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
import math
# from collections import deque
# import heapq
# from math import inf
# from math import gcd

# print(help(deque))
# 26
pprint = lambda s: print(' '.join(map(str, s)))
input = lambda: sys.stdin.readline().strip()
ipnut = input
# a, b, c, d = map(int, input().split())
# n = int(input())
# e = list(map(int,input().split()))
for i in range(int(input())):
    n = int(input())
    a = 1/math.sin(math.pi/(2*n))/2
    # print(a)
    n*=2
    print(a*(math.sqrt(1-math.cos(math.pi*(n-2)/(2*n)))+math.sqrt(1+math.cos(math.pi*(n-2)/(2*n)))))
"""
10
10 11 12 13 14 15 16 17 11 11
"""