#include <stdio.h>

const int bit[21] = {1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288, 1048576};

void chmax(long long* a, long long b)
{
	if (*a < b) *a = b;
}

int main()
{
	int i, N, M, V[100001];
	char S[100001][21];
	scanf("%d %d", &N, &M);
	for (i = 1; i <= N; i++) scanf("%d", &(V[i]));
	for (i = 1; i <= N; i++) scanf("%s", S[i]);
	
	int j, k, l, sum[1048576] = {};
	for (i = 1; i <= N; i++) {
		for (j = 0, k = 0; j < M; j++) if (S[i][j] == 'x') k |= bit[j];
		sum[k] += V[i];
	}
	for (j = 0; j < M; j++) {
		for (k = bit[M] - 1, l = bit[M] - 1 - bit[j]; k >= 0; k--) {
			k &= l;
			sum[k] += sum[k ^ bit[j]];
		}
	}
	
	long long dp[1048576] = {}, tmp;
	for (k = 0; k < bit[M]; k++) {
		for (j = 0; j < M; j++) {
			if ((k & bit[j]) != 0) continue;
			tmp = sum[k ^ bit[j]] - sum[k];
			chmax(&(dp[k ^ bit[j]]), dp[k] + tmp * tmp);
		}
	}
	printf("%lld\n", dp[bit[M] - 1]);
	fflush(stdout);
	return 0;
}