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.
# cook your dish here

t = int(input())

fib = [1,1] 
  
def fibo(n):
    if n<=len(fib): 
        return fib[n-1] 
    else: 
        tempFib = fibo(n-1) + fibo(n-2) 
        fib.append(tempFib) 
        return tempFib
x = fibo(50)

while t > 0:
    l = [int(x) for x in input().split()]
    a1, b1, n = l[0], l[1], l[2]
    a = min(a1,b1)
    b = a1 + b1 - a
    

    forB = fib[1:]
    forA = fib
    
    i,j = 0,0
    ans = 1
    currNum = a*forA[i] + b*forB[j]
    while currNum <= n:
        i += 1
        j += 1
        # print("deb:",i,j)
        currNum = a*forA[i] + b*forB[j]
        ans += 1
        
    print(ans)
        
    
    
    t -= 1