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:
//package CFRound.Round463;
import java.util.*;
import java.io.*;
public class B {
        String INPUT = "4\n" +
                "82 94 6\n" +
                "56 67 4\n" +
                "28 59 9\n" +
                "39 74 4";
        int N = (int)1e6+2;
        int[] a = new int[N];
        int[][] dp = new int[N][10];
        void solve()
        {
                preprocess();
                //out.print(a[4]);
                for (int i = 0; i < 10; i++) {
                        for (int j = 1; j < N; j++) {
                                if(a[j]==i){
                                        dp[j][i] = dp[j-1][i]+1;
                                }
                                else{
                                        dp[j][i] = dp[j-1][i];
                                }
                        }
                }
                //out.print(dp[20][4]);
                int q = i();
                while(q-->0){
                        final int l = i(), r = i(), k = i();
                        out.println(dp[r][k]-dp[l-1][k]);
                }

        }
        void preprocess(){
                for (int i = 0; i <N ; i++) {
                        if(i<10){
                                a[i] = i;
                        }
                        else{
                                a[i] = calculate(i);
                        }
                }
        }
        int calculate(int i){
                if(i<10){
                        return i;
                }
                int ans = calculate(val(String.valueOf(i)));
                return ans;
        }
        int val(String x){
                int ans = 1;
                for (int i = 0; i < x.length(); i++) {
                        if(x.charAt(i)=='0') continue;
                        ans = ans*(x.charAt(i)-'0');
                }
                return ans;
        }
        void run() throws Exception{
                is = oj ? System.in: new ByteArrayInputStream(INPUT.getBytes());
                //is = System.in;
                out = new PrintWriter(System.out);
                long s = System.currentTimeMillis();
                solve();
                out.flush();
                tr(System.currentTimeMillis()-s+"ms");
        }
        public static void main(String[] args)throws Exception {
                new B().run();
        }
        InputStream is;
        PrintWriter out;
        private byte[] inbuf = new byte[1024];
        public int lenbuf = 0, ptrbuf = 0;

        private int readByte()
        {
                if(lenbuf == -1)throw new InputMismatchException();
                if(ptrbuf >= lenbuf){
                        ptrbuf = 0;
                        try { lenbuf = is.read(inbuf); } catch (IOException e) { throw new InputMismatchException(); }
                        if(lenbuf <= 0)return -1;
                }
                return inbuf[ptrbuf++];
        }

        private boolean isSpaceChar(int c) { return !(c >= 33 && c <= 126); }
        private int skip() { int b; while((b = readByte()) != -1 && isSpaceChar(b)); return b; }

        private double d() { return Double.parseDouble(s()); }
        private char c() { return (char)skip(); }

        private String s()
        {
                int b = skip();
                StringBuilder sb = new StringBuilder();
                while(!(isSpaceChar(b))){ // when nextLine, (isSpaceChar(b) && b != ' ')
                        sb.appendCodePoint(b);
                        b = readByte();
                }
                return sb.toString();
        }

        private char[] sa(int n)
        {
                char[] buf = new char[n];
                int b = skip(), p = 0;
                while(p < n && !(isSpaceChar(b))){
                        buf[p++] = (char)b;
                        b = readByte();
                }
                return n == p ? buf : Arrays.copyOf(buf, p);
        }

        private char[][] nm(int n, int m)
        {
                char[][] map = new char[n][];
                for(int i = 0;i < n;i++)map[i] = sa(m);
                return map;
        }

        private int[] ia(int n)
        {
                int[] a = new int[n];
                for(int i = 0;i < n;i++)a[i] = i();
                return a;
        }

        private int i()
        {
                int num = 0, b;
                boolean minus = false;
                while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
                if(b == '-'){
                        minus = true;
                        b = readByte();
                }

                while(true){
                        if(b >= '0' && b <= '9'){
                                num = num * 10 + (b - '0');
                        }else{
                                return minus ? -num : num;
                        }
                        b = readByte();
                }
        }

        private long l()
        {
                long num = 0;
                int b;
                boolean minus = false;
                while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
                if(b == '-'){
                        minus = true;
                        b = readByte();
                }

                while(true){
                        if(b >= '0' && b <= '9'){
                                num = num * 10 + (b - '0');
                        }else{
                                return minus ? -num : num;
                        }
                        b = readByte();
                }
        }

        private boolean oj = System.getProperty("ONLINE_JUDGE") != null;
        private void tr(Object... o) { if(!oj)System.out.println(Arrays.deepToString(o)); }

}