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.InputStreamReader;
import java.io.BufferedReader;
import java.io.IOException;
public final class NewLanguage
{
    public static void main(String[] args)throws IOException{
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        int T = Integer.parseInt(br.readLine().trim());
        while(T-- >0){
             String s1[] = br.readLine().trim().split(" ");
             int a = Integer.parseInt(s1[0]);
             int b = Integer.parseInt(s1[1]);
             int n = Integer.parseInt(s1[2]);
             int count=0,sum=0;
             if(a<b)
             {
                  int temp = b;
                  b = a;
                  a = temp;
             }//making a greater
             while(b<=n && a<=n){
                  if(a>=b)
                    b+=a;
                  else
                    a+=b;
                  count++;
             }
             System.out.println(count);
        }
    }
}