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.lang.*;
import java.util.stream.Collectors;

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

            InputStreamReader isr = new InputStreamReader(System.in);
            BufferedReader br = new BufferedReader(isr);
            int t = Integer.parseInt(br.readLine());
            while (t-- > 0) {
                String str[] = br.readLine().split(" ");
                long a,b,n,cnt=0;
                a = Integer.parseInt(str[0]);
                b = Integer.parseInt(str[1]);
                n = Integer.parseInt(str[2]);
                long max = Math.max(a,b),min = Math.min(a,b);
                while(max<=n ){
                    min += max;
                    long temp = min;
                    min = max;
                    max =temp;
                    cnt++;
                }

                System.out.println(cnt);
            }






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


    private static long gcd(long a, long b) {
        if (b == 0)
            return a;
        return gcd(b, a % b);
    }

    private static long lcm(long a, long b) {
        return (a * b) / gcd(a, b);
    }

    private static ArrayList<Long> allfactorsofn(long n) {
        ArrayList<Long> a = new ArrayList<>();
        ArrayList<Long> b = new ArrayList<>();
        for (long i = 1; i <= Math.sqrt(n); i++) {
            if (n % i == 0) {
                if (n / i == i)
                    a.add(i);

                else {
                    a.add(i);
                    b.add(n / i);
                }
            }
        }

        for (int i = b.size() - 1; i >= 0; i--) {
            a.add(b.get(i));
        }

        return a;
    }
}
