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 PYTHON):

Solution:
import atexit
import io
import sys
import math
from collections import defaultdict

_INPUT_LINES = sys.stdin.read().splitlines()
raw_input = iter(_INPUT_LINES).next
_OUTPUT_BUFFER = io.BytesIO()
sys.stdout = _OUTPUT_BUFFER

@atexit.register
def write():
    sys.__stdout__.write(_OUTPUT_BUFFER.getvalue())
t=int(raw_input())
for i in range(t):
    n=int(raw_input())
    angle=360/float(2*n)
    angle=(math.pi/180)*angle
    a1=angle
    #sum=1.0000000
    s1=1
    for j in range((n-1)/2):
        s1+=2*math.cos(angle)
        angle+=a1
    print s1