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:
from decimal import *
import math
getcontext().prec=100
pi=Decimal(0)
def init_pi():
    global pi
    for i in range(200):
        cur=Decimal(4)/Decimal(8*i+1)-Decimal(2)/Decimal(8*i+4)-Decimal(1)/Decimal(8*i+5)-Decimal(1)/Decimal(8*i+6)
        cur/=(16**i)
        pi+=cur

init_pi()

def cos(x):
    x = Decimal(x)
    getcontext().prec += 2
    i, lasts, s, fact, num, sign = 0, 0, 1, 1, 1, 1
    while s != lasts:
        lasts = s
        i += 2
        fact *= i * (i-1)
        num *= x * x
        sign *= -1
        s += num / fact * sign
    getcontext().prec -= 2
    return +s

def sin(x):
    x=Decimal(x)
    getcontext().prec += 2
    i, lasts, s, fact, num, sign = 1, 0, x, 1, x, 1
    while s != lasts:
        lasts = s
        i += 2
        fact *= i * (i-1)
        num *= x * x
        sign *= -1
        s += num / fact * sign
    getcontext().prec -= 2
    return +s

def asin(x,k=300):
    x=Decimal(x)
    l=Decimal(-pi/2)
    r=Decimal(pi/2)
    for i in range(k):
        mi=(l+r)/2
        if sin(mi)<x:l=mi
        else: r=mi
    return l

def acos(x,k=300):
    x=Decimal(x)
    l=Decimal(0)
    r=Decimal(pi)
    for i in range(k):
        mi=(l+r)/2
        if cos(mi)>x:l=mi
        else: r=mi
    return l

T=eval(input())
for i in range(T):
    n=eval(input())
    y=pi/n/4
    x=y*2
    print(cos(y)/sin(x))