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 Main{
	
// 	public static void main(String[] args) {
// 		Scanner sc = new Scanner(System.in);
// 		int n=sc.nextInt();
// 		// if(n==1){
// 		// 	ans="codeforces";
// 		// }
// 		int i=0;
// 		for( i=0;;i++){
// 			if(i*(i-1)/2+1>=n){
// 				break;
// 			}
// 		}
// 		String s="codeforces";
// 		String x="";
// 		if(i>0)
// 			x=s.substring(10-i+1,10);

// 		String ans=s+x;
// 		System.out.println(ans);
// 	}
// }



import java.util.*;

public class Main{
	public static void fun(int i,int j,int[][]arr){

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

		while(t-->0){
			int ans=0;
			long a=sc.nextInt();
			long b=sc.nextInt();
			long n=sc.nextInt();
			if(n<a || n<b){
				ans=0;
			}
			else{
				ans=0;
				long res=0;
				while(res<=n){
					res=a+b;
					if(a<b){
						a=res;
					}else{
						b=res;
					}
					ans++;
				}
			}
			System.out.println(ans);
		}
	}
}

