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.Scanner;

public class trial_01 {
    public static void main(String[] args) {
        //System.out.println("Hello W");
        Scanner in = new Scanner(System.in);
        int iteration = in.nextInt();

        for(int it=0; it<iteration; it++) {
            int a = in.nextInt(), b = in.nextInt(), n = in.nextInt();
            //System.out.println("a: " + a + " b: " + b + " n: " + n);

            // so that a remains greater
            if(b<a) {
                int tmp = b;
                b = a;
                a = tmp;
            }

            int i=0;
            while(a<=n && b<=n) {
                a += b;
                i++;
                //System.out.println("a: " + a + " i: " + i);

                if (a<=n && b<=n) {
                    b += a;
                    i++;
                    //System.out.println("b: " + b + " i: " + i);
                }
            }
            System.out.println(i + "\n");
        }
    }
}
