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
from math import tan, pi, cos, sin

_INPUT_LINES = sys.stdin.read().splitlines()
input = iter(_INPUT_LINES).__next__
from itertools import islice, cycle


def go():
    n = int(input())
    # a,b,c,d = map(int, input().split())
    # a = list(map(int, input().split()))
    # s = input()
    nn = 2*n
    pin = pi/nn
    l,r = 0, pin
    for i in range(100):
        c = (l+r)/2
        if cos(c)-(cos(pin-c))>0:
            l=c
        else:
            r=c
    return cos(c)/(sin(pin))


# x,s = map(int,input().split())
t = int(input())
# t = 1
ans = []
for _ in range(t):
    # print(go())
    ans.append(str(go()))
#
print('\n'.join(ans))