#line 2 "library/other/template.hpp" #include #ifndef __COUNTER__ #define __COUNTER__ __LINE__ #endif #define REP_SELECTER(a, b, c, d, e, ...) e #define REP1_0(b, c) REP1_1(b, c) #define REP1_1(b, c) for (ll REP_COUNTER_ ## c = 0; REP_COUNTER_ ## c < (ll)(b); ++ REP_COUNTER_ ## c) #define REP1(b) REP1_0(b, __COUNTER__) #define REP2(i, b) for (ll i = 0; i < (ll)(b); ++i) #define REP3(i, a, b) for (ll i = (ll)(a); i < (ll)(b); ++i) #define REP4(i, a, b, c) for (ll i = (ll)(a); i < (ll)(b); i += (ll)(c)) #define rep(...) REP_SELECTER(__VA_ARGS__, REP4, REP3, REP2, REP1) (__VA_ARGS__) #define RREP2(i, a) for (ll i = (ll)(a) - 1; i >= 0; --i) #define RREP3(i, a, b) for (ll i = (ll)(a) - 1; i >= (ll)(b); --i) #define RREP4(i, a, b, c) for (ll i = (ll)(a) - 1; i >= (ll)(b); i -= (ll)(c)) #define rrep(...) REP_SELECTER(__VA_ARGS__, RREP4, RREP3, RREP2) (__VA_ARGS__) #define REPS2(i, b) for (ll i = 1; i <= (ll)(b); ++i) #define REPS3(i, a, b) for (ll i = (ll)(a) + 1; i <= (ll)(b); ++i) #define REPS4(i, a, b, c) for (ll i = (ll)(a) + 1; i <= (ll)(b); i += (ll)(c)) #define reps(...) REP_SELECTER(__VA_ARGS__, REPS4, REPS3, REPS2) (__VA_ARGS__) #define RREPS2(i, a) for (ll i = (ll)(a); i > 0; --i) #define RREPS3(i, a, b) for (ll i = (ll)(a); i > (ll)(b); --i) #define RREPS4(i, a, b, c) for (ll i = (ll)(a); i > (ll)(b); i -= (ll)(c)) #define rreps(...) REP_SELECTER(__VA_ARGS__, RREPS4, RREPS3, RREPS2) (__VA_ARGS__) #define each_for(...) for (auto&& __VA_ARGS__) #define each_const(...) for (const auto& __VA_ARGS__) #define all(v) std::begin(v), std::end(v) #define rall(v) std::rbegin(v), std::rend(v) #if __cplusplus >= 201402L #define CONSTEXPR constexpr #else #define CONSTEXPR #endif #ifdef __cpp_if_constexpr #define IF_CONSTEXPR constexpr #else #define IF_CONSTEXPR #endif using ll = long long; using ull = unsigned long long; using ld = long double; using PLL = std::pair; template using prique = std::priority_queue, std::greater>; template class infinity { public: static constexpr T value = std::numeric_limits::max() / 2; static constexpr T mvalue = std::numeric_limits::min() / 2; static constexpr T max = std::numeric_limits::max(); static constexpr T min = std::numeric_limits::min(); }; #if __cplusplus <= 201402L template constexpr T infinity::value; template constexpr T infinity::mvalue; template constexpr T infinity::max; template constexpr T infinity::min; #endif #if __cplusplus >= 201402L template constexpr T INF = infinity::value; #endif constexpr ll inf = infinity::value; constexpr ld EPS = 1e-8; constexpr ld PI = 3.1415926535897932384626; template std::ostream& operator<<(std::ostream& ost, const std::pair& p) { return ost << p.first << ' ' << p.second; } template std::istream& operator>>(std::istream& ist, std::pair& p) { return ist >> p.first >> p.second; } template::value>::type* = nullptr> auto operator<<(std::ostream& ost, const Container& cont) -> decltype(cont.begin(), cont.end(), ost) { for (auto itr = cont.begin(); itr != cont.end(); ++itr) { if (itr != cont.begin()) ost << ' '; ost << *itr; } return ost; } template::value>::type* = nullptr> auto operator>>(std::istream& ist, Container& cont) -> decltype(cont.begin(), cont.end(), ist) { for (auto itr = cont.begin(); itr != cont.end(); ++itr) ist >> *itr; return ist; } template inline constexpr bool chmin(T &a, const U &b) noexcept { return a > b ? a = b, true : false; } template inline constexpr bool chmax(T &a, const U &b) noexcept { return a < b ? a = b, true : false; } inline CONSTEXPR ll gcd(ll a, ll b) noexcept { while (b) { const ll c = a; a = b; b = c % b; } return a; } inline CONSTEXPR ll lcm(ll a, ll b) noexcept { return a / gcd(a, b) * b; } inline CONSTEXPR bool is_prime(ll N) noexcept { if (N <= 1) return false; for (ll i = 2; i * i <= N; ++i) { if (N % i == 0) return false; } return true; } inline std::vector prime_factor(ll N) noexcept { std::vector res; for (ll i = 2; i * i <= N; ++i) { while (N % i == 0) { res.push_back(i); N /= i; } } if (N != 1) res.push_back(N); return res; } inline CONSTEXPR ll my_pow(ll a, ll b) noexcept { ll res = 1; while (b) { if (b & 1) res *= a; b >>= 1; a *= a; } return res; } inline CONSTEXPR ll mod_pow(ll a, ll b, ll mod) noexcept { a %= mod; ll res = 1; while (b) { if (b & 1) (res *= a) %= mod; b >>= 1; (a *= a) %= mod; } return res; } PLL extGCD(ll a, ll b) noexcept { if (b == 0) return PLL{1, 0}; PLL p = extGCD(b, a % b); std::swap(p.first, p.second); p.second -= p.first * (a / b); if (p.first < 0) { p.first += b; p.second -= a; } return p; } ll mod_inv(ll a, ll mod) noexcept { const PLL p = extGCD(a, mod); assert(p.first * a + p.second * mod == 1); return p.first; } PLL ChineseRemainder(ll b1, ll m1, ll b2, ll m2) noexcept { const PLL p = extGCD(m1, m2); const ll g = p.first * m1 + p.second * m2; const ll l = m1 / g * m2; if ((b2 - b1) % g != 0) return PLL{-1, -1}; const ll x = (b2 - b1) / g * p.first % (m2 / g); return {(x * m1 + b1 + l) % l, l}; } PLL ChineseRemainders(const std::vector& b, const std::vector& m) noexcept { PLL res{0, 1}; rep (i, b.size()) { res = ChineseRemainder(res.first, res.second, b[i], m[i]); if (res.first == -1) return res; } return res; } template class RecLambda { private: F f; public: explicit constexpr RecLambda(F&& f_) : f(std::forward(f_)) {} template constexpr auto operator()(Args&&... args) const -> decltype(f(*this, std::forward(args)...)) { return f(*this, std::forward(args)...); } }; template inline constexpr RecLambda rec_lambda(F&& f) { return RecLambda(std::forward(f)); } template struct multi_dim_vector { using type = std::vector::type>; }; template struct multi_dim_vector { using type = T; }; template constexpr std::vector make_vec(int n, Arg&& arg) { return std::vector(n, std::forward(arg)); } template constexpr typename multi_dim_vector::type make_vec(int n, Args&&... args) { return typename multi_dim_vector::type (n, make_vec(std::forward(args)...)); } inline CONSTEXPR int popcnt(ull x) { #if __cplusplus >= 202002L return std::popcount(x); #endif x = (x & 0x5555555555555555) + ((x >> 1 ) & 0x5555555555555555); x = (x & 0x3333333333333333) + ((x >> 2 ) & 0x3333333333333333); x = (x & 0x0f0f0f0f0f0f0f0f) + ((x >> 4 ) & 0x0f0f0f0f0f0f0f0f); x = (x & 0x00ff00ff00ff00ff) + ((x >> 8 ) & 0x00ff00ff00ff00ff); x = (x & 0x0000ffff0000ffff) + ((x >> 16) & 0x0000ffff0000ffff); return (x & 0x00000000ffffffff) + ((x >> 32) & 0x00000000ffffffff); } template> class presser { protected: std::vector dat; Comp cmp; bool sorted = false; public: presser() : presser(Comp()) {} presser(const Comp& cmp) : cmp(cmp) {} presser(const std::vector& vec, const Comp& cmp = Comp()) : dat(vec), cmp(cmp) {} presser(std::vector&& vec, const Comp& cmp = Comp()) : dat(std::move(vec)), cmp(cmp) {} presser(std::initializer_list il, const Comp& cmp = Comp()) : dat(il.begin(), il.end()), cmp(cmp) {} void reserve(int n) { assert(!sorted); dat.reserve(n); } void push_back(const T& v) { assert(!sorted); dat.push_back(v); } void push_back(T&& v) { assert(!sorted); dat.push_back(std::move(v)); } void push(const std::vector& vec) { assert(!sorted); dat.reserve(dat.size() + vec.size()); std::copy(all(vec), std::back_inserter(dat)); } int build() { assert(!sorted); sorted = true; std::sort(all(dat), cmp); dat.erase(std::unique(all(dat), [&](const T& a, const T& b) -> bool { return !cmp(a, b) && !cmp(b, a); }), dat.end()); return dat.size(); } const T& operator[](int k) const& { assert(sorted); assert(0 <= k && k < (int)dat.size()); return dat[k]; } T operator[](int k) && { assert(sorted); assert(0 <= k && k < (int)dat.size()); return std::move(dat[k]); } int get_index(const T& val) const { assert(sorted); return static_cast(std::lower_bound(all(dat), val, cmp) - dat.begin()); } std::vector pressed(const std::vector& vec) const { assert(sorted); std::vector res(vec.size()); rep (i, vec.size()) res[i] = get_index(vec[i]); return res; } void press(std::vector& vec) const { static_assert(std::is_integral::value, "template argument must be convertible from int type"); assert(sorted); each_for (i : vec) i = get_index(i); } int size() const { assert(sorted); return dat.size(); } const std::vector& data() const& { return dat; } std::vector data() && { return std::move(dat); } }; #line 2 "library/math/ModInt.hpp" #line 4 "library/math/ModInt.hpp" class ModIntBase {}; class StaticModIntBase : ModIntBase {}; class DynamicModIntBase : ModIntBase {}; template using is_ModInt = std::is_base_of; template using is_StaticModInt = std::is_base_of; template using is_DynamicModInt = std::is_base_of; template class StaticModInt : StaticModIntBase { protected: ll val; static constexpr ll inv1000000007[] = {-1, 1, 500000004, 333333336, 250000002, 400000003, 166666668, 142857144, 125000001, 111111112, 700000005}; static constexpr ll inv998244353 [] = {-1, 1, 499122177, 332748118, 748683265, 598946612, 166374059, 855638017, 873463809, 443664157, 299473306}; public: StaticModInt() : StaticModInt(0) {} template::value>::type* = nullptr> StaticModInt(T v) : val(v) { val %= mod; if (val < 0) val += mod; } ll get() const { return val; } static ll get_mod() { return mod; } static StaticModInt raw(ll v) { StaticModInt res; res.val = v; return res; } StaticModInt inv() const { if IF_CONSTEXPR (mod == 1000000007) { if (val <= 10) return inv1000000007[val]; } else if IF_CONSTEXPR (mod == 998244353) { if (val <= 10) return inv998244353[val]; } return mod_inv(val, mod); } StaticModInt& operator++() { ++val; if (val == mod) val = 0; return *this; } StaticModInt operator++(int) { StaticModInt res = *this; ++ *this; return res; } StaticModInt& operator--() { if (val == 0) val = mod; --val; return *this; } StaticModInt operator--(int) { StaticModInt res = *this; -- *this; return res; } StaticModInt& operator+=(const StaticModInt& other) { val += other.val; if (val >= mod) val -= mod; return *this; } StaticModInt& operator-=(const StaticModInt& other) { val -= other.val; if (val < 0) val += mod; return *this; } StaticModInt& operator*=(const StaticModInt& other) { (val *= other.val) %= mod; return *this; } StaticModInt& operator/=(const StaticModInt& other) { (val *= other.inv().get()) %= mod; return *this; } friend StaticModInt operator+(const StaticModInt& lhs, const StaticModInt& rhs) { return StaticModInt(lhs) += rhs; } friend StaticModInt operator-(const StaticModInt& lhs, const StaticModInt& rhs) { return StaticModInt(lhs) -= rhs; } friend StaticModInt operator*(const StaticModInt& lhs, const StaticModInt& rhs) { return StaticModInt(lhs) *= rhs; } friend StaticModInt operator/(const StaticModInt& lhs, const StaticModInt& rhs) { return StaticModInt(lhs) /= rhs; } StaticModInt operator+() const { return StaticModInt(*this); } StaticModInt operator-() const { return StaticModInt(0) - *this; } friend bool operator==(const StaticModInt& lhs, const StaticModInt& rhs) { return lhs.val == rhs.val; } friend bool operator!=(const StaticModInt& lhs, const StaticModInt& rhs) { return lhs.val != rhs.val; } StaticModInt pow(ll a) const { StaticModInt v = *this, res = 1; while (a) { if (a & 1) res *= v; a >>= 1; v *= v; } return res; } friend std::ostream& operator<<(std::ostream& ost, const StaticModInt& sm) { return ost << sm.val; } friend std::istream& operator>>(std::istream& ist, StaticModInt& sm) { ll v; ist >> v; sm = v; return ist; } }; #if __cplusplus < 201703L template constexpr ll StaticModInt::inv1000000007[]; template constexpr ll StaticModInt::inv998244353 []; #endif using modint1000000007 = StaticModInt<1000000007>; using modint998244353 = StaticModInt<998244353>; template class DynamicModInt : DynamicModIntBase { protected: ll val; static ll mod; public: DynamicModInt() : DynamicModInt(0) {} template::value>::type* = nullptr> DynamicModInt(T v) : val(v) { val %= mod; if (val < 0) val += mod; } ll get() const { return val; } static ll get_mod() { return mod; } static void set_mod(ll v) { mod = v; } static DynamicModInt raw(ll v) { DynamicModInt res; res.val = v; return res; } DynamicModInt inv() const { return mod_inv(val, mod); } DynamicModInt& operator++() { ++val; if (val == mod) val = 0; return *this; } DynamicModInt operator++(int) { DynamicModInt res = *this; ++ *this; return res; } DynamicModInt& operator--() { if (val == 0) val = mod; --val; return *this; } DynamicModInt operator--(int) { DynamicModInt res = *this; -- *this; return res; } DynamicModInt& operator+=(const DynamicModInt& other) { val += other.val; if (val >= mod) val -= mod; return *this; } DynamicModInt& operator-=(const DynamicModInt& other) { val -= other.val; if (val < 0) val += mod; return *this; } DynamicModInt& operator*=(const DynamicModInt& other) { (val *= other.val) %= mod; return *this; } DynamicModInt& operator/=(const DynamicModInt& other) { (val *= other.inv().get()) %= mod; return *this; } friend DynamicModInt operator+(const DynamicModInt& lhs, const DynamicModInt& rhs) { return DynamicModInt(lhs) += rhs; } friend DynamicModInt operator-(const DynamicModInt& lhs, const DynamicModInt& rhs) { return DynamicModInt(lhs) -= rhs; } friend DynamicModInt operator*(const DynamicModInt& lhs, const DynamicModInt& rhs) { return DynamicModInt(lhs) *= rhs; } friend DynamicModInt operator/(const DynamicModInt& lhs, const DynamicModInt& rhs) { return DynamicModInt(lhs) /= rhs; } DynamicModInt operator+() const { return DynamicModInt(*this); } DynamicModInt operator-() const { return DynamicModInt(0) - *this; } friend bool operator==(const DynamicModInt& lhs, const DynamicModInt& rhs) { return lhs.val == rhs.val; } friend bool operator!=(const DynamicModInt& lhs, const DynamicModInt& rhs) { return lhs.val != rhs.val; } DynamicModInt pow(ll a) const { DynamicModInt v = *this, res = 1; while (a) { if (a & 1) res *= v; a >>= 1; v *= v; } return res; } friend std::ostream& operator<<(std::ostream& ost, const DynamicModInt& dm) { return ost << dm.val; } friend std::istream& operator>>(std::istream& ist, DynamicModInt& dm) { ll v; ist >> v; dm = v; return ist; } }; template ll DynamicModInt::mod = 1000000007; using modint = DynamicModInt<-1>; /** * @brief ModInt * @docs docs/ModInt.md */ #line 3 "main.cpp" using namespace std; using mint = modint1000000007; int main() { int H, W; cin >> H >> W; vector G(H); cin >> G; auto dp = make_vec(H + W - 1, H, H, mint{0}); dp[0][0][H - 1] = 1; mint ans = 0; // dp[i][j][k] : (j, i - j), (k, (H + W - 2 - i) - k) rep (i, H + W - 1) rep (j, H) rep (k, H) { int x1 = j, y1 = i - j; int x2 = k, y2 = (H + W - 2 - i) - k; if (x1 < 0 || x1 >= H || y1 < 0 || y1 >= W) continue; if (x2 < 0 || x2 >= H || y2 < 0 || y2 >= W) continue; if (G[x1][y1] != G[x2][y2]) continue; if (x1 == x2 && y1 == y2) ans += dp[i][j][k]; if ((x1 == x2 && y1 + 1 == y2) || (x1 + 1 == x2 && y1 == y2)) ans += dp[i][j][k]; if (x1 + y1 + 1 < H + W - 2) dp[x1 + y1 + 1][x1][x2] += dp[i][j][k]; if (x1 + y1 + 1 < H + W - 2 && x1 != H - 1) dp[x1 + y1 + 1][x1 + 1][x2] += dp[i][j][k]; if (x1 + y1 + 1 < H + W - 2 && x2 != 0) dp[x1 + y1 + 1][x1][x2 - 1] += dp[i][j][k]; if (x1 + y1 + 1 < H + W - 2 && x1 != H - 1 && x2 != 0) dp[x1 + y1 + 1][x1 + 1][x2 - 1] += dp[i][j][k]; } cout << ans << endl; }