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
test = int(input())
for k in range (test):
    n = int(input())
    if (n%2 == 0):
        sum = 0
        for x in range(1,n):
            sum += math.sin(x*math.pi/n)
        print (sum)
    else:
        a = n // 4
        horizontal_sum = 1
        for i in range (1,a+1):
            horizontal_sum += 2*math.cos(i*math.pi/n)
        j = a + 1
        vertical_sum = 0
        while (2*j < n):
            vertical_sum += math.sin(j*math.pi/n)
            j += 1
        vertical_sum *= 2
        print (round((vertical_sum + horizontal_sum)/math.sqrt(2),9))