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.*;
public class Main{
    static int M=(int)Math.pow(10,9)+7;
    public static void main(String[] args) throws IOException{
        try{
            BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
            PrintWriter ot=new PrintWriter(System.out);
            int t=Integer.parseInt(br.readLine());
            while(t-->0)
            {
                String s[]=br.readLine().trim().split(" ");
                int a=Integer.parseInt(s[0]);
                int b=Integer.parseInt(s[1]);
                int n=Integer.parseInt(s[2]);
                ot.println(find(a,b,n));
            }
            ot.close();
            br.close();
            
        } catch(Exception e){
            System.err.println("ERROR");
            return;
        }
        
    }
    public static int find(int a,int b,int n){
        int count=0;
        while(a<=n&&b<=n)
        {
            if(a<b)
            {
                a+=b;
                // count++;
            }
            else
            {
                b+=a;
                // count++;
            }
            count++;
        }
        return count;
    }
    
}