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 sys
import heapq
from math import *
import bisect

def input():
    return sys.stdin.readline().strip()
 
def iinput():
    return int(input())
 
def rinput():
    return map(int, input().split())

def rlinput():
    return list(map(int, input().split()))

def srlinput(fl=False):
    return sorted(list(map(int, input().split())) , reverse=fl)


def main():
    n = iinput()
    #n, k = rinput()
    #n, m, k = rinput()
    t = cos(pi * (n - 1) / (2 * n))
    print(((1 - t) ** 0.5 + (1 + t) ** 0.5) / (2 * sin(pi / (2 * n))))

    
    
    
        
    
            
for sdfghjkl in range(iinput()):
    main()