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.Scanner;

public class NewProg {
    
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int x = sc.nextInt();

        for(int i=0; i<x; i++) {
            int a = sc.nextInt();
            int b = sc.nextInt();
            int n = sc.nextInt();

            System.out.println(solve(a, b, n));
        }
 
        sc.close();
    }

    public static int solve(int a, int b, int n) {

        int operations = 0;

        if(a > n || b > n) return operations;

        while(true) {
            if(a > b) {
                b += a;
                operations += 1;
            } else {
                a += b;
                operations += 1;
            }

            if(a > n || b > n) {
                break;
            }
        }

        return operations;
    }
}
