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.* ;
public class NewLanguage{

     public static void main(String []args){
        Scanner sc1 = new Scanner(System.in); 
        
        int t = sc1.nextInt(); 
        
        while(t>0) {
            int a = sc1.nextInt(); 
            int b = sc1.nextInt(); 
            int n = sc1.nextInt(); 
            int temp1 = a ; 
            int temp2 = b ; 
            int count1 =0 ; 
            int count2 =0 ; 
            
            while(a<=n&&b<=n) {
                if(count1%2==0) {
                    a = a+b ; 
                    b = b ; 
                    count1+=1 ; 
                }
                
                else if(count1%2!=0) {
                    b = a+b ; 
                    a = a ; 
                    count1 = count1+1 ; 
                }
            }
            
            a = temp1 ; 
            b = temp2 ; 
            
            while(a<=n&&b<=n) {
                if(count2%2==0) {
                    b = a+b ; 
                    a = a ; 
                    count2+=1; 
                }
                
                else if(count2%2!=0) {
                    a = a+b ; 
                    b = b ; 
                    count2+=1; 
                }
            }
            
            System.out.println(Math.min(count1,count2)); 
            
            t-- ; 
            
        }
     }
}