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.*;
 
/* Name of the class has to be "Main" only if the class is public. */
 public class Main
{
	public static void main (String[] args) throws java.lang.Exception
	{
	Scanner s=new Scanner(System.in);
	int op=s.nextInt();
	while(op>0){
	    int flag1=0;
	    int flag2=0;
	   long a=s.nextInt();
	    long b=s.nextInt();
	    int n=s.nextInt();
	    if(a>=b){
	        b+=a;
	        flag1++;
	    }
	    else{
	        a+=b;
	        flag2++;
	    }
	    int count=0;
	    int step=1;
	    while(a<=n&&b<=n&&flag1>0){
	        if(count%2==0){
	          a+=b;  
	        }
	        else{
	            b+=a;
	        }
	       step++; 
	       count++;
	        
	    }
	    	    while(a<=n&&b<=n&&flag2>0){
	        if(count%2==0){
	          b+=a;  
	        }
	        else{
	            a+=b;
	        }
	       step++; 
	        count++;
	    }
	    if(a==b&&b==n){
	        System.out.println(1);
	    }
	    else{
	    System.out.println(step);
	    }
	    op--;
	    
	    
	}
	}
}
