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 whatever //do not write package name here */

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

public class GFG {
	public static void main (String[] args) {
	Scanner scn = new Scanner(System.in);
	
	int t = scn.nextInt();
	for(int p=0;p<t;p++){
	    
	   int a=scn.nextInt();
	   int b = scn.nextInt();
	   int n = scn.nextInt();
	       
	       int cnt=0;
	        while(n>=a && n>=b){
	            if(a>b)
	                b+=a;
	           else 
	                a+=b;
	                
	            //System.out.println(a+" "+b);
	            cnt++;
	        }
	    System.out.println(cnt);
	    
	    }
	}
}