10512 - 夜空繁星

高高的星空，簇簇闪耀的群星形态万千。一个星座(cluster)是一群连通的星组成的非空集合，所谓连通是指水平，垂直或者对角相邻。一个星座不能是另一个更大星座的一部分。 星座可以相似(similar)。如果两个星座有相同的形状，而且包括相同数目的星体，那么不管其方向性如何，就算相似。一般而言，星座可能的方向有八个，如图1所示。

图1 相似的八个星座

夜空可以表示为一份天体图(sky map)，它是一个由字符0和1组成的二维矩阵，字符1表示所在的位置有一颗星；字符0表示该位置上没有星。 任务 给定一份天体图，用同一个小写英文标识(mark)相似的所有星座。相似的星座必须用相同的字母标识为不同的字母。 标识一个星座，就是将其中各星体对应的字符1替换为相应的小写字母。

文件的前两行分别记录了天体图的宽度W、深度H。而天体图则是由接下来的H行表示，每行包括W个字符。

输出文件记录了天体图与文件STARRY.IN相似，不同之处在于，各个星座按照“任务”中的要求进行了标识(mark)。

Starry Night IOI 98 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 matrix of 0's and 1's. A cell contains the digit 1 if it has a star, and the digit 0 otherwise.

Given a sky map, mark all the clusters with lower case letters. Similar clusters must be marked with the same letter; non-similar clusters must be marked with different letters.

You mark a cluster with a lower case letter by replacing every 1 in the cluster by that lower case letter.

PROGRAM NAME: starry INPUT FORMAT The first two lines contain, respectively, the width W and the height H of a sky map. The sky map is given in the following H lines, of W characters each.

SAMPLE INPUT (file starry.in) 23 15 10001000000000010000000 01111100011111000101101 01000000010001000111111 00000000010101000101111 00000111010001000000000 00001001011111000000000 10000001000000000000000 00101000000111110010000 00001000000100010011111 00000001110101010100010 00000100110100010000000 00010001110111110000000 00100001110000000100000 00001000100001000100101 00000001110001000111000 In this case, the sky map has width 23 and height 15. Just to make it clearer, notice that this input file corresponds to the following picture of the sky.

Figure 2. Picture of the sky

OUTPUT FORMAT The output file contains the same map as the input file, except that the clusters are marked as described in Task.

There will generally be more than one way to label the clusters with letters. Your program should choose the labeling such that if the entire output file is read as a string, this string will be minimal in the lexicographical ordering.

SAMPLE OUTPUT (file starry.out) a000a0000000000b0000000 0aaaaa000ccccc000d0dd0d 0a0000000c000c000dddddd 000000000c0b0c000d0dddd 00000eee0c000c000000000 0000e00e0ccccc000000000 b000000e000000000000000 00b0f000000ccccc00a0000 0000f000000c000c00aaaaa 0000000ddd0c0b0c0a000a0 00000b00dd0c000c0000000 000g000ddd0ccccc0000000 00g0000ddd0000000e00000 0000b000d0000f000e00e0b 0000000ddd000f000eee000 This is one possible result for the sample input above. Notice that this output file corresponds to the following picture.

Figure 3. Picture with the clusters marked

Constraints 0 <= W (width of the sky map) <= 100 0 <= H (height of the sky map) <= 100 0 <= Number of clusters <= 500 0 <= Number of non-similar clusters <= 26 (a..z) 1 <= Number of stars per cluster <= 160