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

MIN_INF, MAX_INF = float('-inf'), float('inf')

def get_len(n, R, alpha, beta):
    maxx, maxy = MIN_INF, MIN_INF
    minx, miny = MAX_INF, MAX_INF
    d = MAX_INF
    for i in range(n):
        theta = alpha * i + beta
        x = math.cos(theta) * R
        y = math.sin(theta) * R
        maxx = max(x, maxx)
        maxy = max(y, maxy)
        minx = min(x, minx)
        miny = min(y, miny)
    d = min(d, max(abs(maxx - minx), abs(maxy - miny)))
    return d

def main():
    T = int(input())
    for t in range(T):
        n = int(input()) * 2

        alpha = 2 * math.pi / n
        R = 1.0 / 2.0 / (math.sin(math.pi / n))

        # ans = float('inf')

        # a, b = 0, alpha
        # va, vb = get_len(n, R, alpha, a), get_len(n, R, alpha, b)

        print(get_len(n, R, alpha, alpha / 4))

        # while True:
        #     d3 = (b - a) / 3
        #     c, d = a + d3, b - d3
        #     vc, vd = get_len(n, R, alpha, c), get_len(n, R, alpha, d)

        #     if abs(vc - vd) < 1e-10:
        #         print(n, R, alpha, c, vc)
        #         break

        #     if vc < vd:
        #         b, vb = d, vd
        #     else:
        #         a, va = c, vc

main()