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
import math

read = sys.stdin.buffer.read
input = sys.stdin.buffer.readline
readlines = sys.stdin.buffer.readlines
t = int(input())
for case in range(t):
    n = int(input())
    r = 0.5000 / math.sin(math.radians(180 / (2 * n)))
    # print(1 / math.tan(math.radians(180 / (2 * n))))
    min_theta = 45  # 45からの角度最小を求める
    for i in range(1, n):
        tmp_i = min(abs((180 * i) / n - 45), abs((180 * i) / n - 135))
        min_theta = min(min_theta, tmp_i)
    # print(r, min_theta)
    print(2 * r * math.cos(math.radians(min_theta)))