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.util.*;

public class Atcoder {
    public static int dirs[][] = {{-1,0},{1,0},{0,1},{0,-1}};
    public static void main(String [] args) throws IOException {

        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        
        int test = Integer.parseInt(br.readLine());
       
        while(test-->0) {
            
            String temp[] = br.readLine().split(" ");
            int a = Integer.parseInt(temp[0]);
            int b = Integer.parseInt(temp[1]);
            int n = Integer.parseInt(temp[2]);
            int c = a;
            a = Math.min(a,b);
            b = Math.max(c,b);
            int count = 0;
            while(a+b<=n) {
                 c = a+b;
                a = b;
                b = c;
                count++;
            }

            System.out.println(count+1);

           
        }
    }

}