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.
def bear():
    input_data = input()
    limak_weight = int(input_data.split(" ")[0])
    bob_weight = int(input_data.split(" ")[1])
    i = 0
    while True:
        limak_weight = limak_weight * 3
        bob_weight = bob_weight * 2
        i += 1
        if limak_weight > bob_weight:
            print(i)
            break


def get_a_and_b_send_n(a, b, n):
    i = 0
    while True:
        if a > n or b > n:
            return i
        if a > b:
            b += a
        elif a < b:
            a += b
        else:
            a += b
        i += 1


def c_programming():
    number_of_inputs = int(input())
    a_s = []
    b_s = []
    n_s = []
    for i in range(number_of_inputs):
        new_line = input()
        numbers = new_line.split(" ")
        a = int(numbers[0])
        b = int(numbers[1])
        n = int(numbers[2])
        a_s.append(a)
        b_s.append(b)
        n_s.append(n)

    for a, b, n in zip(a_s, b_s, n_s):
        print(get_a_and_b_send_n(a, b, n))


c_programming()
