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.
s = int(input())

count = 0
ans = []

while count < s :
    t = input()
    t = [int(x) for x in t.split()]
    a,b,n = sorted(t)
    ste = 0
    while int(a) <= int(n) and int(b) <= int(n):
        a= int(a) + int(b)
        b= int(a) + int(b)
        ste += 2
    if a > int(n) and b > int(n):
        ste -= 1
    ans.append(ste)
    count += 1

    
    
for y in ans:
    print (y)
  

    
        
    



    




    

    
    

        
        
        
    
    

    
        



        
        
        
           
        
        
    
    




    
            
        





            
        
            

        
            



        
        
    
        



            


    
    







    



        
        
        
        


            



        
            

    


    

    



        


        



    
        
        

    







    
    
 

    

        
    
            
    




    


        



    





        
            
        
    
