Problem p03917 (C++)

Buggy submission (status: Runtime Error):
#include <bits/stdc++.h>

using namespace std;

using int64 = long long;
const int mod = 1e9 + 7;
const int inf = (1 << 30) - 1;
const int64 infll = (1LL << 61) - 1;

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

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 <int mod> struct ModInt {
  int x;

  ModInt() : x(0) {}

  ModInt(int64_t y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {}

  ModInt &operator+=(const ModInt &p) {
    if ((x += p.x) >= mod)
      x -= mod;
    return *this;
  }

  ModInt &operator-=(const ModInt &p) {
    if ((x += mod - p.x) >= mod)
      x -= mod;
    return *this;
  }

  ModInt &operator*=(const ModInt &p) {
    x = (int)(1LL * x * p.x % mod);
    return *this;
  }

  ModInt &operator/=(const ModInt &p) {
    *this *= p.inverse();
    return *this;
  }

  ModInt operator-() const { return ModInt(-x); }

  ModInt operator+(const ModInt &p) const { return ModInt(*this) += p; }

  ModInt operator-(const ModInt &p) const { return ModInt(*this) -= p; }

  ModInt operator*(const ModInt &p) const { return ModInt(*this) *= p; }

  ModInt operator/(const ModInt &p) const { return ModInt(*this) /= p; }

  bool operator==(const ModInt &p) const { return x == p.x; }

  bool operator!=(const ModInt &p) const { return x != p.x; }

  ModInt inverse() const {
    int a = x, b = mod, u = 1, v = 0, t;
    while (b > 0) {
      t = a / b;
      swap(a -= t * b, b);
      swap(u -= t * v, v);
    }
    return ModInt(u);
  }

  ModInt pow(int64_t n) const {
    ModInt ret(1), mul(x);
    while (n > 0) {
      if (n & 1)
        ret *= mul;
      mul *= mul;
      n >>= 1;
    }
    return ret;
  }

  friend ostream &operator<<(ostream &os, const ModInt &p) { return os << p.x; }

  friend istream &operator>>(istream &is, ModInt &a) {
    int64_t t;
    is >> t;
    a = ModInt<mod>(t);
    return (is);
  }

  static int get_mod() { return mod; }
};

using modint = ModInt<mod>;

struct UnionFind {
  vector<int> data;

  UnionFind(int sz) { data.assign(sz, -1); }

  bool unite(int x, int y) {
    x = find(x), y = find(y);
    if (x == y)
      return (false);
    if (data[x] > data[y])
      swap(x, y);
    data[x] += data[y];
    data[y] = x;
    return (true);
  }

  int find(int k) {
    if (data[k] < 0)
      return (k);
    return (data[k] = find(data[k]));
  }

  int size(int k) { return (-data[find(k)]); }
};

int main() {
  int H, W;
  cin >> H >> W;
  vector<string> S(H);
  cin >> S;
  modint mul = 1;
  for (int k = 0; k < 2; k++) {
    if (H % 2 == 1) {
      vector<string> P;
      int v = H / 2;
      for (int i = 0; i < H; i++) {
        if (v == i) {
          string U = S[i];
          reverse(begin(U), end(U));
          if (U != S[i])
            mul *= 2;
        } else {
          P.emplace_back(S[i]);
        }
      }
      S.swap(P);
      --H;
    }

    {
      swap(H, W);
      vector<string> Q(H);
      for (int i = 0; i < H; i++) {
        for (int j = 0; j < W; j++) {
          Q[i] += S[j][i];
        }
      }
      Q.swap(S);
    }
  }
  auto type = make_v<int>(H / 2, W / 2);
  UnionFind uf(H / 2 + W / 2);
  modint beet = 1;
  for (int i = 0; i < H / 2; i++) {
    for (int j = 0; j < W / 2; j++) {
      char V[] = {S[i][j], S[i][W - j - 1], S[H - i - 1][W - j - 1],
                  S[H - i - 1][j]};
      sort(V, V + 4);
      for (int k = 1; k < 3; k++) {
        type[i][j] |= V[k - 1] == V[k];
      }
      if (type[i][j]) {
        int sz = 0;
        do {
          ++sz;
        } while (next_permutation(V, V + 4));
        beet *= sz;
      } else {
        beet *= 12;
        uf.unite(i, j + W / 2);
      }
    }
  }
  int sz = 0;
  for (int i = 0; i < H / 2 + W / 2; i++) {
    if (uf.find(i) == i)
      sz++;
  }
  cout << modint(2).pow(H / 2 + W / 2 - sz) * beet * mul << endl;
}


Fixed submission:
#include <bits/stdc++.h>

using namespace std;

using int64 = long long;
const int mod = 1e9 + 7;
const int inf = (1 << 30) - 1;
const int64 infll = (1LL << 61) - 1;

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

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 <int mod> struct ModInt {
  int x;

  ModInt() : x(0) {}

  ModInt(int64_t y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {}

  ModInt &operator+=(const ModInt &p) {
    if ((x += p.x) >= mod)
      x -= mod;
    return *this;
  }

  ModInt &operator-=(const ModInt &p) {
    if ((x += mod - p.x) >= mod)
      x -= mod;
    return *this;
  }

  ModInt &operator*=(const ModInt &p) {
    x = (int)(1LL * x * p.x % mod);
    return *this;
  }

  ModInt &operator/=(const ModInt &p) {
    *this *= p.inverse();
    return *this;
  }

  ModInt operator-() const { return ModInt(-x); }

  ModInt operator+(const ModInt &p) const { return ModInt(*this) += p; }

  ModInt operator-(const ModInt &p) const { return ModInt(*this) -= p; }

  ModInt operator*(const ModInt &p) const { return ModInt(*this) *= p; }

  ModInt operator/(const ModInt &p) const { return ModInt(*this) /= p; }

  bool operator==(const ModInt &p) const { return x == p.x; }

  bool operator!=(const ModInt &p) const { return x != p.x; }

  ModInt inverse() const {
    int a = x, b = mod, u = 1, v = 0, t;
    while (b > 0) {
      t = a / b;
      swap(a -= t * b, b);
      swap(u -= t * v, v);
    }
    return ModInt(u);
  }

  ModInt pow(int64_t n) const {
    ModInt ret(1), mul(x);
    while (n > 0) {
      if (n & 1)
        ret *= mul;
      mul *= mul;
      n >>= 1;
    }
    return ret;
  }

  friend ostream &operator<<(ostream &os, const ModInt &p) { return os << p.x; }

  friend istream &operator>>(istream &is, ModInt &a) {
    int64_t t;
    is >> t;
    a = ModInt<mod>(t);
    return (is);
  }

  static int get_mod() { return mod; }
};

using modint = ModInt<mod>;

struct UnionFind {
  vector<int> data;

  UnionFind(int sz) { data.assign(sz, -1); }

  bool unite(int x, int y) {
    x = find(x), y = find(y);
    if (x == y)
      return (false);
    if (data[x] > data[y])
      swap(x, y);
    data[x] += data[y];
    data[y] = x;
    return (true);
  }

  int find(int k) {
    if (data[k] < 0)
      return (k);
    return (data[k] = find(data[k]));
  }

  int size(int k) { return (-data[find(k)]); }
};

int main() {
  int H, W;
  cin >> H >> W;
  vector<string> S(H);
  cin >> S;
  modint mul = 1;
  for (int k = 0; k < 2; k++) {
    if (H % 2 == 1) {
      vector<string> P;
      int v = H / 2;
      for (int i = 0; i < H; i++) {
        if (v == i) {
          string U = S[i];
          reverse(begin(U), end(U));
          if (U != S[i])
            mul *= 2;
        } else {
          P.emplace_back(S[i]);
        }
      }
      S.swap(P);
      --H;
    }

    {
      swap(H, W);
      vector<string> Q(H);
      for (int i = 0; i < H; i++) {
        for (int j = 0; j < W; j++) {
          Q[i] += S[j][i];
        }
      }
      Q.swap(S);
    }
  }
  auto type = make_v<int>(H / 2, W / 2);
  UnionFind uf(H / 2 + W / 2);
  modint beet = 1;
  for (int i = 0; i < H / 2; i++) {
    for (int j = 0; j < W / 2; j++) {
      char V[] = {S[i][j], S[i][W - j - 1], S[H - i - 1][W - j - 1],
                  S[H - i - 1][j]};
      sort(V, V + 4);
      for (int k = 1; k < 3; k++) {
        type[i][j] |= V[k - 1] == V[k];
      }
      if (type[i][j]) {
        int sz = 0;
        do {
          ++sz;
        } while (next_permutation(V, V + 4));
        beet *= sz;
      } else {
        beet *= 12;
        uf.unite(i + W / 2, j);
      }
    }
  }
  int sz = 0;
  for (int i = 0; i < H / 2 + W / 2; i++) {
    if (uf.find(i) == i)
      sz++;
  }
  cout << modint(2).pow(H / 2 + W / 2 - sz) * beet * mul << endl;
}