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 math

PI = 3.14159265358979323846

def check(radius, half, start, n):
    for i in range(n // 2):
        x = math.cos(start + 2 * PI * i / n)
        y = math.sin(start + 2 * PI * i / n)


        if abs(x) > half / radius or abs(y) > half / radius:
            return False


    return True


t = int(input().strip())
#t = 1

for _ in range(t):


    n = int(input().strip())
    #n = 5

    #1.931851653
    #3.196226611
    #126.687663595

    radius = 0.5 / math.sin(PI / (2 * n))


    left = 0.0
    right = 500.0

    epsilon = 1e-9
    c = None
    while abs(right - left) > epsilon:
        c = (right + left) / 2

        half = c / 2.0


        if radius <= half:
            right = c
        else:
            angle = math.acos(half / radius)
            if check(radius, half, angle, 2 * n):
                right = c
            else:
                left = c

    print (f'{c:.15f}')