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.*;
import java.util.StringTokenizer;
import java.util.*;
import java.math.*; 
import java.time.LocalDate;
import java.time.format.DateTimeFormatter;
import java.time.temporal.ChronoUnit;



public class Solution{
   
      public static void main(String[] args) throws Exception {
        FastScanner cin = new FastScanner(System.in);
        StringBuffer ans = new StringBuffer();
        int t = cin.nextInt();
        while(t-->0)
        {
            long a = cin.nextLong();
            long b = cin.nextLong();
            long n = cin.nextLong();
            boolean flag = true;

            long q = 0;
            if(a>n || b>n)
            {
                ans.append("0\n");
                continue;
            }
            do
            {
              long tempa = a+b;
              long tempb = a+b;
              if(a>=b)
                b+=a;
              else
                a+=b;
              q++;
            }while(n>=a && n>=b);
          ans.append(q+"\n");
        }
    System.out.print(ans);

    }
        
    static class FastScanner {
        private BufferedReader reader = null;
        private StringTokenizer tokenizer = null;
 
        public FastScanner(InputStream in) {
            reader = new BufferedReader(new InputStreamReader(in));
            tokenizer = null;
        }
 
        public String next() {
            if (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }
 
        public String nextLine() {
            if (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    return reader.readLine();
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
 
            return tokenizer.nextToken("\n");
        }
 
        public long nextLong() {
            return Long.parseLong(next());
        }
         
        public int nextInt() {
            return Integer.parseInt(next());
        }
 
    }
  }
  

