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.
#                           जय श्री राम

import sys; import math; from collections import *
# sys.setrecursionlimit(10**6)

def get_ints(): return map(int, input().split())
def get_list(): return list(get_ints())
def printspx(*args): return print(*args, end="")
def printsp(*args): return print(*args, end=" ")

UGLYMOD = int(1e9+7); SEXYMOD = 998244353; MAXN = int(1e5)

#sys.stdin  = open("input.txt","r"); sys.stdout = open("output.txt","w")

for _testcases_ in range(int(input())):
    a, b, m = get_ints()
    a, b = max(a, b), min(a, b)
    c = 0
    while a <= m:
        a, b = a+b, a
        c += 1
    print(c)


'''
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