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 pi,sin,tan



def solve(n):
    half_angle = (2*pi/(2*n)) / 2.0
    #print(n,half_angle)
    if n % 2 == 1:
        # odd case (even number of sides)
        s = 0.5 / sin(half_angle)
    else:
        # even case (number of sides div by 4)
        s = 0.5 / tan(half_angle)
    return 2*s


if __name__ == '__main__':
    IN = [x.strip() for x in sys.stdin.readlines()]

    T = int(IN[0])
    cur = 1
    for ti in range(T):
        #l = int(IN[cur])
        n = int(IN[cur])
        result = solve(n)
        print(result)
        cur += 1