#include <bits/stdc++.h>

using namespace std;

using int64 = long long;
//const int mod = 1e9 + 7;
const int mod = 998244353;

const int64 infll = (1LL << 62) - 1;
const int inf = (1 << 30) - 1;

struct IoSetup {
  IoSetup() {
    cin.tie(nullptr);
    ios::sync_with_stdio(false);
    cout << fixed << setprecision(10);
    cerr << fixed << setprecision(10);
  }
} iosetup;


template< typename T1, typename T2 >
ostream &operator<<(ostream &os, const pair< T1, T2 > &p) {
  os << p.first << " " << p.second;
  return os;
}

template< typename T1, typename T2 >
istream &operator>>(istream &is, pair< T1, T2 > &p) {
  is >> p.first >> p.second;
  return is;
}

template< typename T >
ostream &operator<<(ostream &os, const vector< T > &v) {
  for(int i = 0; i < (int) v.size(); i++) {
    os << v[i] << (i + 1 != v.size() ? " " : "");
  }
  return os;
}

template< typename T >
istream &operator>>(istream &is, vector< T > &v) {
  for(T &in: v) is >> in;
  return is;
}

template< typename T1, typename T2 >
inline bool chmax(T1 &a, T2 b) { return a < b && (a = b, true); }

template< typename T1, typename T2 >
inline bool chmin(T1 &a, T2 b) { return a > b && (a = b, true); }

template< typename T = int64 >
vector< T > make_v(size_t a) {
  return vector< T >(a);
}

template< typename T, typename... Ts >
auto make_v(size_t a, Ts... ts) {
  return vector< decltype(make_v< T >(ts...)) >(a, make_v< T >(ts...));
}

template< typename T, typename V >
typename enable_if< is_class< T >::value == 0 >::type fill_v(T &t, const V &v) {
  t = v;
}

template< typename T, typename V >
typename enable_if< is_class< T >::value != 0 >::type fill_v(T &t, const V &v) {
  for(auto &e: t) fill_v(e, v);
}

template< typename F >
struct FixPoint : F {
  FixPoint(F &&f) : F(forward< F >(f)) {}

  template< typename... Args >
  decltype(auto) operator()(Args &&... args) const {
    return F::operator()(*this, forward< Args >(args)...);
  }
};

template< typename F >
inline decltype(auto) MFP(F &&f) {
  return FixPoint< F >{forward< F >(f)};
}

#include <immintrin.h>

/**
 * @brief Superset Zeta/Moebius Transform SIMD (上位集合のゼータ/メビウス変換, SIMD)
 */
__attribute__((target("avx2")))
void superset_zeta_transform_simd(int *buf, int n) {
  assert((n & (n - 1)) == 0);
  for(int i = 1; i < n; i <<= 1) {
    for(int j = 0; j < n; j += i << 1) {
      if(i <= 2) {
        for(int k = 0; k < i; k++) {
          buf[j + k] += buf[j + k + i];
        }
      } else if(i == 4) {
        for(int k = 0; k < i; k += 4) {
          auto a = _mm_loadu_si128((__m128i * )(buf + j + k));
          auto b = _mm_loadu_si128((__m128i * )(buf + j + k + i));
          a = _mm_add_epi32(a, b);
          _mm_storeu_si128((__m128i * )(buf + j + k), a);
        }
      } else {
        for(int k = 0; k < i; k += 8) {
          auto a = _mm256_loadu_si256((__m256i * )(buf + j + k));
          auto b = _mm256_loadu_si256((__m256i * )(buf + j + k + i));
          a = _mm256_add_epi32(a, b);
          _mm256_storeu_si256((__m256i * )(buf + j + k), a);
        }
      }
    }
  }
}

int dp2[20][1 << 20];

int main() {
  int N, M;
  cin >> N >> M;
  vector< int > V(N);
  cin >> V;
  vector< int > T(N);
  for(int i = 0; i < N; i++) {
    string s;
    cin >> s;
    for(int j = 0; j < M; j++) {
      if(s[j] == 'x') {
        T[i] |= 1 << j;
      }
    }
  }
  for(int i = 0; i < N; i++) {
    for(int j = 0; j < M; j++) {
      if((~T[i] >> j) & 1) {
        dp2[j][T[i]] += V[i];
      }
    }
  }
  for(int i = 0; i < M; i++) {
    superset_zeta_transform_simd(dp2[i], (1 << M));
  }
  vector< int64 > dp(1 << M, -infll);
  dp[0] = 0;
  auto get_cost = [&](int bit, int p) {
    bit |= 1 << p;
    bit ^= (1 << M) - 1;
    return 1LL * dp2[p][bit] * dp2[p][bit];
  };
  for(int i = 0; i < (1 << M); i++) {
    for(int j = 0; j < M; j++) {
      if((~i >> j) & 1) {
        chmax(dp[i | (1 << j)], dp[i] + get_cost(i, j));
      }
    }
  }
  cout << dp.back() << "\n";
}