Problem: Let us define two functions f and g on positive integer numbers. 

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You need to process Q queries. In each query, you will be given three integers l, r and k. You need to print the number of integers x between l and r inclusive, such that g(x) = k. 

Input

The first line of the input contains an integer Q (1 ≤ Q ≤ 2 × 105) representing the number of queries. 

Q lines follow, each of which contains 3 integers l, r and k (1 ≤ l ≤ r ≤ 106, 1 ≤ k ≤ 9).

Output

For each query, print a single line containing the answer for that query.

Examples

Input

4
22 73 9
45 64 6
47 55 7
2 62 4


Output

1
4
0
8


Input

4
82 94 6
56 67 4
28 59 9
39 74 4


Output

3
1
1
5

Note

In the first example:

  * g(33) = 9 as g(33) = g(3 × 3) = g(9) = 9
  * g(47) = g(48) = g(60) = g(61) = 6
  * There are no such integers between 47 and 55. 
  * g(4) = g(14) = g(22) = g(27) = g(39) = g(40) = g(41) = g(58) = 4

Solution (in JAVA):

Solution:
import java.util.*;
import java.io.*;
import java.util.Queue;
import java.util.LinkedList;
import java.math.*;
 
     public class Sample implements Runnable
    { 
        
         
         
         public  static void solve()
          {   
            int[] a=new int[1000005];
            int[] b=new int[1000005];

            for(int i=0;i<1000005;i++)
            {
              int num=i;
              int mul=1;
              while(num>0)
              {
                if(num%10!=0)
                    mul*=(num%10);
                num/=10;
              }
              a[i]=mul;
            }
            for(int i=0;i<1000005;i++)
            {
               if(i<10)
               {
                b[i]=i;
               }
               else
               {
                b[i]=b[a[i]];
               }
            }
            
            int q=i();
            int[][] prefix=new int[1000005][10];
            for(int i=0;i<10;i++)
            {
              if(b[0]==i)
              {
                prefix[0][i]=1;
              }
               for(int j=1;j<1000005;j++)
               {
                if(b[j]==i)
                {
                  prefix[j][i]=prefix[j-1][i]+1;
                }
                else
                {
                  prefix[j][i]=prefix[j-1][i];
                }
               }
            }
            while(q-->0)
            {
              int l=i(); int r=i(); int k=i();

              out.println(prefix[r][k]-prefix[l-1][k]);
            }
            
              
          }
          

          public void run()
          {   
              solve();
              out.close();
          }
 
          public static void main(String[] args) throws IOException
          { 
                new Thread(null, new Sample(), "whatever", 1<<26).start();
          }
           static class Pair implements Comparator<Pair>{ 
            String a;
            long b;
            long c;
            
            Pair(){}
            Pair(String a,long b,long c)
            {
                       this.a=a;
                       this.b=b;
                       this.c=c;
            }
            public int compare(Pair p1,Pair p2)
            {
               if(p1.c==0 && p2.c==0)
               {
                return Long.compare(p1.b,p2.b);
               }
               if(p1.c==0)
               {
                return -1;
               }
               if(p2.c==0)
               {
                return 1;
               }
               else
              return Long.compare(p2.b*p1.c,p1.b*p2.c);

            }
   
            
        }
    
        
       
         
    ////////////////////////////////////////////////////// Merge Sort ////////////////////////////////////////////////////////////////////////
     
   static class Merge 
   {
 
        public static void sort(long inputArr[]) 
        {
            int length = inputArr.length;
            doMergeSort(inputArr,0, length - 1);
        }
 
        private static void doMergeSort(long[] arr,int lowerIndex, int higherIndex) 
        {        
            if (lowerIndex < higherIndex) {
                int middle = lowerIndex + (higherIndex - lowerIndex) / 2;
                doMergeSort(arr,lowerIndex, middle);
                doMergeSort(arr,middle + 1, higherIndex);
                mergeParts(arr,lowerIndex, middle, higherIndex);
            }
        }
 
        private static void mergeParts(long[]array,int lowerIndex, int middle, int higherIndex) 
        {
            long[] temp=new long[higherIndex-lowerIndex+1];
            for (int i = lowerIndex; i <= higherIndex; i++) 
            {
                temp[i-lowerIndex] = array[i];
            }
            int i = lowerIndex;
            int j = middle + 1;
            int k = lowerIndex;
            while (i <= middle && j <= higherIndex) 
            {
                if (temp[i-lowerIndex] < temp[j-lowerIndex]) 
                {
                    array[k] = temp[i-lowerIndex];
                    i++;
                } else {
                    array[k] = temp[j-lowerIndex];
                    j++;
                }
                k++;
            }
            while (i <= middle) 
            {
                array[k] = temp[i-lowerIndex];
                k++;
                i++;
            }
            while(j<=higherIndex)
            {
                array[k]=temp[j-lowerIndex];
                k++;
                j++;
            }
        }
 
    }
        
      
    /////////////////////////////////////////////////////////// Methods ////////////////////////////////////////////////////////////////////////
 
 
     static boolean isPal(String s)
     {
        for(int i=0, j=s.length()-1;i<=j;i++,j--)
        {
                if(s.charAt(i)!=s.charAt(j)) return false;
        }
        return true;
     }
     static String rev(String s)
     {
                StringBuilder sb=new StringBuilder(s);
                sb.reverse();
                return sb.toString();
     }
     static int gcd(int a,int b){return (a==0)?b:gcd(b%a,a);}
     static long gcdExtended(long a,long b,long[] x)
     {
 
        if(a==0){
            x[0]=0;
            x[1]=1;
            return b;
        }
        long[] y=new long[2];
        long gcd=gcdExtended(b%a, a, y);
 
        x[0]=y[1]-(b/a)*y[0];
        x[1]=y[0];
 
        return gcd;
    }
 
     boolean findSum(int set[], int n, long sum)
    {
      if (sum == 0)
         return true;
      if (n == 0 && sum != 0)
         return false;
      if (set[n-1] > sum)
         return findSum(set, n-1, sum);
      return findSum(set, n-1, sum) ||findSum(set, n-1, sum-set[n-1]);
    }
   
      public static long modPow(long base, long exp, long mod)
     {
        base = base % mod;
        long result = 1;
        while (exp > 0)
       {
            if (exp % 2 == 1) 
            {
                result = (result * base) % mod;
            }
            base = (base * base) % mod;
            exp = exp >> 1;
       }
        return result;
    }
 
    static long[] fac;
    static long[] inv;
    static long mod=(long)1e9+7;
    public static void cal() 
    {
        fac = new long[1000005];
        inv = new long[1000005];
        fac[0] = 1;
        inv[0] = 1;
        for (int i = 1; i <= 1000000; i++)
        {
            fac[i] = (fac[i - 1] * i) % mod;
            inv[i] = (inv[i - 1] * modPow(i, mod - 2, mod)) % mod;
        }
    }
 
    public static long ncr(int n, int r) 
    {
        return (((fac[n] * inv[r]) % mod) * inv[n - r]) % mod;
    }
 
 
////////////////////////////////////////// Input Reader ////////////////////////////////////////////////////////////////////////////////////////////////////
     
    static InputReader sc = new InputReader(System.in);
    static PrintWriter out= new PrintWriter(System.out);   
    
    static class InputReader {
 
          private final InputStream stream;
          private final byte[] buf = new byte[8192];
          private int curChar, snumChars;
          private SpaceCharFilter filter;
 
          public InputReader(InputStream stream) {
                  this.stream = stream;
          }
 
          public int snext()
         {
                  if (snumChars == -1)
                          throw new InputMismatchException();
                  if (curChar >= snumChars) {
                          curChar = 0;
                          try {
                                  snumChars = stream.read(buf);
                          } catch (IOException e) {
                                  throw new InputMismatchException();
                          }
                          if (snumChars <= 0)
                                  return -1;
                  }
                  return buf[curChar++];
          }
 
          public int nextInt()
         {
                  int c = snext();
                  while (isSpaceChar(c)) 
                  {
                          c = snext();
                  }
                  int sgn = 1;
                  if (c == '-')
                  {
                          sgn = -1;
                          c = snext();
                  }
                  int res = 0;
                  do {
                          if (c < '0' || c > '9')
                                  throw new InputMismatchException();
                          res *= 10;
                          res += c - '0';
                          c = snext();
                  } while (!isSpaceChar(c));
                  return res * sgn;
          }
 
          public long nextLong() 
          {
                  int c = snext();
                  while (isSpaceChar(c)) 
                  {
                          c = snext();
                  }
                  int sgn = 1;
                  if (c == '-') 
                  {
                          sgn = -1;
                          c = snext();
                  }
                  long res = 0;
                  do {
                          if (c < '0' || c > '9')
                                  throw new InputMismatchException();
                          res *= 10;
                          res += c - '0';
                          c = snext();
                  } while (!isSpaceChar(c));
                  return res * sgn;
          }
 
          public int[] nextIntArray(int n)
          {
                  int a[] = new int[n];
                  for (int i = 0; i < n; i++) 
                  {
                          a[i] = nextInt();
                  }
                  return a;
          }
 
          public long[] nextLongArray(int n)
          {
                  long a[] = new long[n];
                  for (int i = 0; i < n; i++) 
                  {
                          a[i] = nextLong();
                  }
                  return a;
          }
 
          
          public String nextLine()
         {
                  int c = snext();
                  while (isSpaceChar(c))
                          c = snext();
                  StringBuilder res = new StringBuilder();
                  do {
                          res.appendCodePoint(c);
                          c = snext();
                  } while (!isEndOfLine(c));
                  return res.toString();
          }
 
          public boolean isSpaceChar(int c) 
          {
                  if (filter != null)
                          return filter.isSpaceChar(c);
                  return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
          }
 
          private boolean isEndOfLine(int c) 
          {
                  return c == '\n' || c == '\r' || c == -1;
          }
 
          public interface SpaceCharFilter 
          {
                  public boolean isSpaceChar(int ch);
          }
 
    }
 
    static int i()
    {
        return sc.nextInt();
    }
    static long l(){
        return sc.nextLong();
    }
    static int[] iarr(int n)
    {
        return sc.nextIntArray(n);
    }
    static long[] larr(int n)
    {
        return sc.nextLongArray(n);
    }
    static String s(){
        return sc.nextLine();
    }
  
 
 }