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
def eprint(*args):
    print(*args, file=sys.stderr)
zz=1
from math import *
import copy
#sys.setrecursionlimit(10**6)
if zz:
	input=sys.stdin.readline
else:	
	sys.stdin=open('input.txt', 'r')
	sys.stdout=open('all.txt','w')
def li():
	return [int(x) for x in input().split()]
def fi():
	return int(input())
def si():
	return list(input().rstrip())	
def mi():
	return 	map(int,input().split())	
 
 
t=fi()
 
def yes(f):
	#print(f)
	for i in range(2*n):
		if -f/2<=d[i][0]<=f/2 and -f/2<=d[i][1]<=f/2:
			continue
		else:
			return False
	return True				
 
while t>0:
	t-=1
	n=fi()
	r=1/(2*tan((pi/180)*(360/(4*n))))
	th=pi/(n)
	d=[]
	for i in range(2*n+1):
		#print(i*th*180/pi)
		d.append([r*cos(i*th),r*sin(i*th)])
	#print(d)	
	ans=0
	l=0
	r=10**9
	while r-l>=10**-7:
		mid=l+(r-l)/2
 
		if yes(mid):
			ans=mid
			r=mid
		else:
			l=mid
	print(ans)