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 collections import *
from bisect import *
from math import *
from heapq import *
import sys
input=sys.stdin.readline
t=int(input())
while(t):
    t-=1
    n=int(input())
    cir=pi/(2*n)
    s=1/(2*(sin(cir)))
    q=(n//2)-1
    q=q*(360/(2*n))
    q=(q*pi)/180
    si=sin(q)
    si=si*si
    co=pow(1-si,0.5)
    d=2*s*s
    d*=(1-co)
    c=d/2
    c=pow(c,0.5)
    print(1+(2*c))