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.
from sys import stdin, stdout
import math
from itertools import permutations, combinations
from collections import defaultdict
from collections import Counter
from bisect import bisect_left
import sys
from queue import PriorityQueue

mod = 1000000007

def L():
	return list(map(int, stdin.readline().split()))

def In():
	return map(int, stdin.readline().split())

def I():
	return int(stdin.readline())

def printIn(ob):
	return stdout.write(str(ob)+'\n')

def powerLL(n, p):
	result = 1
	while (p):
		if (p&1):
			result = result * n % mod
		p = int(p / 2)
		n = n * n % mod
	return result

#--------------------------------------

def myCode():
	a,b,n = In()
	ops = 0
	while(max(a,b)<=n):
		ops+=1
		if a<b:a+=b
		else:b+=a
	print(ops)
def main():
    for t in range(I()):
	    myCode()
if __name__ == '__main__':
    # print(math.sqrt(4))
    main()