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.String;
import java.lang.Math;
import java.util.Arrays;

public class Capitalization2
{
 
   
  
    public static void main(String[] args)
    {
        Scanner sc=new Scanner(System.in);
       int t;
    t=sc.nextInt();
    for(int i=0;i<t;i++)
    {
        int a,b,n;
        a=sc.nextInt();
        b=sc.nextInt();
        n=sc.nextInt();
        int res=0;
        while(a<=n&&b<=n)
        {
            if(a<=b)
            a=a+b;
            else
            b=b+a;
            
            res++;
            
        }
        System.out.println(res);
    }
    
           
       }
           
        }


        
       
        
   
    
       
        
        
    
      
       
    
       
    
        
       
    
 
    


