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

import sys
input = sys.stdin.readline

Q = int(input())
Query = [int(input()) for _ in range(Q)]


def get(N, theta):
    r = 1/(2*math.sin(math.pi/N))
    return 2*max(r*math.cos(theta), r*math.cos(math.pi/N-theta))

for N in Query:
    if N%2 == 0:
        print(1/math.tan(math.pi/(N*2)))
    else:
        N *= 2
        l1 = 0
        l2 = math.pi/N
        while l2 - l1 > 10**(-15):
            m1 = (2*l1+l2)/3
            m2 = (l1+2*l2)/3
            s_l1 = get(N, l1)
            s_l2 = get(N, l2)
            if s_l1 >= s_l2:
                l1 = m1
            else:
                l2 = m2
        print(get(N, l1))