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 io,os
input=io.BytesIO(os.read(0,os.fstat(0).st_size)).readline
import sys
from math import sin,tan,pi

def main():
    t=int(input())
    for _ in range(t):
        n=int(input())
        n*=2
        k=(n+7)//8-1
        #print(k)
        s=pi/4-k*2*pi/n
        x=1/(2*sin(pi/n))
        c=2*pi/n*(k+1/2)
        b=(n-2)*pi/(2*n)+s
        a=pi-b-c
        #print(n,s/pi,a/pi,b/pi,c/pi)
        y=x*sin(b)/sin(a)
        ans=y*(2**0.5)
        sys.stdout.write(str(ans)+'\n')
    
if __name__=='__main__':
    main()