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.
import sys
input = sys.stdin.readline

from bisect import *

def linput(tt=int):
	return list(map(tt,input().split()))

def gcd(a: int, b: int):
	while b: a, b = b, a%b
	return a

def lcm(a: int, b: int):
	return a * b // gcd(a, b)

def main():
	Q = int(input())
	
	vR = []
	for _ in range(Q):
		A,B,N = linput()
		R = 0
		x,y = min(A,B), max(A,B)
		while y<=N:
			x += y
			x,y = min(x,y), max(x,y)
			R += 1
		vR.append(R)
	
	print(*vR, sep="\n")
	#sT = "NO YES".split()
	#for r in vR:
	#	print(sT[r])

if __name__ == "__main__":
	main()
