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 com.company;
import java.util.*;


import java.util.Scanner;

public class Main {
    public static void main(String[] args){
        int t =scanner.nextInt();
        for(int i1 = 0 ;i1<t;i1++){
            int a = scanner.nextInt();
            int b = scanner.nextInt();
            int n = scanner.nextInt();
            int ans =  0;
            int  x = Math.max(a,b);
            int y = Math.min(a,b);
            while (true){
                y+=x;
                ans++;
                if(y>n){
                    break;
                }
                x+=y;
                ans++;
                if(x>n){
                    break;
                }
            }
            System.out.println(ans);
        }
    }
    private static Scanner scanner = new Scanner(System.in);
    private static int max(int[] array ){
        int min = Integer.MIN_VALUE;
        for(int i = 0;i< array.length;i++){
            if(array[i]>min){
                min = array[i];
            }
        }
        return min;
    }
    private static int min(int[] array ){
        int min = Integer.MAX_VALUE;
        for(int i = 0;i< array.length;i++){
            if(array[i]<min){
                min = array[i];
            }
        }
        return min;
    }
    private static void readArray(int[] array){
        for(int i = 0;i< array.length;i++){
            array[i] = scanner.nextInt();
        }
    }
    private static void printarray(int[] array){
        for(int i = 0; i< array.length;i++){
            System.out.print(array[i]);
        }
    }
    private static int gcd(int a , int b){
        int k = 0;
        for(int i  =1 ;i<Math.max(a,b);i++){
            if(a%i==0 && b%i==0){
                k = i;
            }
        }
        return k;
    }
    private static int fact(int n){
        if(n==1){
            return 1;
        }
        else {
            return n*fact(n-1);
        }
    }
}