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
sys.setrecursionlimit(10000)

from math import tan, radians, sqrt, sin

class Memoize:
    def __init__(self, f):
        self.f = f
        self.memo = {}
    def __call__(self, *args):
        if not args in self.memo:
            self.memo[args] = self.f(*args)
        return self.memo[args]

class Recurse(Exception):
    def __init__(self, *args, **kwargs):
        self.args = args
        self.kwargs = kwargs

def recurse(*args, **kwargs):
    raise Recurse(*args, **kwargs)
        
def tail_recursive(f):
    def decorated(*args, **kwargs):
        while True:
            try:
                return f(*args, **kwargs)
            except Recurse as r:
                args = r.args
                kwargs = r.kwargs
                continue
    return decorated

t = int(input())
for _ in range(t):
    n = int(input())
    n = 2*n
    area = n/(4*tan(radians(180)/n))
    radius = sqrt(2*area/(n*sin(radians(360)/n)))
    ans = 2*(sqrt(radius*radius - 0.5*0.5))
    print("%.6f" % ans)