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.
//https://codeforces.com/contest/1368/problem/0
//A. C+=
import java.util.*;
import java.io.*;
public class C{
	public static void main(String[] args) throws Exception{
		
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		PrintWriter pw = new PrintWriter(new OutputStreamWriter(System.out));
		StringBuilder sb = new StringBuilder();

 		int t = Integer.parseInt(br.readLine().trim());

 		while(t-->0){

 			StringTokenizer st = new StringTokenizer(br.readLine().trim());
 			int min = Integer.parseInt(st.nextToken());
 			int max = Integer.parseInt(st.nextToken());
 			int n = Integer.parseInt(st.nextToken());
 			if(min>max){
 				int temp = max;
 				max = min;
 				min = temp;
 			}
 			int count = 0;
 			while(max<=n){
 				min = min+max;
 				count++;
 				if(min>max){
	 				int temp = max;
	 				max = min;
	 				min = temp;
 				}
 			}
 			sb.append(count).append("\n");
 		}

		pw.print(sb);
		pw.flush();
		pw.close();
	}
}