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:
#!/usr/bin/env python3
import sys
input = sys.stdin.readline
import math

t = int(input())
for _ in range(t):
    n = int(input())
    a = 1.0 / (2.0 * math.tan(math.pi / (n * 2)))
    b = 1.0 * math.sin(math.pi / 2.0) / (math.sin(math.pi / (n * 2)))
    if n % 2 == 0:
        print(a * 2.0)
    else:
        rotation = [math.pi * 2.0 / (2 * n) * item for item in range(2 * n)]
        l = 0.0; r = math.pi / 2.0 
        eps_rot = [(math.pi * 2.0 / (2 * n) / 10**2) * item for item in range(10**2)]
        ret = b
        for eps in eps_rot:
            max_rad = 0.0 
            for rad in rotation:
                val = max(b * abs(math.sin(rad + eps)), b * abs(math.cos(rad + eps)))
                max_rad = max(max_rad, val)
            ret = min(ret, max_rad)
        print(ret)