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 LongestCommonSubsequence {
	static Scanner sc = new Scanner(System.in);
	
		
	
	

	public static void main(String[] args) {
		int t = sc.nextInt();

		while (t > 0) {

			int a = sc.nextInt();
			int b = sc.nextInt();

			int n= sc.nextInt();
			int i=0;
			int k=Math.min(a, b);
			if(a>n||b>n) {
				System.out.println(i);
				t--;
				continue;
			}
			k+=Math.max(a,b);
			if(a<b) {
				a=k;
				i++;
				while(a<=n&&b<=n) {
					 
				if(i%2!=0) {
					b+=a;
					//a=k;
				}
				else {
					a+=b;
					
				}
			//	System.out.println(a+" "+b);
				i++;
				}	
				
				System.out.println(i);
				t--;
				continue;
			}
			else {
				b=k;
				i++;
				while(a<=n&&b<=n) {
					 
					if(i%2!=0) {
						a+=b;
						
					}
					else {
						b+=a;
						
					}
				//	System.out.println(a+" "+b);
					i++;
					}	
				System.out.println(i);
				t--;
				continue;
			}
			
		
			
			//String y = sc.next();
			
			
			//t--;
		}
	}
}
