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.*;

public class CodeForces {

    
  
    public static void main(String[] args) {
        Scanner in=new Scanner(System.in);
        int c,k=0,t;
        int[] a,b,n;
        t=in.nextInt();
        a=new int [t];
        b=new int[t];
        n=new int[t];
        for(int i=0;i<t;i++)
        {
            a[i]=in.nextInt();
            b[i]=in.nextInt();
            n[i]=in.nextInt();
        }
        for(int i=0;i<t;i++)
        {
            
            if(a[i]>b[i])
            {
                int temp=a[i];
                a[i]=b[i];
                b[i]=temp;
            }
            while(a[i]+b[i]<=n[i])
            {
                a[i]+=b[i];
                k++;
                c=a[i]+b[i];
                if(c<=n[i])
                {
                    b[i]+=a[i];
                    k++;
                }
            }
                System.out.println(++k);
                k=0;
        }
        
        
    }
    
}
