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.
//  package cp;
import java.io.*;
import java.math.*;
import java.util.*;

public class Cf_one {

	public static void main(String[] args) throws IOException {	
		PrintWriter out = new PrintWriter(System.out);
		Readers.init(System.in);
		int t=Readers.nextInt();
		for (int i = 0; i < t; i++) {
			long a=Readers.nextLong();
			long b=Readers.nextLong();
			long n=Readers.nextLong();
			long maxx=Math.max(a, b);
			long minn=Math.min(a, b);
			long summ=0;
			if(maxx>n)System.out.println(0);
			else {
				ArrayList<Long> arr=new ArrayList<>();
				arr.add(minn);
				arr.add(maxx);
				long cnt=0;
				while(summ<=n) {
					summ=arr.get(arr.size()-1)+arr.get(arr.size()-2);
					arr.add(summ);
					cnt++;
				}
				System.out.println(cnt);
			}
		}
		out.flush();
	}
	
}
class Readers {
 
    static BufferedReader reader;
 
    static StringTokenizer tokenizer;
 
 
 
    /** call this method to initialize reader for InputStream */
 
    static void init(InputStream input) {
 
        reader = new BufferedReader(
 
                     new InputStreamReader(input) );
 
        tokenizer = new StringTokenizer("");
 
    }
 
 
 
    /** get next word */
 
    static String next() throws IOException {
 
        while ( ! tokenizer.hasMoreTokens() ) {
 
            //TODO add check for eof if necessary
 
            tokenizer = new StringTokenizer(
 
                   reader.readLine() );
 
        }
 
        return tokenizer.nextToken();
 
    }
 
 
 
    static int nextInt() throws IOException {
 
        return Integer.parseInt( next() );
 
    }
 
	
 
    static double nextDouble() throws IOException {
 
        return Double.parseDouble( next() );
 
    }
    
    
    static long nextLong() throws IOException{
    	
		return Long.parseLong(next());
	}
 
}