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
from math import pi, cos

TEST = 0

if TEST == 1:
    input_file = open("inputC.txt", "r")
    input_from_file = input_file.readlines()

def read_int():
    if TEST:
        return int(input_from_file.pop(0))
    else:
        return int(sys.stdin.readline())

def read_ints():
    if TEST:
        return list(map(int, input_from_file.pop(0).rstrip().split()))
    else:
        return list(map(int, sys.stdin.readline().split()))




t = read_int()


for test in range(t):
    n = read_int()

    alpha = ((n-1)/n) * 180
    steps = int((n-2)/2)
    beta = 0
    half_side = 0.5
    for k in range(steps):
        beta = 90 - (alpha - 90 - beta)
        half_side += cos(beta*pi/180)

    print(2*half_side)