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.
__author__ = 'Devesh Bajpai'

'''
https://codeforces.com/problemset/problem/1368/A

Solution: We simply simulate the operation of += on the given operands. To decide which variable
gets updated, we employ the greedy strategy to update the smaller value. This way, we have a
bigger value to be updated in the next round. e.g.

a = 3, b = 5
We can get:
 a += b, a = 8, b = 5
 or
 b += a, a = 3, b = 8
 
 The first case will lead to b getting updated to 13 in the next round while in the later one
 we can only update a or b to 11.  
'''


def solve(a, b, n):

    operations = 0

    while a <= n and b <= n:

        if a < b:
            a += b
        else:
            b += a

        operations += 1

    return operations


if __name__ == "__main__":

    t = int(raw_input())

    results = list()
    for _ in xrange(0, t):
        a, b, n = map(int, raw_input().split(" "))
        results.append(solve(a, b, n))

    for result in results:
        print result
