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 math import cos, sin, pi, tan, radians
class Vector:
    def __init__(self, x=0, y=0):
        self.x = x
        self.y = y

    def dot(self, other):
        return self.x * other.x + self.y * other.y
    
    def scale(self, c):
        self.x *= c
        self.y *= c
    
    def magnitude(self):
        return self.dot(self)**0.5
    
    # rotate vector by theta degrees CCW w.r.t. origin (0, 0)
    def rotate(self, theta):
        theta %= 360
        if theta % 90:      # not a multiple of 90 (avoid using expensive cosine function when possible)
            theta = (theta / 180) * pi      # cos and sin require radians (not degrees)
            self.x, self.y = self.x*cos(theta) - self.y*sin(theta), self.x*sin(theta) + self.y*cos(theta)
        elif theta == 90:
            self.x, self.y = -self.y,  self.x
        elif theta == 180:
            self.x, self.y = -self.x, -self.y
        elif theta == 270:
            self.x, self.y =  self.y, -self.x
    

for _ in range(int(input())):
    n = 2*int(input())
    apot = 0.5*tan(radians((90*n - 180)/n))
    diag = 2*(0.25 + apot**2)**0.5
    v = Vector(diag, 0)
    u = Vector(diag, 0)
    v.rotate(90/n)
    u.scale(u.dot(v) / u.dot(u))
    print(u.magnitude())