#include <bits/stdc++.h>
using namespace std;
vector<vector<int> > a(10);
void solve(int l, int r, int k) {
  int b = 0, c = a[k].size() - 1, ans = -1;
  while (b <= c) {
    int m = (b + c) / 2;
    if (a[k][m] >= l) {
      ans = m;
      c = m - 1;
    } else
      b = m + 1;
  }
  if (ans == -1) {
    printf("0\n");
    return;
  }
  int ans1 = -1;
  b = ans;
  c = a[k].size() - 1;
  while (b <= c) {
    int m = (b + c) / 2;
    if (a[k][m] <= r) {
      ans1 = m;
      b = m + 1;
    } else
      c = m - 1;
  }
  if (ans1 == -1) {
    printf("0\n");
    return;
  }
  printf("%d\n", ans1 - ans + 1);
}
int first(int n) {
  int x = 1;
  while (n > 0) {
    if (n % 10 != 0) x *= n % 10;
    n /= 10;
  }
  return x;
}
int g(int n) {
  if (n < 10)
    return n;
  else
    return g(first(n));
}
int main() {
  for (int i = 1; i <= 1000000; i++) {
    a[g(i)].push_back(i);
  }
  int q;
  scanf("%d", &q);
  for (int i = 0; i < q; i++) {
    int l, r, k;
    scanf("%d%d%d", &l, &r, &k);
    solve(l, r, k);
  }
  return 0;
}

### Prompt

Your challenge is to write a cpp solution to the following problem:

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

<image>

<image>

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

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
vector<vector<int> > a(10);
void solve(int l, int r, int k) {
  int b = 0, c = a[k].size() - 1, ans = -1;
  while (b <= c) {
    int m = (b + c) / 2;
    if (a[k][m] >= l) {
      ans = m;
      c = m - 1;
    } else
      b = m + 1;
  }
  if (ans == -1) {
    printf("0\n");
    return;
  }
  int ans1 = -1;
  b = ans;
  c = a[k].size() - 1;
  while (b <= c) {
    int m = (b + c) / 2;
    if (a[k][m] <= r) {
      ans1 = m;
      b = m + 1;
    } else
      c = m - 1;
  }
  if (ans1 == -1) {
    printf("0\n");
    return;
  }
  printf("%d\n", ans1 - ans + 1);
}
int first(int n) {
  int x = 1;
  while (n > 0) {
    if (n % 10 != 0) x *= n % 10;
    n /= 10;
  }
  return x;
}
int g(int n) {
  if (n < 10)
    return n;
  else
    return g(first(n));
}
int main() {
  for (int i = 1; i <= 1000000; i++) {
    a[g(i)].push_back(i);
  }
  int q;
  scanf("%d", &q);
  for (int i = 0; i < q; i++) {
    int l, r, k;
    scanf("%d%d%d", &l, &r, &k);
    solve(l, r, k);
  }
  return 0;
}

```