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.
"use strict";

let count = 0;

let resFunc = function (a, b, n) {
  let temp;
  if (b < a) {
    temp = b;
    b = a;
    a = temp;
  }

  a += b;
  if (b <= n) {
    count++;
    return resFunc(a, b, n);
  } else {
    return count;
  }
};

let t = parseInt(readline());

let i, arr;

for (i = 0; i < t; i++) {
  arr = readline().split(" ");

  arr[0] = Number(arr[0]);
  arr[1] = Number(arr[1]);
  arr[2] = Number(arr[2]);

  print(resFunc(arr[0], arr[1], arr[2]));
  count = 0;
}
