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:
# cook your dish here
# import sys
# sys.stdin = open('input.txt', 'r') 
# sys.stdout = open('output.txt', 'w')

import math
import collections
from sys import stdin,stdout,setrecursionlimit
import bisect as bs
T = int(stdin.readline())

for _ in range(T):
    n = int(stdin.readline())
    # a,b,c,d = list(map(int,stdin.readline().split()))
    # h = list(map(int,stdin.readline().split()))
    # b = list(map(int,stdin.readline().split()))
    # a = stdin.readline().strip('\n')
    t = 2*n
    x = math.pi/t
    h = 0.5 / (math.tan(x))
    print(round(2*h,7))