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.*;
import java.io.*;
public class Main
{
    public static void main(String args[])throws Exception
    {
        BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
        PrintWriter pw=new PrintWriter(System.out);
        int t=Integer.parseInt(br.readLine());
        for(int x=0;x<t;x++)
        {
            String str[]=br.readLine().split(" ");
            int a=Integer.parseInt(str[0]);
            int b=Integer.parseInt(str[1]);
            int n=Integer.parseInt(str[2]);
            int c=Math.min(a,b);
            int d=Math.max(a,b);
            int cntr=0;
            while(c<=n&&d<=n)
            {
                if(c<=n&&d<=n)
                {
                    c+=d;
                    cntr++;
                }
                if(c<=n&&d<=n)
                {
                    d+=c;
                    cntr++;
                }
            }
            pw.println(cntr);
        }
        pw.flush();
        pw.close();
    }
}