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
	{
	    
// -----------------------------Fast IO using BufferedReader--------------------------------------------	    
//         BufferedReader br = new BufferedReader(new InputStreamReader(System.in));  
//         StringTokenizer st = new StringTokenizer(br.readLine());
//          PrintWriter out = new PrintWriter(System.out); 
//         int T = Integer.parseInt(st.nextToken()); 
        
// ----------------------------------------------------------------------------------------------------------	    
    Scanner sc=new Scanner(System.in); 
    int T=sc.nextInt();
		while(T-- >0)
		{
		    
          int a=sc.nextInt();int b=sc.nextInt();int N=sc.nextInt();
          int c=0;
          while(true)
          {
              if(a>N || b>N)
              break;
              
              if(a>b)
              b+=a;
              else
              a+=b;
              c++;
          }
          System.out.println(c);
		      
		}
// 		out.close();   
	}
}