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
reader = (s.rstrip() for s in sys.stdin)
input = reader.__next__
#3222211133
from math import tan,pi 
  
# Function to find the apothem 
# of a regular polygon 
def polyapothem(n, a): 
      
    # Side and side length cannot be negative 
    if (a < 0 and n < 0): 
        return -1
  
    # Degree converted to radians 
    return a / (2 * tan((180 / n) * 
                   pi / 180)) 
  

        
def gift():
    for _ in range(t):
        n = int(input())
        yield '{0:.12}'.format(2*polyapothem(n*2, 1))

            

if __name__ == '__main__':
    t= int(input())
    ans = gift()
    print(*ans,sep='\n')