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.
/* package codechef; // don't place package name! */

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

/* Name of the class has to be "Main" only if the class is public. */
public class Codechef
{
	public static void main (String[] args) throws java.lang.Exception
	{
		Scanner sc = new Scanner(System.in);
		PrintWriter out = new PrintWriter(System.out);
		int T = sc.nextInt();
		for(int t = 0; t<T; t++){
		    long a = sc.nextLong();
		    long b = sc.nextLong();
		    long n = sc.nextLong();
		    long temp = a;
		    a = Math.min(a, b);
		    b = Math.max(temp, b);
		    int k = 0;
		    int count = 0;
		    while(a <= n && b <= n){
		        if(k % 2 == 0){
		            a += b;
		        }
		        else b += a;
		        k++;
		        count++;
		    }
		    out.println(count);
		}
		out.flush();
	}
}
