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 sys

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

import math

t = int(input())

for _ in range(t):
	n = int(input())

	sides = 2 * n
	interiorAngle = ((sides - 2) * 180) / sides
	centreAngle = 180 - interiorAngle
	reqdAngle = (centreAngle * ((sides // 4) + 1)) / 2
	radius = math.sin(math.radians(interiorAngle / 2)) / math.sin(math.radians(centreAngle))
	
	x = (math.sqrt(2) * (radius) * math.sin(math.radians(reqdAngle))) - 1
	
	print(1 + 2 * x)