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 OutputStream out=new BufferedOutputStream(System.out);

  //nl-->neew line; //l-->line;  //arp-->array print;  //arpnl-->array print new line
  public static void nl(Object o) throws IOException{out.write((o+"\n").getBytes());}
  public static void l(Object o) throws IOException{out.write((o+"").getBytes());}
  public static void arp(int[] o) throws IOException{for(int i=0;i<o.length;i++) out.write((o[i]+" ").getBytes());}
  public static void arpnl(int[] o) throws IOException{for(int i=0;i<o.length;i++) out.write((o[i]+"\n").getBytes());}
  //
  static long cnt;
  static int[] dp;


  public static void main(String[] args) throws IOException{
    long sttm=System.currentTimeMillis();
    Scanner sc=new Scanner(System.in);

    int t=sc.nextInt();
    while(t-->0){
      // taking input
      long a=sc.nextLong(),b=sc.nextLong(),n=sc.nextLong();
      int cnt=0;
      while(a<=n && b<=n){
        cnt++;
        if(a<b) a+=b;
        else b+=a;
      }
      nl(cnt);
    }
    out.flush();
  }
}

class Pair{
  int st,nd;
  Pair(int st,int nd){
    this.st=st;
    this.nd=nd;
  }
}
