Leo has developed a new programming language C+=. In C+=, integer variables can only be changed with a "+=" operation that adds the right-hand side value to the left-hand side variable. For example, performing "a += b" when a = 2, b = 3 changes the value of a to 5 (the value of b does not change).

In a prototype program Leo has two integer variables a and b, initialized with some positive values. He can perform any number of operations "a += b" or "b += a". Leo wants to test handling large integers, so he wants to make the value of either a or b strictly greater than a given value n. What is the smallest number of operations he has to perform?

Input

The first line contains a single integer T (1 ≤ T ≤ 100) — the number of test cases.

Each of the following T lines describes a single test case, and contains three integers a, b, n (1 ≤ a, b ≤ n ≤ 10^9) — initial values of a and b, and the value one of the variables has to exceed, respectively.

Output

For each test case print a single integer — the smallest number of operations needed. Separate answers with line breaks.

Example

Input


2
1 2 3
5 4 100


Output


2
7

Note

In the first case we cannot make a variable exceed 3 in one operation. One way of achieving this in two operations is to perform "b += a" twice.
#include <bits/stdc++.h>
using namespace std;
long long int max(long long int a, long long int b) {
  if (a >= b)
    return a;
  else
    return b;
}
long long int min(long long int a, long long int b) {
  if (a >= b)
    return b;
  else
    return a;
}
int main() {
  int t;
  scanf("%d", &t);
  for (int i = 0; i < t; i++) {
    long long int a, b, n, c, d;
    scanf("%lld %lld %lld", &a, &b, &n);
    int cnt = 0;
    c = min(a, b), d = max(a, b);
    while (c <= n && d <= n) {
      if (cnt % 2 == 1) {
        d += c;
        cnt++;
      } else {
        c += d;
        cnt++;
      }
    }
    printf("%d\n", cnt);
  }
}
