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


 
 
// Warning: Printing unwanted or ill-formatted data to output will cause the test cases to fail
 
public class TestClass {
    public static void main(String args[] ) throws Exception {
        /* Sample code to perform I/O:
         * Use either of these methods for input
 
        //BufferedReader
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        String name = br.readLine();                // Reading input from STDIN
        System.out.println("Hi, " + name + ".");    // Writing output to STDOUT
 
        //Scanner
        Scanner s = new Scanner(System.in);
        String name = s.nextLine();                 // Reading input from STDIN
        System.out.println("Hi, " + name + ".");    // Writing output to STDOUT
 
        */
 
        // Write your code here
        PrintWriter pw=new PrintWriter(System.out);
        Scanner scn=new Scanner(System.in);
        int q = scn.nextInt();
        while(q-->0){
            int a = scn.nextInt();
            int b = scn.nextInt();
            int n = scn.nextInt();
            int mn=Math.min(a,b);
            int mx=Math.max(a,b);
            int res=0;
            boolean f = true;
            while(mn+mx<=n){
                res++;
                if(f)
                    mn+=mx;
                else
                    mx+=mn;
                f=!f;
            }
            pw.println(res+1);
        }
        pw.close();
        
        
        
        
        
        
        
        
        
        
        
        
        
        
        
        
        
        
        
        
        
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
    }
   
    
}