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 numpy as np
t = int(input())

def solve():
    ans = [1.0, 1.0000000000048965, 2.000000000005654, 2.414213562381454, 3.2360679775095433, 3.73205080758106, 4.4939592074487065, 5.027339492141929, 5.758770483161403, 6.313751514695053, 7.026674183354025, 7.595754112749101, 8.29622981058449, 8.875245474997657, 9.56677223353534, 10.153170387640715, 10.83795144749311, 11.430052302797156, 12.10956558547868, 12.706204736214477, 13.38148999969639, 13.981826955149476, 14.65364354363252, 15.257051688313236, 15.925971109958237, 16.53197076510891, 17.1984339577779, 17.806649745405885, 18.471004054789297, 19.0811366877878, 19.743660615389683, 20.355467625050743, 21.016387900550605, 21.629670104788527, 22.289173773542153, 22.903765548502687, 23.562008724905073, 24.177770865014228, 24.834885197906797, 25.451699579436504, 26.107797111705136, 26.725562639335852, 27.380739517752733, 27.9993690008772, 28.653708347933108, 29.273126061965474, 29.92670022707008, 30.546839987039345, 31.199712331397585, 31.82051595387322, 32.47274228036004, 33.09415834339747, 33.74578805293073, 34.36777088731738, 35.0188479222017, 35.64135678408649, 36.291920403753814, 36.91491879087618, 37.565004214534554, 38.18845929714471, 38.838098239830416, 39.461980383962505, 40.111201506533725, 40.73548387221034, 41.384313161347464, 42.0089713620117, 42.65743245289564, 43.28244426520461, 43.9305587169463, 44.55590383224541, 45.20369136413321, 45.829351174627455, 46.476829869696715, 47.10278728366355, 47.74997376486666, 48.37621304630207, 49.023122629588784, 49.64962925850936, 50.29627608635629, 50.92303663664432, 51.56943379495564, 52.19643582716821, 52.84259544797215, 53.469827414966986, 54.11576076693036, 54.743211930512274, 55.38892949896682, 56.0165898560456, 56.662101413951746, 57.289961630938045, 57.93527630199021, 58.56332765635062, 59.208453971245895, 59.83668829929967, 60.48163424603983, 61.110043896213945, 61.75481696518434, 62.3833947560562, 63.028001980519, 63.65674116307005, 64.30118915562062, 64.93008337920367, 65.57437836466343, 66.20342164625373, 66.84756949140973, 67.47675618776674, 68.12076242831363, 68.75008721072905, 69.39395707572348, 70.02341490707228, 70.6671533411706, 71.2967394550178, 71.94035113873356, 72.57006102027937, 73.21355038846873, 73.84337975714152, 74.48675101589933, 75.11669580942811, 75.75995295155589, 76.3900093113742, 77.0331561305625, 77.66332038841212, 78.30636049226318, 78.9366291578812, 79.57956597988435, 80.2099357296704, 80.85277254022901, 81.48324020680019, 82.12598012339951, 82.756542685951, 83.39918868254566, 84.0298432579436, 84.67239817363554, 85.30314200817628, 85.94560855524675, 86.57643901702374, 87.2188197883759, 87.8497343602011, 88.49203183626462, 89.12302810909664, 89.76524466424017, 90.39632033107661, 91.03845823956982, 91.66961108976457, 92.3116725313268, 92.94290044529772, 93.58488751026762, 94.21618845456244, 94.85810314871894, 95.48947517141106, 96.13131942047373, 96.76276064686152, 97.4045363006953, 98.03604492928136, 98.67775376582894, 99.30932806455758, 99.9509717935203, 100.5826100962538, 101.22419036253973, 101.8558910657554, 102.49740945271263, 103.12917101240386, 103.77062904485462, 104.40244997362159, 105.04384912071146, 105.67572798502741, 106.31706966290345, 106.94900508054405, 107.59029065487361, 108.22228129249767, 108.86351208083968, 109.49555665171101, 110.13673392574913, 110.76883118758951, 111.40995617523765, 112.04210492820204, 112.68317881559018, 113.3153779003559, 113.95640183370472, 114.58865012966683, 115.22962521705821, 115.86192164062473, 116.50284895367524, 117.13519245665456, 117.77607303209827, 118.40846260017386, 119.04929744135981, 119.68173209264604, 120.32252217095677, 120.95500095463099, 121.5957472108259, 122.22826920583165, 122.86897255132116, 123.50153686513869, 124.14219818319216, 124.77480395067161, 125.41542409756433, 126.04807047981775, 126.68865028591975, 127.32133646926904]
    n = int(input())
    return ans[n-1]

ans = []
for i in range(t):
    ans.append(solve())

for a in ans:
    print(a)