题目描述
Probably you all are familiar with famous tiles problem in which you have to fill 2n size field using tiles of size 21. Now consider that same 2n size field is composed of 11 size cells. So there are total 2n cells in field. Now we will fill that field with tiles randomly. There would be
a number of ways in which we can fill that field using these tiles ( Actually in classic version of problem, we count the no of ways). Now assume that when a tile is
put vertically in the field (for example when tile is placed covering cell no (1,1) and (2,1)), it adds a weight of 1 unit each on both cells. But when a tile is
placed horizontally ( for example when tile is placed covering cell no (1,1) and (1,2)), it doesn't add any weight on any cell. Now as you know there are a lot of
ways to fill a 2n size field, in some ways there can be weight on some particular cell, in some other ways there might not be weight on that particular cell
(depending upon whether the tile covering that particular cell is horizontal or vertical). So there will be some expected value of weight on every cell when you will
fill a 2*n size field randomly. You have to calculate expected value of weight on every cell and find their sum. So you will be given 'n' in input and you have to output desired
sum of expected value of weight on each cell.
Ex: If n=2, then there are two ways to arrange tiles. In one way both tiles will be horizontal and in other both are vertical. Let four cells are
(1,1), (1,2), (2,1), (2,2). So in first method there will be '0' weight on each cell and in second there will be '1' weight on each cell. So for every cell
expected value of weight is 0.5 , so sum of all four cell will be 0.5 * 4 = 2.
Input: First line will contain 't', number of test cases. 't' lines follow, each containing value of n.
Output: For each test case output the sum of expected weight on each cell (answer must be correct upto 6 decimal places).
Constraints:
1 ≤ t ≤ 1000
1 ≤ n ≤ 50
SAMPLE INPUT
4
1
2
3
4
SAMPLE OUTPUT
2.000000
2.000000
3.333333
4.000000
输入格式
见题面
输出格式
见题面
样例输入
1000
36
32
13
9
7
49
9
9
15
2
44
39
42
32
34
37
44
29
40
41
14
16
24
1
32
39
27
24
47
49
29
12
44
38
27
49
6
28
1
9
34
18
25
35
10
47
24
19
6
35
32
26
16
33
45
13
30
8
30
24
30
44
21
4
30
4
31
36
45
38
49
10
43
36
24
14
14
45
14
28
33
40
41
24
10
24
16
2
4
1
8
28
23
14
47
16
46
24
41
1
1
10
14
29
18
37
13
11
34
44
33
22
15
16
21
4
18
8
12
14
36
45
40
22
4
46
30
23
7
26
26
6
30
11
1
26
47
47
17
35
15
2
22
9
25
16
43
34
1
18
34
27
24
39
4
41
18
15
27
43
9
7
33
7
24
14
23
43
20
36
38
40
17
9
45
40
38
49
41
9
30
29
37
26
14
33
20
44
10
49
9
44
50
4
30
5
3
42
47
48
7
19
2
11
18
12
39
10
38
10
5
2
9
33
38
44
37
1
21
35
4
12
45
1
8
23
45
29
41
22
3
36
48
7
25
7
10
29
17
11
47
49
14
31
46
8
40
25
19
47
7
35
42
4
41
19
45
4
43
4
8
1
4
13
10
20
11
50
49
42
28
28
49
32
7
27
24
3
40
24
37
34
21
17
49
46
44
14
21
43
18
29
38
15
43
17
27
44
27
43
9
8
33
40
48
30
43
13
30
19
7
22
20
7
48
7
28
44
8
30
12
19
49
20
1
14
17
11
2
2
7
45
47
50
33
5
43
37
9
7
32
15
50
16
6
35
29
22
21
8
31
40
25
33
25
15
32
23
49
20
50
22
32
32
31
16
1
46
31
27
31
25
13
11
5
42
3
17
29
24
31
19
12
12
33
10
27
5
45
20
34
30
17
16
21
21
18
18
19
40
14
33
41
24
39
19
13
4
35
32
6
6
44
7
48
4
10
1
24
1
40
47
11
24
5
34
30
42
25
25
24
15
3
21
31
25
8
39
5
13
24
3
3
17
10
27
37
28
29
5
45
45
45
7
6
11
7
45
47
38
20
41
47
41
12
44
14
27
50
35
38
42
41
41
26
23
33
50
21
31
8
15
7
28
28
16
4
43
19
22
28
8
39
6
23
35
35
10
12
21
27
15
9
44
37
15
18
31
27
37
31
12
17
16
1
29
13
47
29
22
2
7
3
36
11
31
31
40
50
11
39
29
1
1
38
15
32
9
1
11
42
32
25
27
42
43
47
26
32
44
49
25
50
12
29
29
37
30
36
11
33
44
13
17
34
17
18
12
27
27
46
28
43
31
30
47
18
4
46
6
42
33
1
41
20
37
33
7
13
17
15
14
27
25
12
46
35
47
3
22
40
46
38
25
24
22
34
1
7
41
16
38
18
47
2
35
4
15
39
39
36
49
49
11
20
21
19
5
10
21
18
43
1
12
18
41
18
43
33
15
12
47
45
14
38
36
38
20
10
2
20
46
50
46
13
8
37
8
28
10
18
45
47
33
24
37
33
20
50
18
43
26
30
42
43
24
5
21
21
2
8
38
12
20
17
35
19
6
19
24
18
8
32
39
29
47
44
24
37
44
14
7
6
32
39
8
12
21
45
12
38
15
39
36
25
26
13
46
38
35
16
34
14
38
8
30
29
48
1
9
27
1
4
40
39
28
36
18
49
14
44
33
13
40
3
9
41
43
46
9
49
17
34
36
29
16
16
29
2
32
8
1
37
21
10
3
49
17
16
46
50
30
38
33
47
16
5
25
30
42
24
29
35
39
41
30
50
25
27
4
11
38
11
10
47
36
22
33
1
31
38
21
7
1
50
46
49
47
30
36
43
39
37
42
9
45
7
21
38
36
40
37
24
45
1
16
36
2
49
35
15
49
9
41
4
44
46
42
32
12
44
18
16
48
26
42
2
48
28
33
46
37
43
17
36
2
36
36
1
17
43
2
20
26
9
38
28
46
9
9
3
20
47
12
10
42
25
4
39
47
24
28
33
25
3
4
45
43
8
6
20
13
41
16
3
28
41
35
26
47
40
24
41
41
19
49
28
40
39
46
50
42
42
19
33
7
16
8
47
24
21
50
17
13
33
9
5
3
29
6
33
10
37
34
15
24
10
30
46
20
23
18
42
8
28
24
1
21
32
43
21
4
49
11
21
4
34
16
11
38
27
27
30
43
48
21
21
26
32
22
32
9
7
5
26
50
12
44
1
31
47
26
40
8
29
50
4
46
46
43
47
4
23
43
33
3
35
21
42
37
样例输出
43.426932
23.749534
2.000000
9.438202
23.749534
19.277398
8.545455
8.545455
5.000000
38.954796
30.904952
23.749534
13.910841
29.116097
2.000000
28.221670
14.805260
9.438202
5.846154
6.761905
30.010524
37.165942
11.227468
6.761905
24.643961
43.426932
21.960680
29.116097
5.000000
45.215787
10.333333
39.849224
36.271515
28.221670
16.594116
3.333333
27.327243
24.643961
14.805260
29.116097
39.849224
24.643961
31.799379
44.321360
4.000000
40.743651
15.699690
18.382971
4.000000
28.221670
28.221670
5.000000
30.010524
42.532505
28.221670
3.333333
13.910841
34.482660
18.382971
28.221670
37.165942
25.538389
2.000000
8.545455
44.321360
24.643961
33.588233
18.382971
7.647059
44.321360
29.116097
38.060369
16.594116
13.016393
35.377088
14.805260
10.333333
42.532505
19.277398
8.545455
10.333333
2.000000
2.000000
4.000000
20.171825
32.693806
30.904952
36.271515
37.165942
20.171825
11.227468
21.066253
5.000000
34.482660
22.855107
5.846154
24.643961
5.846154
9.438202
20.171825
45.215787
10.333333
38.060369
45.215787
3.333333
5.846154
7.647059
25.538389
22.855107
15.699690
38.060369
7.647059
29.116097
14.805260
17.488544
28.221670
21.960680
9.438202
34.482660
31.799379
6.761905
17.488544
30.904952
23.749534
7.647059
30.904952
4.000000
4.000000
38.060369
15.699690
26.432816
2.000000
41.638078
41.638078
35.377088
43.426932
38.954796
20.171825
32.693806
29.116097
10.333333
21.960680
15.699690
10.333333
12.122016
39.849224
2.000000
13.016393
44.321360
45.215787
41.638078
7.647059
15.699690
20.171825
17.488544
33.588233
45.215787
42.532505
9.438202
3.333333
3.333333
45.215787
15.699690
21.960680
23.749534
24.643961
24.643961
27.327243
36.271515
23.749534
22.855107
38.060369
16.594116
37.165942
39.849224
22.855107
18.382971
13.016393
23.749534
39.849224
38.954796
21.960680
14.805260
37.165942
27.327243
27.327243
9.438202
32.693806
43.426932
10.333333
4.000000
32.693806
13.910841
33.588233
6.761905
8.545455
18.382971
15.699690
21.960680
18.382971
24.643961
33.588233
7.647059
5.000000
2.000000
15.699690
35.377088
38.060369
19.277398
21.960680
42.532505
42.532505
5.000000
21.066253
8.545455
29.116097
9.438202
14.805260
24.643961
30.904952
7.647059
7.647059
43.426932
17.488544
25.538389
28.221670
37.165942
17.488544
42.532505
5.000000
37.165942
36.271515
6.761905
15.699690
25.538389
30.010524
30.010524
8.545455
20.171825
2.000000
19.277398
3.333333
44.321360
29.116097
37.165942
12.122016
2.000000
28.221670
2.000000
40.743651
3.333333
41.638078
32.693806
32.693806
38.954796
15.699690
20.171825
40.743651
24.643961
36.271515
9.438202
3.333333
33.588233
13.016393
37.165942
44.321360
5.846154
2.000000
35.377088
13.910841
39.849224
22.855107
43.426932
42.532505
23.749534
17.488544
19.277398
4.000000
42.532505
45.215787
21.960680
35.377088
28.221670
39.849224
24.643961
21.066253
33.588233
7.647059
30.010524
28.221670
45.215787
43.426932
17.488544
41.638078
10.333333
41.638078
21.066253
39.849224
23.749534
5.846154
42.532505
34.482660
15.699690
16.594116
41.638078
40.743651
18.382971
45.215787
4.000000
6.761905
25.538389
31.799379
13.910841
24.643961
15.699690
7.647059
42.532505
29.116097
38.954796
36.271515
28.221670
42.532505
33.588233
26.432816
43.426932
23.749534
38.060369
6.761905
44.321360
42.532505
27.327243
3.333333
8.545455
6.761905
44.321360
45.215787
41.638078
41.638078
13.910841
8.545455
17.488544
12.122016
5.000000
44.321360
13.910841
38.954796
11.227468
9.438202
38.954796
5.846154
13.016393
33.588233
7.647059
13.016393
13.910841
33.588233
13.016393
25.538389
34.482660
28.221670
18.382971
31.799379
24.643961
17.488544
21.066253
5.000000
23.749534
35.377088
13.910841
17.488544
5.000000
18.382971
30.904952
45.215787
13.910841
29.116097
2.000000
43.426932
8.545455
23.749534
5.000000
38.060369
29.116097
26.432816
25.538389
18.382971
44.321360
23.749534
30.010524
9.438202
15.699690
19.277398
21.066253
18.382971
29.116097
7.647059
42.532505
24.643961
24.643961
5.000000
10.333333
38.954796
45.215787
29.116097
28.221670
32.693806
38.060369
42.532505
5.846154
9.438202
13.016393
38.954796
33.588233
25.538389
7.647059
36.271515
3.333333
13.016393
3.333333
13.016393
6.761905
3.333333
11.227468
25.538389
30.010524
35.377088
21.960680
25.538389
21.066253
21.066253
11.227468
28.221670
20.171825
3.333333
2.000000
28.221670
44.321360
45.215787
11.227468
2.000000
23.749534
4.000000
13.016393
30.904952
16.594116
22.855107
13.910841
13.016393
17.488544
17.488544
3.333333
30.904952
24.643961
25.538389
41.638078
14.805260
38.060369
34.482660
24.643961
14.805260
39.849224
13.910841
28.221670
27.327243
9.438202
7.647059
37.165942
43.426932
27.327243
23.749534
30.904952
16.594116
14.805260
10.333333
2.000000
19.277398
39.849224
18.382971
33.588233
20.171825
9.438202
13.016393
2.000000
2.000000
33.588233
30.010524
6.761905
17.488544
41.638078
16.594116
8.545455
38.060369
38.954796
4.000000
30.904952
18.382971
35.377088
38.060369
8.545455
31.799379
2.000000
3.333333
35.377088
34.482660
45.215787
5.000000
18.382971
5.000000
42.532505
20.171825
45.215787
34.482660
33.588233
2.000000
12.122016
2.000000
28.221670
3.333333
23.749534
30.010524
28.221670
37.165942
30.904952
7.647059
17.488544
9.438202
41.638078
13.016393
8.545455
9.438202
38.954796
21.066253
26.432816
45.215787
37.165942
13.016393
3.333333
12.122016
4.000000
5.846154
28.221670
14.805260
28.221670
14.805260
6.761905
25.538389
27.327243
25.538389
9.438202
14.805260
24.643961
34.482660
40.743651
20.171825
8.545455
43.426932
25.538389
11.227468
36.271515
38.060369
21.960680
12.122016
6.761905
7.647059
25.538389
4.000000
41.638078
17.488544
4.000000
6.761905
15.699690
36.271515
44.321360
38.060369
42.532505
23.749534
32.693806
10.333333
5.846154
13.016393
21.960680
6.761905
31.799379
12.122016
29.116097
16.594116
31.799379
29.116097
39.849224
42.532505
26.432816
13.016393
20.171825
4.000000
41.638078
16.594116
32.693806
25.538389
6.761905
21.066253
34.482660
29.116097
16.594116
37.165942
25.538389
44.321360
24.643961
20.171825
5.846154
36.271515
36.271515
16.594116
27.327243
2.000000
26.432816
16.594116
27.327243
26.432816
26.432816
36.271515
7.647059
9.438202
37.165942
21.960680
30.010524
41.638078
42.532505
16.594116
26.432816
10.333333
4.000000
24.643961
19.277398
36.271515
23.749534
7.647059
27.327243
38.954796
11.227468
5.846154
32.693806
17.488544
23.749534
18.382971
34.482660
29.116097
19.277398
13.910841
3.333333
23.749534
13.016393
34.482660
4.000000
29.116097
13.016393
45.215787
15.699690
23.749534
22.855107
14.805260
42.532505
41.638078
22.855107
28.221670
37.165942
20.171825
5.846154
5.000000
19.277398
33.588233
20.171825
25.538389
16.594116
30.010524
31.799379
42.532505
36.271515
4.000000
30.904952
9.438202
2.000000
3.333333
27.327243
6.761905
27.327243
21.960680
13.910841
2.000000
22.855107
17.488544
8.545455
33.588233
21.960680
3.333333
39.849224
33.588233
23.749534
10.333333
16.594116
40.743651
30.904952
15.699690
17.488544
20.171825
38.060369
14.805260
30.904952
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