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
{
    static int fun(int a,int b,int n,int ct){
        if(b>n || a>n){
            return ct;
        }
        else if(a<=b){
            a+=b;
            ct++;
            return fun(a,b,n,ct);
        }
        else{
            b+=a;
            ct++;
            return fun(a,b,n,ct);
        }
    }
	public static void main (String[] args) throws java.lang.Exception
	{
		BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
		int t=Integer.parseInt(br.readLine());
		while(t-- >0){
		    String ss[]=br.readLine().split(" ");
		    int a=Integer.parseInt(ss[0]);
		    int b=Integer.parseInt(ss[1]);
		    int n=Integer.parseInt(ss[2]);
		    //int a[]=new int[n];
		    //String s=br.readLine();
		    int ct=0,x=0;
		    if(a<=b){
		        x=fun(a,b,n,ct);
		    }
		    else{
		        x=fun(b,a,n,ct);
		    }
		   // while()
		    
		    
		    System.out.println(x);
		}
	}
}
