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.
T = int(input())

def getFibo(k):
    phi = (1 +pow(5,0.5))/2
    ksi = (1 -pow(5,0.5))/2

    if k==0 or k==1 or k == 2:
        return 1
    return (phi**k - ksi**k)/(phi-ksi)

def Fibo2(n,m):

    if n == 1 or n == 0:
        return 1

    if n not in m:
        
        m[n] = Fibo2(n-1,m) + Fibo2(n-2,m)
    return m[n]
m = {}


while T>0:
    a,b,n = [int(el) for el in input().split(' ')]

    bb = max(a,b)
    aa = min(a,b)

    if bb > n:
        print(0)
    else:
        for i in range(0,51):
            """ 
            if aa*getFibo(i) + bb*getFibo(i+1)>n:
                print(i)

                break
            """
            if aa*Fibo2(i,m) + bb*Fibo2(i+1,m)>n:
                print(i+1)

                break


    T-=1
    
   
