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, sys
from collections import defaultdict, Counter, deque
 
INF = float('inf')
MOD = int(1e9) + 7
 
def gcd(a, b):
	while b:
		a, b = b, a%b
	return a
 
def isPrime(n):
	if (n <= 1): 
		return False
	i = 2
	while i ** 2 <= n:
		if n % i == 0:
			return False
		i += 1
	return True
 
def primeFactors(n):
	factors = defaultdict(int)
	i = 2
	while i ** 2 <= n:
		while n % i == 0:
			factors[i] += 1
			n //= i 
		i += 1
	if n > 1:
		factors[n] += 1 
	return factors
 
def vars():
	return map(int, input().split())
 
def array():
	return list(map(int, input().split()))

def main():
	n = int(input())
	n *= 2
	deg = 180 / n 
	rad = deg * math.pi / 180
	
	print(1 / math.tan(rad))

if __name__ == "__main__":
	t = 1
	t = int(input())
	for _ in range(t):
		main()