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
from sys import stdin


for _ in range(int(stdin.readline())):
    n = int(stdin.readline()) * 2
    b = 0.5 / math.tan(math.pi / n)
    print(b * 2)




# # n, q = (int(i) for i in stdin.readline().split())
# # a = [int(i) for i in stdin.readline().split()]
#
# n, q = 1000000, 1000000
# a = [1] * n
# b = [1] * q
# c = []
# d = []
#
# # for bi in (int(i) for i in stdin.readline().split()):
# for bi in b:
#     if bi > 0:
#         d.append(bi)
#     else:
#         c.append(bi * -1 - 1)
#
# cl = len(c)
# for i in range(cl):
#     ci = c[i]
#     for j in range(i+1, cl):
#         if ci <= c[j]:
#             c[j] += 1
#
# c.sort()
#
# if c:
#     for i, ci in enumerate(c):
#         if i != ci:
#             print((a + d)[i])
#             break
#     else:
#         print(0)
# else:
#     print(a[0])