#include <bits/stdc++.h>
using namespace std;
long long int power1(long long int a, long long int b) {
  if (b <= 0) return 1;
  if (b == 1) return a;
  long long int c = power1(a, b / 2);
  c *= c;
  if (b % 2 == 1) c *= a;
  return c;
}
long long int mi(long long int a, long long int m) {
  long long int c = power1(a, m - 2);
  return c;
}
struct less_then_greater {
  template <typename T, typename U>
  bool operator()(T const& lhs, U const& rhs) const {
    if (lhs.first < rhs.first) return true;
    if (rhs.first < lhs.first) return false;
    return lhs.second > rhs.second;
  }
};
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  ;
  long long int t;
  cin >> t;
  while (t--) {
    long long int a, b, n;
    cin >> a >> b >> n;
    long long int ans = 0;
    while (max(a, b) <= n) {
      if (a > b) swap(a, b);
      a += b;
      ans++;
    }
    cout << ans << endl;
  }
  return 0;
}

### Prompt

Create a solution in CPP for the following problem:

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.

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
long long int power1(long long int a, long long int b) {
  if (b <= 0) return 1;
  if (b == 1) return a;
  long long int c = power1(a, b / 2);
  c *= c;
  if (b % 2 == 1) c *= a;
  return c;
}
long long int mi(long long int a, long long int m) {
  long long int c = power1(a, m - 2);
  return c;
}
struct less_then_greater {
  template <typename T, typename U>
  bool operator()(T const& lhs, U const& rhs) const {
    if (lhs.first < rhs.first) return true;
    if (rhs.first < lhs.first) return false;
    return lhs.second > rhs.second;
  }
};
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  ;
  long long int t;
  cin >> t;
  while (t--) {
    long long int a, b, n;
    cin >> a >> b >> n;
    long long int ans = 0;
    while (max(a, b) <= n) {
      if (a > b) swap(a, b);
      a += b;
      ans++;
    }
    cout << ans << endl;
  }
  return 0;
}

```