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 PYTHON):

Solution:
import sys

__author__ = 'ratmir'

from collections import deque
from math import asin, pi, tan

alphabet = "abcdefghijklmnopqrstuvwxyz"

def solve(n, a, graph):
    return 1

def execute():
    [t] = [int(x) for x in sys.stdin.readline().split()]
    results = []
    for ti in range(0, t):
        [n] = [int(x1) for x1 in sys.stdin.readline().split()]
        kv = 2 * n
        ugol = pi * 2 / kv
        ugol2 = (pi - ugol)/2
        tg = tan(ugol2)
        ans = tg
        results.append(ans)

    print(''.join('{}\n'.format(k) for k in results))


execute()