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.

import java.util.*;
import java.lang.*;
import java.io.*;

public class Cplus {
	public static void main(String[] args) throws Exception {

		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		int t = Integer.parseInt(br.readLine());
		while (t-- > 0) {
			String[] str = (br.readLine()).trim().split(" ");
			int a = Integer.parseInt(str[0]);
			int b = Integer.parseInt(str[1]);
			int n = Integer.parseInt(str[2]);
			System.out.println(oper(Math.max(a, b), Math.min(a, b), n));
		}
		return;
	}

	// a max
	static int oper(int a, int b, int n) {
		if (a + b > n) {
			return 1;
		}
		b = b + a;
		return oper(b, a, n) + 1;

	}
}
