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.
//Codeforces 1368A 
import java.util.Scanner;

public class CF1368A {
    static final Scanner SC = new Scanner(System.in);
    public static void main(String[] args) {
        int tests = SC.nextInt();
        for (int t = 0; t < tests; ++t) {
            int num1 = SC.nextInt();
            int num2 = SC.nextInt();
            int target = SC.nextInt(); // Exceed this number
            int operations = computeOperationsNeeded(num1, num2, target);
            System.out.println(operations);
        }
    }

    // Computes and returns minimum number of operations required
    static int computeOperationsNeeded(int num1, int num2, int target) {
        int prev = Math.max(num1, num2); // Largest previously
        int operations = 1;
        int curr = num1 + num2; // Current largest
        while (curr <= target) {
            operations += 1;
            curr = curr + prev;
            prev = curr - prev;
        }
        return operations;
    }
}