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.ArrayList;
import java.util.Arrays;
import java.util.List;
import java.util.Scanner;

public class Main {
	
	private static long varA;	//the first operand
	private static long varB;	//the second operand
	private static long varN;	//maximum value

	
	
	public static void main(String[] args) {
		
		Scanner sc = new Scanner(System.in);

		int linesNum = sc.nextInt();
		
		List<String> inputStrings = new ArrayList<String>();
		
		sc.nextLine();
		
		for (int i = 0; i < linesNum; i++) {
			String line = sc.nextLine();
			inputStrings.add(line);
		}
		
		for (int i = 0; i < inputStrings.size(); i++) {

			System.out.println(calcVariants(inputStrings.get(i)));
		}
		
	}
	
	
	public static int calcVariants(String task) {
			
		int[] x;
		
		x = Arrays.stream(task.split(" ")).mapToInt(p -> Integer.parseInt(p)).toArray();
		
		varA = x[0];
		varB = x[1];
		varN = x[2];
		
		if (varA > varB) {
			long tmp = varA;
			varA = varB;
			varB = tmp;
		}
		
        int count = 0;
        while((varA <= varN) && (varB <= varN)){
            if(count%2 == 0){
            	varA += varB;
                count++;
            }
            else{
            	varB += varA;
                count++;
            }
        }
	
		return count;
	}

}
