Problem: The statement of this problem is the same as the statement of problem C2. The only difference is that, in problem C1, n is always even, and in C2, n is always odd.

You are given a regular polygon with 2 ⋅ n vertices (it's convex and has equal sides and equal angles) and all its sides have length 1. Let's name it as 2n-gon.

Your task is to find the square of the minimum size such that you can embed 2n-gon in the square. Embedding 2n-gon in the square means that you need to place 2n-gon in the square in such way that each point which lies inside or on a border of 2n-gon should also lie inside or on a border of the square.

You can rotate 2n-gon and/or the square.

Input

The first line contains a single integer T (1 ≤ T ≤ 200) — the number of test cases.

Next T lines contain descriptions of test cases — one per line. Each line contains single even integer n (2 ≤ n ≤ 200). Don't forget you need to embed 2n-gon, not an n-gon.

Output

Print T real numbers — one per test case. For each test case, print the minimum length of a side of the square 2n-gon can be embedded in. Your answer will be considered correct if its absolute or relative error doesn't exceed 10^{-6}.

Example

Input


3
2
4
200


Output


1.000000000
2.414213562
127.321336469

Solution (in PYTHON3):

Solution:

import math
t = int(input())

pi = math.acos(-1)
sqr2 = 2 ** (1/2)
for i in range(t):
	n = int(input())
	step = (2*pi)/(2 * n)

	side = 1.0/math.sin(step/2)
	side /= 2
	l = 1
	r = 400
	ans = 400
	for _ in range(90):
		mid = (l + r)/2
		k = mid * sqr2/2
		ang = 0
		flag = 1
		for j in range(n):
			x = side * math.cos(ang)
			y = side * math.sin(ang)

			if x + y > k or x + y < -k or y - x > k or y - x < -k:
				flag = 0
			ang += step

		if flag == 1:
			ans = mid
			r = mid
		else:
			l = mid
	print(ans)