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;

/**
 * 
 */

/**
 * @author rajee
 *
 */
public class CodeForces1 {

    /**
    * 
    * Function name - main
    * Description   - 
    * @param     - 
    * @return        - void
    */
    public static void main(String[] args) { 
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
       
        final int cases;
        try {
            cases = Integer.parseInt(br.readLine().trim());      
            
            for (int t = 1; t <= cases; t++) {
                String ABN[] =  br.readLine().trim().split(" ");
                int a =Integer.parseInt(ABN[0]);
                int b = Integer.parseInt(ABN[1]);
                int n = Integer.parseInt(ABN[2]);
                int ops = 0;
                if(a > b) {
                    int temp = a;
                    a = b;
                    b = temp;
                }
                while(a <= n && b <= n ) {
                    if(ops % 2 == 0) {
                        a = a + b;
                    }else {
                        b = b + a;
                    }
                    ops++;
                }
                System.out.println(ops);
                
            }
            
           
           

        } catch (IOException e) {
            
            e.printStackTrace();
        }
       
       
    }

}
