               
                   
                 140 
                 400300 
               
               
                   
                 141 
                 400301 
               
               
                   
                 142 
                 400310 
               
               
                   
                 143 
                 400303 
               
               
                   
                 144 
                 410000 
               
               
                   
                 145 
                 410001 
               
               
                   
                 146 
                 410010 
               
               
                   
                 147 
                 410003 
               
               
                   
                 148 
                 410100 
               
               
                   
                 149 
                 410101 
               
               
                   
                 150 
                 410030 
               
               
                   
                 151 
                 410103 
               
               
                   
                 152 
                 403000 
               
               
                   
                 153 
                 403001 
               
               
                   
                 154 
                 403010 
               
               
                   
                 155 
                 403003 
               
               
                   
                 156 
                 403100 
               
               
                   
                 157 
                 403101 
               
               
                   
                 158 
                 403030 
               
               
                   
                 159 
                 413101 
               
               
                   
                 160 
                 420000 
               
               
                   
                 161 
                 420001 
               
               
                   
                 162 
                 420010 
               
               
                   
                 163 
                 420003 
               
               
                   
                 164 
                 420100 
               
               
                   
                 165 
                 420101 
               
               
                   
                 166 
                 420030 
               
               
                   
                 167 
                 420103 
               
               
                   
                 168 
                 421000 
               
               
                   
                 169 
                 421001 
               
               
                   
                 170 
                 421010 
               
               
                   
                 171 
                 421003 
               
               
                   
                 172 
                 420300 
               
               
                   
                 173 
                 420301 
               
               
                   
                 174 
                 420310 
               
               
                   
                 175 
                 420303 
               
               
                   
                 176 
                 430000 
               
               
                   
                 177 
                 430001 
               
               
                   
                 178 
                 430010 
               
               
                   
                 179 
                 430003 
               
               
                   
                 180 
                 430100 
               
               
                   
                 181 
                 430101 
               
               
                   
                 182 
                 430030 
               
               
                   
                 183 
                 430103 
               
               
                   
                 184 
                 431000 
               
               
                   
                 185 
                 431001 
               
               
                   
                 186 
                 431010 
               
               
                   
                 187 
                 431003 
               
               
                   
                 188 
                 430300 
               
               
                   
                 189 
                 430301 
               
               
                   
                 190 
                 430310 
               
               
                   
                 191 
                 430303 
               
               
                   
                 192 
                 440000 
               
               
                   
                 193 
                 440001 
               
               
                   
                 194 
                 440010 
               
               
                   
                 195 
                 440003 
               
               
                   
                 196 
                 440100 
               
               
                   
                 197 
                 440101 
               
               
                   
                 198 
                 440030 
               
               
                   
                 199 
                 440103 
               
               
                   
                 200 
                 433000 
               
               
                   
                 201 
                 433001 
               
               
                   
                 202 
                 433010 
               
               
                   
                 203 
                 433003 
               
               
                   
                 204 
                 440300 
               
               
                   
                 205 
                 440301 
               
               
                   
                 206 
                 440310 
               
               
                   
                 207 
                 440303 
               
               
                   
                 208 
                 434000 
               
               
                   
                 209 
                 434001 
               
               
                   
                 210 
                 434010 
               
               
                   
                 211 
                 434003 
               
               
                   
                 212 
                 434100 
               
               
                   
                 213 
                 434101 
               
               
                   
                 214 
                 434030 
               
               
                   
                 215 
                 434103 
               
               
                   
                 216 
                 443000 
               
               
                   
                 217 
                 443001 
               
               
                   
                 218 
                 443010 
               
               
                   
                 219 
                 443003 
               
               
                   
                 220 
                 434300 
               
               
                   
                 221 
                 434301 
               
               
                   
                 222 
                 434310 
               
               
                   
                 223 
                 434303 
               
               
                   
                 224 
                 444000 
               
               
                   
                 225 
                 444001 
               
               
                   
                 226 
                 444010 
               
               
                   
                 227 
                 444003 
               
               
                   
                 228 
                 444100 
               
               
                   
                 229 
                 444101 
               
               
                   
                 230 
                 444030 
               
               
                   
                 231 
                 444103 
               
               
                   
                 232 
                 444200 
               
               
                   
                 233 
                 444201 
               
               
                   
                 234 
                 444210 
               
               
                   
                 235 
                 444203 
               
               
                   
                 236 
                 444300 
               
               
                   
                 237 
                 444301 
               
               
                   
                 238 
                 444310 
               
               
                   
                 239 
                 444303 
               
               
                   
                 240 
                 444400 
               
               
                   
                 241 
                 444401 
               
               
                   
                 242 
                 444410 
               
               
                   
                 243 
                 444403 
               
               
                   
                 244 
                 444420 
               
               
                   
                 245 
                 444421 
               
               
                   
                 246 
                 444430 
               
               
                   
                 247 
                 444431 
               
               
                   
                 248 
                 444440 
               
               
                   
                 249 
                 444441 
               
               
                   
                 250 
                 444442 
               
               
                   
                 251 
                 444443 
               
               
                   
                 252 
                 444444