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

def solve(n):
    if n == 2:
        return 1.0
    each_angle = math.pi / n
    height = 0
    width = 0
    for i in range(n):
        angle = each_angle * i
        height += math.sin(angle) * 1.0
        width += abs(math.cos(angle)) * 1.0
    if width > height:
        sectors = n // 2
        angle = each_angle * (0.5 + sectors / 2) - math.pi / 4
        ans = width * math.cos(angle)
    else:
        ans = height
    # print(height, width, ans)
    return ans

def main():
    T = int(input())
    for _ in range(1, T + 1):
        n = int(input())
        print(solve(n))

if __name__ == '__main__':
    main()