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, math
readline = sys.stdin.readline

def rou(x):
    _x = int(x)
    if x - _x < 0.5:
        return _x
    else:
        return _x + 1

def solve():
    N = int(readline())
    N2 = N * 2
    a = math.pi * 2 / N2
    k = rou(N2 / 8)
    r = 1/ 2 / math.sin(math.pi / N2)
    p = r * math.cos(k * a)
    q = r * math.sin(k * a)
    ans = 2**0.5 * (p + q)
    print(ans)

T = int(readline())
for i in range(T):
    solve()