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.InputStreamReader;
import java.io.PrintWriter;
import java.util.StringTokenizer;

public class Problem8A {
	public static void main(String[] args) throws Exception {
		BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));
		PrintWriter writer = new PrintWriter(System.out);

		int t = Integer.parseInt(reader.readLine());
		for (int tt = 0; tt < t; tt++) {
			StringTokenizer tokenizer = new StringTokenizer(reader.readLine());
			int a = Integer.parseInt(tokenizer.nextToken());
			int b = Integer.parseInt(tokenizer.nextToken());
			int n = Integer.parseInt(tokenizer.nextToken());

			if (b < a) {
				int temp = a;
				a = b;
				b = temp;
			}
			int c = a + b;
			int count = 1;
			while (c <= n) {
				a = b;
				b = c;
				c = a + b;
				count++;
			}
			writer.println(count);



		}

		reader.close();
		writer.close();
	}
}
