The statement of this problem is the same as the statement of problem C1. 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 $2 \cdot n$ 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 $T$ ($1 \le T \le 200$) — the number of test cases.

Next $T$ lines contain descriptions of test cases — one per line. Each line contains single odd integer $n$ ($3 \le n \le 199$). 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
3
5
199

Output
1.931851653
3.196226611
126.687663595

```python

USER_FILENAME = "<user_code>"
import sys, json, builtins
import math, heapq, bisect, itertools, functools, collections, statistics, fractions, decimal, operator, array, random, re, string, os, pathlib
try:
    import resource as _res
except Exception:
    _res = None
from collections import Counter, defaultdict, deque, OrderedDict
from functools import lru_cache, reduce
from itertools import accumulate, permutations, combinations, product
from math import gcd, ceil, floor, sqrt
from decimal import Decimal
try:
    from typing import *
except Exception:
    pass
try:
    sys.setrecursionlimit(1_000_000)
except Exception:
    pass
try:
    import site as _site
    try:
        _sys_sites = _site.getsitepackages() if hasattr(_site, "getsitepackages") else []
        for _p in _sys_sites:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
    try:
        _usp = _site.getusersitepackages()
        if isinstance(_usp, str):
            _usp = [_usp]
        for _p in _usp:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
except Exception:
    pass

ns = {"__name__": "__main__"}
for _k, _v in list(globals().items()):
    if not _k.startswith("_"):
        ns[_k] = _v
_CODE = '\n\n# for n in range(3, 200, 2):\n\n#     N = 2 * n\n\n#     alpha = (2 * pi) / (2 * n)\n#     beta = (pi - alpha) / 2\n\n#     L = sin(beta) / sin(alpha)\n\n#     ans = 10 ** 10\n#     MAX = 1000\n#     for i in range(MAX):\n#         t0 = alpha * i / MAX\n\n#         xx = []\n#         yy = []\n#         for i in range(N):\n#             t = alpha * i + t0\n#             x, y = L * cos(t), L * sin(t)\n#             xx.append(x)\n#             yy.append(y)\n\n#         tmpr = max(max(xx) - min(xx), max(yy) - min(yy))\n#         ans = min(ans, tmpr)\n\n#     print(f"{n} : {ans},")\n\n\nans = {3: 1.931851652578137,\n       5: 3.1962266107498305,\n       7: 4.465702135190254,\n       9: 5.736856622834928,\n       11: 7.00877102284205,\n       13: 8.281093789118495,\n       15: 9.553661304648701,\n       17: 10.826387080174316,\n       19: 12.099221090606225,\n       21: 13.372132387773904,\n       23: 14.64510079714694,\n       25: 15.918112604548812,\n       27: 17.191158161652254,\n       29: 18.464230483075124,\n       31: 19.737324386897843,\n       33: 21.010435947900465,\n       35: 22.283562138356153,\n       37: 23.556700585376017,\n       39: 24.829849402946724,\n       41: 26.10300707314532,\n       43: 27.376172360514047,\n       45: 28.649344249275092,\n       47: 29.922521896579926,\n       49: 31.195704597210476,\n       51: 32.46889175658776,\n       53: 33.742082869893075,\n       55: 35.015277505745324,\n       57: 36.28847529331536,\n       59: 37.561675912061524,\n       61: 38.8348790834848,\n       63: 40.10808456445453,\n       65: 41.38129214176658,\n       67: 42.65450162767617,\n       69: 43.927712856207805,\n       71: 45.20092568008886,\n       73: 46.47413996818731,\n       75: 47.747355603359544,\n       77: 49.02057248063344,\n       79: 50.29379050566765,\n       81: 51.56700959343902,\n       83: 52.84022966711982,\n       85: 54.1134506571136,\n       87: 55.386672500223845,\n       89: 56.659895138934914,\n       91: 57.93311852078775,\n       93: 59.20634259783608,\n       95: 60.47956732617132,\n       97: 61.75279266550647,\n       99: 63.026018578810074,\n       101: 64.29924503198401,\n       103: 65.57247199357865,\n       105: 66.84569943454059,\n       107: 68.11892732798874,\n       109: 69.39215564901495,\n       111: 70.66538437450639,\n       113: 71.93861348298648,\n       115: 73.21184295447279,\n       117: 74.4850727703492,\n       119: 75.75830291325114,\n       121: 77.03153336696215,\n       123: 78.3047641163205,\n       125: 79.57799514713487,\n       127: 80.85122644610789,\n       129: 82.12445800076682,\n       131: 83.39768979940062,\n       133: 84.67092183100281,\n       135: 85.94415408521901,\n       137: 87.21738655229956,\n       139: 88.49061922305593,\n       141: 89.76385208882093,\n       143: 91.0370851414123,\n       145: 92.31031837309914,\n       147: 93.58355177657134,\n       149: 94.85678534491129,\n       151: 96.13001907156787,\n       153: 97.40325295033253,\n       155: 98.67648697531708,\n       157: 99.94972114093346,\n       159: 101.22295544187476,\n       161: 102.49618987309775,\n       163: 103.76942442980673,\n       165: 105.04265910743855,\n       167: 106.31589390164861,\n       169: 107.58912880829797,\n       171: 108.8623638234414,\n       173: 110.13559894331603,\n       175: 111.40883416433105,\n       177: 112.68206948305792,\n       179: 113.95530489622139,\n       181: 115.22854040069092,\n       183: 116.50177599347283,\n       185: 117.77501167170294,\n       187: 119.04824743263957,\n       189: 120.32148327365705,\n       191: 121.5947191922398,\n       193: 122.86795518597636,\n       195: 124.14119125255439,\n       197: 125.41442738975526,\n       199: 126.68766359544964,\n       }\n\n\nT = int(input())\n\nfor t in range(T):\n    n = int(input())\n    print(ans[n])\n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 18257