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:
from math import *
import sys

def rad(deg):
	PI = 3.141592653
	return deg/180*PI
def rdl():
	return sys.stdin.readline().strip()

def test_case():
	n = int(rdl())
	nn = 2*n
	g = (nn-2)*180/nn
	a = g-90
	b = 90-a
	ll = 0
	for i in range(int(nn/4)):
		tt = abs(cos(rad(a)))
		ll += tt
		a = g-90-b
		b = 90-a
	print(2*ll-1)
	pass
T = int(rdl())
while T:
	test_case()
	T-=1