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.*;

public class CP {
    public static void main(String[] args) throws IOException{
        FastReader sc = new FastReader();
        int t = sc.Int();
        for(;t > 0;t--){
            int a = sc.Int();
            int b = sc.Int();
            int n = sc.Int();
            int count = 0;
            for(;!(a > n || b > n);){
                if(Math.min(a, b) == a){
                    a = a + b;
                }
                else{
                    b = a + b;
                }
                count++;
            }
            System.out.println(count);
        }
    }
}
class FastReader {
    private BufferedReader br;
    private StringTokenizer st;
    public FastReader(){
        br = new BufferedReader(new InputStreamReader(System.in));
    }
    public String next() throws IOException{
        for(;st == null || !st.hasMoreTokens();){
            st = new StringTokenizer(br.readLine());
        }
        return st.nextToken();
    }
    public String nextLine() throws IOException{
        return br.readLine();
    }
    public int Int()throws IOException{
        return Integer.parseInt(next());
    }
    public long Long()throws IOException{
        return Long.parseLong(next());
    }
    public double Double() throws IOException{
        return Double.parseDouble(next());
    }
    public float Float() throws IOException{
        return Float.parseFloat(next());
    }
    public char Char() throws IOException{
        return next().charAt(0);
    }
    public void close()throws IOException{
        br.close();
    }
}