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.
T = int(input())
ans = []
for i in range(T):
 
	a, b, n = map(int, input().split())
	cum = 0
	tot = 0
	if (a>b):
		useA = False
	else:
		useA = True
 
	for j in range(n+1):
		if (a > n or b > n):
			ans.append(tot)
			break
		else:
			if useA:
				useA = False
				a += b
			else:
				useA = True
				b += a
			tot += 1
 
if (len(ans) == 0):
	print(0)
else:
	for i in range(len(ans)):
		print(ans[i])