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.lang.*;
import java.io.*;
import java.math.*;

/* Name of the class has to be "Main" only if the class is public. */
public class Codechef {
  static int n,m;
  static int a[];
  static StringBuffer str = new StringBuffer("");
  static BufferedReader bf;

  static void solve() throws Exception{
      
    long ans=0;
    String s[]=bf.readLine().trim().split("\\s+");
    long a,b,n;
    a=Long.parseLong(s[0]);
    b=Long.parseLong(s[1]);
    n=Long.parseLong(s[2]);
    while(a<=n&&b<=n)
    {
        if(a<=b)
            a+=b;
        else
            b+=a;
        
        ans++;    
    }
    str.append(ans+"\n");
  }

  public static void main(String[] args) throws java.lang.Exception {
    bf = new BufferedReader(new InputStreamReader(System.in));
    int t;
    t=Integer.parseInt(bf.readLine());
    while(t-->0)
     solve();
    System.out.print(str);
  }
}