Print a multiplication table for all digits from 1 to a certain number.  

Input

An integer \(n \in \mathbb{N}_0\).

Output

A multiplication table for all digits from 1 to a \(n\). The labels on the rows are multiplied by the labels on the columns, and the result is shown in the cell that is on that row/column combination.

The width of each column corresponds to the width of the largest number in that column. Cells in a column are right aligned. Columns are separated by a single space.

Example

Input:

3

Output:

  | 1 2 3
=========
1 | 1 2 3
2 | 2 4 6
3 | 3 6 9

Example

Input:

8

Output:

  | 1  2  3  4  5  6  7  8
==========================
1 | 1  2  3  4  5  6  7  8
2 | 2  4  6  8 10 12 14 16
3 | 3  6  9 12 15 18 21 24
4 | 4  8 12 16 20 24 28 32
5 | 5 10 15 20 25 30 35 40
6 | 6 12 18 24 30 36 42 48
7 | 7 14 21 28 35 42 49 56
8 | 8 16 24 32 40 48 56 64

Example

Input:

16

Output:

   |  1  2  3  4  5  6   7   8   9  10  11  12  13  14  15  16
==============================================================
 1 |  1  2  3  4  5  6   7   8   9  10  11  12  13  14  15  16
 2 |  2  4  6  8 10 12  14  16  18  20  22  24  26  28  30  32
 3 |  3  6  9 12 15 18  21  24  27  30  33  36  39  42  45  48
 4 |  4  8 12 16 20 24  28  32  36  40  44  48  52  56  60  64
 5 |  5 10 15 20 25 30  35  40  45  50  55  60  65  70  75  80
 6 |  6 12 18 24 30 36  42  48  54  60  66  72  78  84  90  96
 7 |  7 14 21 28 35 42  49  56  63  70  77  84  91  98 105 112
 8 |  8 16 24 32 40 48  56  64  72  80  88  96 104 112 120 128
 9 |  9 18 27 36 45 54  63  72  81  90  99 108 117 126 135 144
10 | 10 20 30 40 50 60  70  80  90 100 110 120 130 140 150 160
11 | 11 22 33 44 55 66  77  88  99 110 121 132 143 154 165 176
12 | 12 24 36 48 60 72  84  96 108 120 132 144 156 168 180 192
13 | 13 26 39 52 65 78  91 104 117 130 143 156 169 182 195 208
14 | 14 28 42 56 70 84  98 112 126 140 154 168 182 196 210 224
15 | 15 30 45 60 75 90 105 120 135 150 165 180 195 210 225 240
16 | 16 32 48 64 80 96 112 128 144 160 176 192 208 224 240 256