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 io, sys, atexit, os
import math as ma
from sys import exit
from decimal import Decimal as dec
from itertools import permutations
from itertools import combinations


def li():
    return list(map(int, sys.stdin.readline().split()))


def num():
    return map(int, sys.stdin.readline().split())


def nu():
    return int(input())


def find_gcd(x, y):
    while (y):
        x, y = y, x % y
    return x


def lcm(x, y):
    gg = find_gcd(x, y)
    return (x * y // gg)


mm = 1000000007

def solve():
    t = nu()
    for tt in range(t):
        n=nu()
        x=ma.pi/(2*n)
        yy=ma.tan(x)
        print(1/yy)






                 


if __name__ == "__main__":
    solve()