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
T = int(input())

while T:
    n = int(input())
    if n%2 == 0:
        rad = 0.0174533
        internal_angle = ((n-1)*180*1.0)/(n*1.0)
        prevAngle = 0
        ans = 1.0
        while True:
            cur_angle = (180-internal_angle)+prevAngle
            prevAngle = cur_angle
            co = math.cos(cur_angle*rad)
            if co<=0:
                break
            ans = ans + 2.0 * co
        print(ans)
    else:
        angle = (math.pi/n)/4
        ans = (0.5)/math.sin(angle)
        print(ans)

    T-=1