Problem:
Problem B: The Sorcerer's Donut

Your master went to the town for a day. You could have a relaxed day without hearing his
scolding. But he ordered you to make donuts dough by the evening. Loving donuts so much, he
can't live without eating tens of donuts everyday. What a chore for such a beautiful day.

But last week, you overheard a magic spell that your master was using. It was the time to
try. You casted the spell on a broomstick sitting on a corner of the kitchen. With a flash of
lights, the broom sprouted two arms and two legs, and became alive. You ordered him, then he
brought flour from the storage, and started kneading dough. The spell worked, and how fast he
kneaded it!

A few minutes later, there was a tall pile of dough on the kitchen table. That was enough for
the next week. \OK, stop now." You ordered. But he didn't stop. Help! You didn't know the
spell to stop him! Soon the kitchen table was filled with hundreds of pieces of dough, and he
still worked as fast as he could. If you could not stop him now, you would be choked in the
kitchen filled with pieces of dough.

Wait, didn't your master write his spells on his notebooks? You went to his den, and found the
notebook that recorded the spell of cessation.

But it was not the end of the story. The spell written in the notebook is not easily read by
others. He used a plastic model of a donut as a notebook for recording the spell. He split the
surface of the donut-shaped model into square mesh (Figure B.1), and filled with the letters
(Figure B.2). He hid the spell so carefully that the pattern on the surface looked meaningless.
But you knew that he wrote the pattern so that the spell "appears" more than once (see the next
paragraph for the precise conditions). The spell was not necessarily written in the left-to-right
direction, but any of the 8 directions, namely left-to-right, right-to-left, top-down, bottom-up,
and the 4 diagonal directions.

You should be able to find the spell as the longest string that appears more than once. Here,
a string is considered to appear more than once if there are square sequences having the string
on the donut that satisfy the following conditions.

Each square sequence does not overlap itself. (Two square sequences can share some squares.)

The square sequences start from different squares, and/or go to different directions.

Figure B.1: The Sorcerer's Donut Before
Filled with Letters, Showing the Mesh and 8
Possible Spell Directions

Figure B.2: The Sorcerer's Donut After Filled
with Letters

Note that a palindrome (i.e., a string that is the same whether you read it backwards or forwards)
that satisfies the first condition "appears" twice.

The pattern on the donut is given as a matrix of letters as follows.

ABCD
EFGH
IJKL

Note that the surface of the donut has no ends; the top and bottom sides, and the left and right
sides of the pattern are respectively connected. There can be square sequences longer than both
the vertical and horizontal lengths of the pattern. For example, from the letter F in the above
pattern, the strings in the longest non-self-overlapping sequences towards the 8 directions are
as follows.

FGHE
FKDEJCHIBGLA
FJB
FIDGJAHKBELC
FEHG
FALGBIHCJEDK
FBJ
FCLEBKHAJGDI

Please write a program that finds the magic spell before you will be choked with pieces of donuts
dough.

Input

The input is a sequence of datasets. Each dataset begins with a line of two integers h and w,
which denote the size of the pattern, followed by h lines of w uppercase letters from A to Z,
inclusive, which denote the pattern on the donut. You may assume 3 ≤ h ≤ 10 and 3 ≤ w ≤ 20.

The end of the input is indicated by a line containing two zeros.

Output

For each dataset, output the magic spell. If there is more than one longest string of the same
length, the first one in the dictionary order must be the spell. The spell is known to be at least
two letters long. When no spell is found, output 0 (zero).

Sample Input

5 7
RRCABXT
AABMFAB
RROMJAC
APTADAB
YABADAO
3 13
ABCDEFGHIJKLM
XMADAMIMADAMY
ACEGIKMOQSUWY
3 4
DEFG
ACAB
HIJK
3 6
ABCDEF
GHIAKL
MNOPQR
10 19
JFZODYDXMZZPEYTRNCW
XVGHPOKEYNZTQFZJKOD
EYEHHQKHFZOVNRGOOLP
QFZOIHRQMGHPNISHXOC
DRGILJHSQEHHQLYTILL
NCSHQMKHTZZIHRPAUJA
NCCTINCLAUTFJHSZBVK
LPBAUJIUMBVQYKHTZCW
XMYHBVKUGNCWTLLAUID
EYNDCCWLEOODXYUMBVN
0 0

Output for the Sample Input

ABRACADABRA
MADAMIMADAM
ABAC
0
ABCDEFGHIJKLMNOPQRSTUVWXYZHHHHHABCDEFGHIJKLMNOPQRSTUVWXYZ

Solution in C (judge verdict: Accepted)

#include <stdio.h>
#include <string.h>
#define HASHTABLE_SIZE 2000
#define SPELL_LENGTH 191
#define NULL_INDEX -1

char hashtable[HASHTABLE_SIZE][SPELL_LENGTH+1]; /* 配列から取り出せる全ての文字列 */
int flag[HASHTABLE_SIZE];
int maxl, maxi;

/* 文字列の最初の2文字からハッシュ値を求める */
int hash(const char* s) {
	int i, h = 0, a = 3141, b = 2718;
	for (i = 0; s[i] != '\0' && i < 2; i++, a = a * b % (HASHTABLE_SIZE - 1)) h = (a * h + s[i]) % HASHTABLE_SIZE;
	return h;
}

/* ハッシュ表を初期化する */
void init() {
	int i;
	for (i = 0; i < HASHTABLE_SIZE; i++) flag[i] = 0;
	maxl = 0;
}

int add(const char* s) {
	int i, j;
	/* これまでに追加した文字列と比較する */
	for (i = hash(s); flag[i]; i = (i + 1) % HASHTABLE_SIZE) {
		for (j = 0; s[j] != '\0' && hashtable[i][j] != '\0' && s[j] == hashtable[i][j]; j++);
		if (j > maxl) {
			/* 最も長い文字列 */
			maxl = j;
			maxi = i;
		} else if (j == maxl) {
			/* 長さが等しい場合は辞書順で最も若い文字列 */
			if (strncmp(s, hashtable[maxi], maxl) < 0) maxi = i;
		}
	}
	/* 新しい文字列を追加する */
	strncpy(hashtable[i], s, SPELL_LENGTH + 1);
	flag[i] = 1;
	return i;
}

int VECTOR[8][2] = {{0, 1}, {1, 1}, {1, 0}, {1, -1}, {0, -1}, {-1, -1}, {-1, 0}, {-1, 1}};

int main(void) {
	int h, w; /* 文字配列の大きさ */
	char data[10][20];
	int i, j, k;

	/* データセット毎の処理 */
	while (scanf("%d%d\n", &h, &w) == 2 && h >= 3 && h <= 10 && w >= 3 && w <= 20) {
		/* 文字配列を読み込む */
		for (i = 0; i < h; i++) for (j = 0; j < w; j++) {
			scanf("%c\n", &data[i][j]);
		}

		init(); /* 初期化 */

		/* 配列から取り出せる全ての文字列を探索する */
		for (i = 0; i < h; i++) for (j = 0; j < w; j++) /* 始点 */ for (k = 0; k < 8; k++) /* 方向 */ {
			/* 文字列を取り出す */
			int used[10*20] = {}; /* 配列中のある文字を使ったか */
			int ii = i, jj = j; /* 現在の参照位置 */
			char s[SPELL_LENGTH] = {}; /* 取り出した文字列 */
			int l; /* 長さ */
			for (l = 0; used[w*ii+jj] == 0; l++, ii = (h + ii + VECTOR[k][0]) % h, jj = (w + jj + VECTOR[k][1]) % w) {
				used[w*ii+jj] = 1;
				s[l] = data[ii][jj]; /* 1文字加える */
			}
			/* これまでに取り出した文字列と比較する */
			add(s);
		}

		/* 出力 */
		if (maxl < 2) {
			printf("0\n");
		} else {
			hashtable[maxi][maxl] = '\0';
			printf("%s\n", hashtable[maxi]);
		}
	}

	return 0;
}