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.io.*;
import java.util.*;
 
public class Main
{
	static Scanner scan = new Scanner(System.in);
	public static void solve() throws Exception
	{
		//BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
		//StringTokenizer tk = new StringTokenizer(in.readLine());
		long a = scan.nextLong();
		long b = scan.nextLong();
		long n = scan.nextLong();
		long c=0;
		while(true)
		{
			if(a>n || b>n)
			{
				break;
			}
			c+=1;
			if(a<b)
			{
				a+=b;
			}
			else
				b+=a;
		}
		System.out.println(c);
	}
	public static void main(String[] args) throws Exception
	{
		if(scan.hasNext())
		{
			int t= scan.nextInt();
			//int t= 1;
			outer:while(t-->0)
			{	
				solve();
			}
		}
	}
}