IOI '98 - Setúbal, Portugal
High up in the night sky, the shining stars appear in clusters of various shapes. A cluster is a non-empty group of neighbouring stars, adjacent in horizontal, vertical or diagonal direction. A cluster cannot be a part of a larger cluster.
Clusters may be similar. Two clusters are similar if they have the same shape and number of stars, irrespective of their orientation. In general, the number of possible orientations for a cluster is eight, as Figure 1 exemplifies.
Figure 1. Eight similar clusters
The night sky is represented by a sky map, which is a two-dimensional
1's. A cell contains the digit
1 if it has a star, and
Given a sky map, mark all the clusters ~(0 \le~ number of clusters ~\le 500)~
with lower case letters. Similar clusters must be marked with the same
letter; non-similar clusters ~(0 \le~ number of non-similar clusters ~\le 26)~
must be marked with different letters (
z). You mark a cluster
with a lower case letter by replacing every
1 in the cluster by that
lower case letter. The number of stars per cluster will be between ~1~ and
The first two lines of input contain, respectively, the width ~W~ and the height ~H~ ~(0 \le W, H \le 100)~ of a sky map. The sky map is given in the following ~H~ lines, of ~W~ characters each.
The output contains the same map as the input, except that the clusters are marked as described above. Your program should choose the labeling such that if the entire output is read as a string, this string will be minimal in the lexicographical ordering.
23 15 10001000000000010000000 01111100011111000101101 01000000010001000111111 00000000010101000101111 00000111010001000000000 00001001011111000000000 10000001000000000000000 00101000000111110010000 00001000000100010011111 00000001110101010100010 00000100110100010000000 00010001110111110000000 00100001110000000100000 00001000100001000100101 00000001110001000111000
a000a0000000000b0000000 0aaaaa000ccccc000d0dd0d 0a0000000c000c000dddddd 000000000c0b0c000d0dddd 00000eee0c000c000000000 0000e00e0ccccc000000000 b000000e000000000000000 00b0f000000ccccc00a0000 0000f000000c000c00aaaaa 0000000ddd0c0b0c0a000a0 00000b00dd0c000c0000000 000g000ddd0ccccc0000000 00g0000ddd0000000e00000 0000b000d0000f000e00e0b 0000000ddd000f000eee000
In this case, the sky map has width 23 and height 15. Just to make it clearer, notice that this input corresponds to the following picture of the sky:
Figure 2. Picture of the sky
The output corresponds to the following picture:
Figure 3. Picture of the sky with clusters marked