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 IOException {
        // write your code here
        Scanner in = new Scanner(System.in);
        BufferedReader bu=new BufferedReader(new InputStreamReader(System.in));
        StringBuilder sb=new StringBuilder();
        int t=Integer.parseInt(bu.readLine());
        int []ansarr=new int[t];
        for(int q=0;q<t;q++)
        {
            String []s=bu.readLine().split(" ");
            int a=Integer.parseInt(s[0]);
            int b=Integer.parseInt(s[1]);
            int n=Integer.parseInt(s[2]);
            int count=0;
            while(a<=n & b<=n)
            {
                if(a<b)
                {
                    a=a+b;
                    count++;
                }
                else
                {
                    b=b+a;
                    count++;
                }
            }
            ansarr[q]=count;

        }
        for(int q=0;q<t;q++)
        {
            System.out.println(ansarr[q]);
        }



    }
    public static int hcf(int a,int b)
    {
        int ans=1;
        for(int i=1;i<=Math.min(a,b);i++)
        {
            if(a%i==0 & b%i==0)
            {
                ans=i;
            }
        }
        return ans;
    }
    public static int gcd(int a,int b)
    {
        if(b==0)
        {
            return a;
        }
        else
        {
            return gcd(b,a%b);
        }
    }
}

