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.*;
import java.math.*;

public class Main {

    static Scanner sc = new Scanner(new BufferedReader(new InputStreamReader(System.in)));
    static PrintWriter out = new PrintWriter(System.out);

    public static void main(String[] args) throws Exception {

        int t = sc.nextInt();
        while (t-- > 0) {
            int a = sc.nextInt();
            int b = sc.nextInt();
            BigInteger n = BigInteger.valueOf(sc.nextInt());

            BigInteger first = BigInteger.valueOf(a);
            BigInteger second = BigInteger.valueOf(b);
            int count = 0;

            while(second.compareTo(n) < 1) {
                if(second.compareTo(first) == 1) {
                    BigInteger temp = second;
                    second = first;
                    first = temp;
                }
                second = first.add(second);
                ++count;
            }

            out.println(count);
        }

        out.flush();
        out.close();
        sc.close();
    }

    static final int MOD = (int) 1e9 + 7;
    static final double PI = 3.14159265358979323846;

    // takes array input
    public static int[] init(int n) {

        int[] arr = new int[n];

        for (int i = 0; i < n; ++i)
            arr[i] = sc.nextInt();

        return arr;
    }

    // finds GCD of two number
    public static int gcd(int a, int b) {

        if (a == 0) {
            return b;
        }

        return gcd(b % a, a);
    }

    // checks whether a number is prime or not
    public static boolean prime(int n) {

        if (n < 2)
            return false;

        for (int i = 2; i * i <= n; ++i)
            if (n % i == 0)
                return false;

        return true;
    }
}
