// #include "my_template.hpp" // #include "math/static_modint.hpp" // using mint = mint998; // #include "math/binomial.hpp" // Binomial B; // using namespace std; // // void solve() { // INT(N, M); // VEC(string, S, N); // vector bcnt(3), qcnt(3); // REP(i, N) { // REP(j, M) { // if (S[i][j] == '?') qcnt[(i + j) % 3]++; // if (S[i][j] == 'B') bcnt[(i + j) % 3]++; // } // } // // (x, y, z) にそれぞれ +1 / -1 のどちらか -> 偶奇が常に一致 // mint ans = 0; // mint cnt[3][2] = {}; // REP(i, 3) REP(x, bcnt[i], bcnt[i] + qcnt[i] + 1) cnt[i][x % 2] += B.C(qcnt[i], x - bcnt[i]); // REP(i, 2) ans += cnt[0][i] * cnt[1][i] * cnt[2][i]; // print(ans); // return; // } // // int main() { // solve(); // return 0; // } #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #ifdef RUTHEN_LOCAL #include #else #define show(x) true #endif // type definition using i64 = long long; using u32 = unsigned int; using u64 = unsigned long long; using f32 = float; using f64 = double; using f128 = long double; template using pque = std::priority_queue; template using pqueg = std::priority_queue, std::greater>; // overload #define overload4(_1, _2, _3, _4, name, ...) name #define overload3(_1, _2, _3, name, ...) name #define overload2(_1, _2, name, ...) name // for loop #define REP1(a) for (long long _ = 0; _ < (a); _++) #define REP2(i, a) for (long long i = 0; i < (a); i++) #define REP3(i, a, b) for (long long i = (a); i < (b); i++) #define REP4(i, a, b, c) for (long long i = (a); i < (b); i += (c)) #define REP(...) overload4(__VA_ARGS__, REP4, REP3, REP2, REP1)(__VA_ARGS__) #define RREP1(a) for (long long _ = (a)-1; _ >= 0; _--) #define RREP2(i, a) for (long long i = (a)-1; i >= 0; i--) #define RREP3(i, a, b) for (long long i = (b)-1; i >= (a); i--) #define RREP(...) overload3(__VA_ARGS__, RREP3, RREP2, RREP1)(__VA_ARGS__) #define FORE1(x, a) for (auto &&x : a) #define FORE2(x, y, a) for (auto &&[x, y] : a) #define FORE3(x, y, z, a) for (auto &&[x, y, z] : a) #define FORE(...) overload4(__VA_ARGS__, FORE3, FORE2, FORE1)(__VA_ARGS__) #define FORSUB(t, s) for (long long t = (s); t >= 0; t = (t == 0 ? -1 : (t - 1) & (s))) // function #define ALL(a) (a).begin(), (a).end() #define RALL(a) (a).rbegin(), (a).rend() #define SORT(a) std::sort((a).begin(), (a).end()) #define RSORT(a) std::sort((a).rbegin(), (a).rend()) #define REV(a) std::reverse((a).begin(), (a).end()) #define UNIQUE(a) \ std::sort((a).begin(), (a).end()); \ (a).erase(std::unique((a).begin(), (a).end()), (a).end()) #define LEN(a) (int)((a).size()) #define MIN(a) *std::min_element((a).begin(), (a).end()) #define MAX(a) *std::max_element((a).begin(), (a).end()) #define SUM1(a) std::accumulate((a).begin(), (a).end(), 0LL) #define SUM2(a, x) std::accumulate((a).begin(), (a).end(), (x)) #define SUM(...) overload2(__VA_ARGS__, SUM2, SUM1)(__VA_ARGS__) #define LB(a, x) std::distance((a).begin(), std::lower_bound((a).begin(), (a).end(), (x))) #define UB(a, x) std::distance((a).begin(), std::upper_bound((a).begin(), (a).end(), (x))) template inline bool chmin(T &a, const U &b) { return (a > T(b) ? a = b, 1 : 0); } template inline bool chmax(T &a, const U &b) { return (a < T(b) ? a = b, 1 : 0); } template inline T floor(const T x, const S y) { assert(y); return (y < 0 ? floor(-x, -y) : (x > 0 ? x / y : x / y - (x % y == 0 ? 0 : 1))); } template inline T ceil(const T x, const S y) { assert(y); return (y < 0 ? ceil(-x, -y) : (x > 0 ? (x + y - 1) / y : x / y)); } template std::pair inline divmod(const T x, const S y) { T q = floor(x, y); return {q, x - q * y}; } // 10 ^ n constexpr long long TEN(int n) { return (n == 0) ? 1 : 10LL * TEN(n - 1); } // 1 + 2 + ... + n #define TRI1(n) ((n) * ((n) + 1LL) / 2) // l + (l + 1) + ... + r #define TRI2(l, r) (((l) + (r)) * ((r) - (l) + 1LL) / 2) #define TRI(...) overload2(__VA_ARGS__, TRI2, TRI1)(__VA_ARGS__) // bit operation // bit[i] (= 0 or 1) #define IBIT(bit, i) (((bit) >> (i)) & 1) // (0, 1, 2, 3, 4) -> (0, 1, 3, 7, 15) #define MASK(n) ((1LL << (n)) - 1) #define POW2(n) (1LL << (n)) // (0, 1, 2, 3, 4) -> (0, 1, 1, 2, 1) int popcnt(int x) { return __builtin_popcount(x); } int popcnt(u32 x) { return __builtin_popcount(x); } int popcnt(i64 x) { return __builtin_popcountll(x); } int popcnt(u64 x) { return __builtin_popcountll(x); } // (0, 1, 2, 3, 4) -> (-1, 0, 1, 1, 2) int topbit(int x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); } int topbit(u32 x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); } int topbit(i64 x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); } int topbit(u64 x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); } // (0, 1, 2, 3, 4) -> (-1, 0, 1, 0, 2) int lowbit(int x) { return (x == 0 ? -1 : __builtin_ctz(x)); } int lowbit(u32 x) { return (x == 0 ? -1 : __builtin_ctz(x)); } int lowbit(i64 x) { return (x == 0 ? -1 : __builtin_ctzll(x)); } int lowbit(u64 x) { return (x == 0 ? -1 : __builtin_ctzll(x)); } // binary search (integer) template T bin_search(T ok, T ng, F &f) { while ((ok > ng ? ok - ng : ng - ok) > 1) { T md = (ng + ok) >> 1; (f(md) ? ok : ng) = md; } return ok; } // binary search (real number) template T bin_search_real(T ok, T ng, F &f, const int iter = 100) { for (int _ = 0; _ < iter; _++) { T md = (ng + ok) / 2; (f(md) ? ok : ng) = md; } return ok; } // floor(sqrt(x)) template constexpr T sqrt_floor(T x) { return T(sqrtl(x)); } // check if [l1, r1) and [l2, r2) intersect template constexpr bool intersect(const T l1, const T r1, const T l2, const T r2) { return std::max(l1, l2) < std::min(r1, r2); } // check if [a.first, a.second) and [b.first, b.second) intersect template constexpr bool intersect(const std::pair &a, const std::pair &b) { return intersect(a.first, a.second, b.first, b.second); } // rotate matrix counterclockwise by pi / 2 template void rot(std::vector> &a) { if ((int)(a.size()) == 0) return; if ((int)(a[0].size()) == 0) return; int n = (int)(a.size()), m = (int)(a[0].size()); std::vector res(m, std::vector(n)); for (int i = 0; i < n; i++) { for (int j = 0; j < m; j++) { res[m - 1 - j][i] = a[i][j]; } } a.swap(res); } // const value constexpr int dx[8] = {1, 0, -1, 0, 1, -1, -1, 1}; constexpr int dy[8] = {0, 1, 0, -1, 1, 1, -1, -1}; // infinity template constexpr T INF = 0; template <> constexpr int INF = 1'000'000'000; // 1e9 template <> constexpr i64 INF = i64(INF) * INF * 2; // 2e18 template <> constexpr u32 INF = INF; // 1e9 template <> constexpr u64 INF = INF; // 2e18 template <> constexpr f32 INF = INF; // 2e18 template <> constexpr f64 INF = INF; // 2e18 template <> constexpr f128 INF = INF; // 2e18 // I/O // input template std::istream &operator>>(std::istream &is, std::vector &v) { for (auto &&i : v) is >> i; return is; } template void in(T &...a) { (std::cin >> ... >> a); } void scan() {} template void scan(Head &head, Tail &...tail) { in(head); scan(tail...); } // input macro #define INT(...) \ int __VA_ARGS__; \ scan(__VA_ARGS__) #define I64(...) \ i64 __VA_ARGS__; \ scan(__VA_ARGS__) #define U32(...) \ u32 __VA_ARGS__; \ scan(__VA_ARGS__) #define U64(...) \ u64 __VA_ARGS__; \ scan(__VA_ARGS__) #define F32(...) \ f32 __VA_ARGS__; \ scan(__VA_ARGS__) #define F64(...) \ f64 __VA_ARGS__; \ scan(__VA_ARGS__) #define F128(...) \ f128 __VA_ARGS__; \ scan(__VA_ARGS__) #define STR(...) \ std::string __VA_ARGS__; \ scan(__VA_ARGS__) #define CHR(...) \ char __VA_ARGS__; \ scan(__VA_ARGS__) #define VEC(type, name, size) \ std::vector name(size); \ scan(name) #define VEC2(type, name1, name2, size) \ std::vector name1(size), name2(size); \ for (int i = 0; i < size; i++) scan(name1[i], name2[i]) #define VEC3(type, name1, name2, name3, size) \ std::vector name1(size), name2(size), name3(size); \ for (int i = 0; i < size; i++) scan(name1[i], name2[i], name3[i]) #define VEC4(type, name1, name2, name3, name4, size) \ std::vector name1(size), name2(size), name3(size), name4(size); \ for (int i = 0; i < size; i++) scan(name1[i], name2[i], name3[i], name4[i]) #define VV(type, name, h, w) \ std::vector name((h), std::vector((w))); \ scan(name) // output template std::ostream &operator<<(std::ostream &os, const std::vector &v) { auto n = v.size(); for (size_t i = 0; i < n; i++) { if (i) os << ' '; os << v[i]; } return os; } template void out(const T &...a) { (std::cout << ... << a); } void print() { out('\n'); } template void print(Head &&head, Tail &&...tail) { out(head); if (sizeof...(Tail)) out(' '); print(tail...); } // for interactive problems void printi() { std::cout << std::endl; } template void printi(Head &&head, Tail &&...tail) { out(head); if (sizeof...(Tail)) out(' '); printi(tail...); } // bool output void YES(bool t = 1) { print(t ? "YES" : "NO"); } void Yes(bool t = 1) { print(t ? "Yes" : "No"); } void yes(bool t = 1) { print(t ? "yes" : "no"); } void NO(bool t = 1) { YES(!t); } void No(bool t = 1) { Yes(!t); } void no(bool t = 1) { yes(!t); } void POSSIBLE(bool t = 1) { print(t ? "POSSIBLE" : "IMPOSSIBLE"); } void Possible(bool t = 1) { print(t ? "Possible" : "Impossible"); } void possible(bool t = 1) { print(t ? "possible" : "impossible"); } void IMPOSSIBLE(bool t = 1) { POSSIBLE(!t); } void Impossible(bool t = 1) { Possible(!t); } void impossible(bool t = 1) { possible(!t); } void FIRST(bool t = 1) { print(t ? "FIRST" : "SECOND"); } void First(bool t = 1) { print(t ? "First" : "Second"); } void first(bool t = 1) { print(t ? "first" : "second"); } void SECOND(bool t = 1) { FIRST(!t); } void Second(bool t = 1) { First(!t); } void second(bool t = 1) { first(!t); } // I/O speed up struct SetUpIO { SetUpIO() { std::ios::sync_with_stdio(false); std::cin.tie(0); std::cout << std::fixed << std::setprecision(20); } } set_up_io; // constexpr ... for constexpr bool prime() template struct StaticModint { using mint = StaticModint; unsigned int _v; static constexpr int mod() { return m; } static constexpr unsigned int umod() { return m; } constexpr StaticModint() : _v(0) {} template constexpr StaticModint(T v) { long long x = (long long)(v % (long long)(umod())); if (x < 0) x += umod(); _v = (unsigned int)(x); } constexpr unsigned int val() const { return _v; } constexpr mint &operator++() { _v++; if (_v == umod()) _v = 0; return *this; } constexpr mint &operator--() { if (_v == 0) _v = umod(); _v--; return *this; } constexpr mint operator++(int) { mint result = *this; ++*this; return result; } constexpr mint operator--(int) { mint result = *this; --*this; return result; } constexpr mint &operator+=(const mint &rhs) { _v += rhs._v; if (_v >= umod()) _v -= umod(); return *this; } constexpr mint &operator-=(const mint &rhs) { _v -= rhs._v; if (_v >= umod()) _v += umod(); return *this; } constexpr mint &operator*=(const mint &rhs) { unsigned long long z = _v; z *= rhs._v; _v = (unsigned int)(z % umod()); return *this; } constexpr mint &operator/=(const mint &rhs) { return (*this *= rhs.inv()); } constexpr mint operator+() const { return *this; } constexpr mint operator-() const { return mint() - *this; } constexpr mint pow(long long n) const { assert(n >= 0); mint x = *this, r = 1; while (n) { if (n & 1) r *= x; x *= x; n >>= 1; } return r; } constexpr mint inv() const { if (prime) { assert(_v); return pow(umod() - 2); } else { auto eg = inv_gcd(_v, m); assert(eg.first == 1); return eg.second; } } friend constexpr mint operator+(const mint &lhs, const mint &rhs) { return mint(lhs) += rhs; } friend constexpr mint operator-(const mint &lhs, const mint &rhs) { return mint(lhs) -= rhs; } friend constexpr mint operator*(const mint &lhs, const mint &rhs) { return mint(lhs) *= rhs; } friend constexpr mint operator/(const mint &lhs, const mint &rhs) { return mint(lhs) /= rhs; } friend constexpr bool operator==(const mint &lhs, const mint &rhs) { return lhs._v == rhs._v; } friend constexpr bool operator!=(const mint &lhs, const mint &rhs) { return lhs._v != rhs._v; } friend std::ostream &operator<<(std::ostream &os, const mint &v) { return os << v.val(); } static constexpr bool prime = []() -> bool { if (m == 1) return false; if (m == 2 || m == 7 || m == 61) return true; if (m % 2 == 0) return false; unsigned int d = m - 1; while (d % 2 == 0) d /= 2; for (unsigned int a : {2, 7, 61}) { unsigned int t = d; mint y = mint(a).pow(t); while (t != m - 1 and y != 1 and y != m - 1) { y *= y; t <<= 1; } if (y != m - 1 and t % 2 == 0) { return false; } } return true; }(); static constexpr std::pair inv_gcd(int a, int b) { if (a == 0) return {b, 0}; int s = b, t = a, m0 = 0, m1 = 1; while (t) { const int u = s / t; s -= t * u; m0 -= m1 * u; std::swap(s, t); std::swap(m0, m1); } if (m0 < 0) m0 += b / s; return {s, m0}; } }; using mint107 = StaticModint<1000000007>; using mint998 = StaticModint<998244353>; using mint = mint998; // 二項係数ライブラリ template struct Binomial { std::vector f, g, h; Binomial(const int n_max = 0) { f.resize(1, Mint(1)); g.resize(1, Mint(1)); h.resize(1, Mint(1)); if (n_max > 0) extend(n_max); } // 基本は長さを倍にする void extend(int m = -1) { const int n = (int)(f.size()); // n >= 1 if (m == -1) m = n * 2; // m >= 2 m = std::min(m, Mint::mod()); if (n >= m) return; f.resize(m); g.resize(m); h.resize(m); // calc f for (int i = n; i < m; i++) f[i] = f[i - 1] * Mint(i); // calc g g[m - 1] = 1 / f[m - 1]; for (int i = m - 2; i >= n; i--) g[i] = g[i + 1] * Mint(i + 1); // calc h h[m - 1] = g[m - 1] * f[m - 2]; for (int i = m - 2; i >= n; i--) h[i] = g[i] * f[i - 1]; } // fact(n) = n! Mint fact(const int n) { if (n < 0) return Mint(0); while (n >= (int)(f.size())) extend(); return f[n]; } // finv(n) = 1 / n! Mint finv(const int n) { if (n < 0) return Mint(0); while (n >= (int)(g.size())) extend(); return g[n]; } // inv(n) = 1 / n Mint inv(const int n) { if (n < 0) return Mint(0); while (n >= (int)(h.size())) extend(); } // n C k Mint C(const int n, const int k) { if (n < 0 or k < 0 or n < k) return Mint(0); return fact(n) * finv(n - k) * finv(k); } // n P k Mint P(const int n, const int k) { if (n < 0 or k < 0 or n < k) return Mint(0); return fact(n) * finv(n - k); } // n H k // n 個から k 個重複を許して取る組合せ Mint H(const int n, const int k) { if (n < 0 or k < 0) return Mint(0); if (k == 0) return Mint(1); return C(n + k - 1, k); } Mint C_naive(int n, int k) { if (n < 0 or k < 0 or n < k) return Mint(0); Mint res = Mint(1), res_inv = Mint(1); k = std::min(k, n - k); for (int i = 1; i <= k; i++) { res *= (n--); res_inv *= i; } res /= res_inv; return res; } }; Binomial B; using namespace std; void solve() { INT(N, M); VEC(string, S, N); vector bcnt(3), qcnt(3); REP(i, N) { REP(j, M) { if (S[i][j] == '?') qcnt[(i + j) % 3]++; if (S[i][j] == 'B') bcnt[(i + j) % 3]++; } } // (x, y, z) にそれぞれ +1 / -1 のどちらか -> 偶奇が常に一致 mint ans = 0; mint cnt[3][2] = {}; REP(i, 3) REP(x, bcnt[i], bcnt[i] + qcnt[i] + 1) cnt[i][x % 2] += B.C(qcnt[i], x - bcnt[i]); REP(i, 2) ans += cnt[0][i] * cnt[1][i] * cnt[2][i]; print(ans); return; } int main() { solve(); return 0; }