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.*;



public class geek {

    public static int gcd(int a, int b) {
        if (b == 0) {
            return a;
        }
        return gcd(b, a % b);
    }

    public static void main(String[] args) {
        Scanner s = new Scanner(System.in);
        int t=s.nextInt();
        while(t-->0){
            int a=s.nextInt() ;
            int b=s.nextInt();
            int n=s.nextInt();
            int ans=0;
            if(a>b){
                b=a+b;
                ans++;
                if(b<=n) {
                    while (b <= n) {
                        int tp =b;
                                b = b + a;
                                a=tp;
                        ans++;
                    }
                }
            }else{
                a=a+b;
                ans++;
                if(a<=n) {
                    while (a <= n) {
                        int tp=a;
                        a = a + b;
                        b=tp;
                        ans++;
                    }
                }
            }
            System.out.println(ans);

        }

    }
}


























