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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.math.BigInteger;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.Scanner;
import java.util.StringTokenizer;


@SuppressWarnings("unused")
public class A {
	public  static  FastScannerA scan = new FastScannerA();
	public static PrintWriter out = new PrintWriter(System.out);
	
	public static void solve () {
		int t=scan.nextInt();
		for(int i=0;i<t;i++) {
			long a=scan.nextLong();
			long b=scan.nextLong();
			long n=scan.nextLong();
			int cnt=0;
			while(Math.max(a, b)<=n) {
				if(a<b)a+=b;
				else b+=a;
				cnt++;
			}
			System.out.println(cnt);
		}
	}
	public static void main(String[] args) {
	
		solve();
		out.close();
	}

}
class FastScannerA {
	BufferedReader br= new BufferedReader(new InputStreamReader(System.in));
	StringTokenizer st= new StringTokenizer("");
	String next() {
		while (!st.hasMoreTokens())
			try {
				st=new StringTokenizer(br.readLine());
			} catch (IOException e) {
				e.printStackTrace();
			}
		return st.nextToken();
	}
	int nextInt() {
		return Integer.parseInt(next());
	}
	int[] readArray(int n) {
		int[] a=new int[n];
		for (int i=0; i<n; i++) a[i]=nextInt();
		return a;
	}
	long nextLong() {
		return Long.parseLong(next());
	}
	
}


