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:
#JMD
#Nagendra Jha-4096

 
import sys
import math

#import fractions
#import numpy
 
###File Operations###
fileoperation=0
if(fileoperation):
    orig_stdout = sys.stdout
    orig_stdin = sys.stdin
    inputfile = open('W:/Competitive Programming/input.txt', 'r')
    outputfile = open('W:/Competitive Programming/output.txt', 'w')
    sys.stdin = inputfile
    sys.stdout = outputfile

###Defines...###
mod=1000000007
 
###FUF's...###
def nospace(l):
    ans=''.join(str(i) for i in l)
    return ans
 
 
 
##### Main ####
t=int(input())
for tt in range(t):
    n=int(input())
    v= math.cos((math.pi)/n)
    v=(1-v)
    v=(1/v)
    v/=2
    v=pow(v,0.5)
    cc = math.cos(((n-1)*math.pi)/n)
    xx = (1-cc)*(2*v*v)
    xx=pow(xx,0.5)
    print(xx)
    #n,k,s= map(int, sys.stdin.readline().split(' '))
    #a=list(map(int,sys.stdin.readline().split(' ')))
    
    
#####File Operations#####
if(fileoperation):
    sys.stdout = orig_stdout
    sys.stdin = orig_stdin
    inputfile.close()
    outputfile.close()