1354_C2. Not So Simple Polygon Embedding_647
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 ⋅ 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 odd integer n (3 ≤ n ≤ 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
# Why do we fall ? So we can learn to pick ourselves up.

from math import pi,cos
t = int(input())
for _ in range(0,t):
    n = int(input())
    theta = pi/4
    delta = pi/n
    maxi,mini,x = 0,0,0
    for i in range(0,2*n):
        x += cos(theta)
        theta -= delta
        maxi = max(maxi,x)
        mini = min(mini,x)
    print(maxi-mini)









"""

3
3
5
199


"""
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.

### Description:
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 ⋅ 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 odd integer n (3 ≤ n ≤ 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

### Input:
3
3
5
199

### Output:
1.931851653
3.196226611
126.687663797


### Input:
99
3
5
7
9
11
13
15
17
19
21
23
25
27
29
31
33
35
37
39
41
43
45
47
49
51
53
55
57
59
61
63
65
67
69
71
73
75
77
79
81
83
85
87
89
91
93
95
97
99
101
103
105
107
109
111
113
115
117
119
121
123
125
127
129
131
133
135
137
139
141
143
145
147
149
151
153
155
157
159
161
163
165
167
169
171
173
175
177
179
181
183
185
187
189
191
193
195
197
199

### Output:
1.931851653
3.196226611
4.465702219
5.736856623
7.008771102
8.281093968
9.553661305
10.826387200
12.099221274
13.372132512
14.645100987
15.918112605
17.191158259
18.464230694
19.737324500
21.010436133
22.283562263
23.556700727
24.829849560
26.103007187
27.376172462
28.649344249
29.922522051
31.195704692
32.468891893
33.742082996
35.015277559
36.288475370
37.561676016
38.834879126
40.108084606
41.381292209
42.654501797
43.927712932
45.200925705
46.474140148
47.747355603
49.020572617
50.293790682
51.567009723
52.840229758
54.113450760
55.386672671
56.659895296
57.933118569
59.206342682
60.479567372
61.752792818
63.026018737
64.299245193
65.572472013
66.845699518
68.118927442
69.392155812
70.665384422
71.938613686
73.211842992
74.485072905
75.758303055
77.031533374
78.304764251
79.577995147
80.851226648
82.124458183
83.397689899
84.670921988
85.944154279
87.217386648
88.490619395
89.763852237
91.037085184
92.310318534
93.583551972
94.856785462
96.130019187
97.403253104
98.676487172
99.949721352
101.222955607
102.496189900
103.769424507
105.042659319
106.315894015
107.589128889
108.862363946
110.135599080
111.408834331
112.682069666
113.955304906
115.228540565
116.501776008
117.775011837
119.048247602
120.321483288
121.594719211
122.867955301
124.141191342
125.414427604
126.687663797


### Code:
# Why do we fall ? So we can learn to pick ourselves up.

from math import pi,cos
t = int(input())
for _ in range(0,t):
    n = int(input())
    theta = pi/4
    delta = pi/n
    maxi,mini,x = 0,0,0
    for i in range(0,2*n):
        x += cos(theta)
        theta -= delta
        maxi = max(maxi,x)
        mini = min(mini,x)
    print(maxi-mini)









"""

3
3
5
199


"""