#include #define VARNAME(x) #x #define show(x) cerr << #x << " = " << x << endl using namespace std; using ll = long long; using ld = long double; template ostream& operator<<(ostream& os, const vector& v) { os << "sz:" << v.size() << "\n["; for (const auto& p : v) { os << p << ","; } os << "]\n"; return os; } template ostream& operator<<(ostream& os, const pair& p) { os << "(" << p.first << "," << p.second << ")"; return os; } constexpr ll MOD = 201712111LL; constexpr ld PI = static_cast(3.1415926535898); template constexpr T INF = numeric_limits::max() / 10; int H, W; vector& prev(vector>>& dp, const int i, const int j) { return (j == 0 ? dp[i - 1][W - 1] : dp[i][j - 1]); } int main() { cin.tie(0); ios::sync_with_stdio(false); cin >> H >> W; vector A(H); for (int i = 0; i < H; i++) { cin >> A[i]; } if (H < W) { vector A_(W); for (int i = 0; i < W; i++) { for (int j = 0; j < H; j++) { A_[i].push_back(A[j][i]); } } swap(H, W); A.clear(); A = A_; } vector> dist(H, vector(W, 0)); for (int i = 0; i < H; i++) { for (int j = 0; j < W; j++) { dist[i][j] = (isdigit(A[i][j]) ? A[i][j] - '0' : 1); } } for (int i = 1; i < W; i++) { dist[0][i] += dist[0][i - 1]; } for (int i = 1; i < H; i++) { dist[i][0] += dist[i - 1][0]; } for (int i = 1; i < H; i++) { for (int j = 1; j < W; j++) { dist[i][j] = min(dist[i - 1][j], dist[i][j - 1]) + dist[i][j]; } } // return (j == 0 ? A[i][W - 1] : A[i + 1][j - 1]); auto fromLeft = [&](const int i, const int j) { assert(j != 1); return (j == 0 ? (dist[i][W - 1] == dist[i][W - 2] + (isdigit(A[i][W - 1]) ? A[i][W - 1] - '0' : 1)) : (dist[i + 1][j - 1] == dist[i + 1][j - 2] + (isdigit(A[i + 1][j - 1]) ? A[i + 1][j - 1] - '0' : 1))); }; auto fromAbove = [&](const int i, const int j) { return (j == 0 ? (dist[i][W - 1] == dist[i - 1][W - 1] + (isdigit(A[i][W - 1]) ? A[i][W - 1] - '0' : 1)) : (dist[i + 1][j - 1] == dist[i][j - 1] + (isdigit(A[i + 1][j - 1]) ? A[i + 1][j - 1] - '0' : 1))); }; const ll T = dist[H - 1][W - 1]; cout << T << endl; if (W == 1) { cout << 1 << endl; return 0; } const int maximum = 1 << W; vector>> dp(H, vector>(W, vector(maximum, 0))); //dist[i][j]から始まるWマスで正しい値の位置がbit表示でmask ll num = 1; int mask = maximum - 1; dp[0][0][mask] = 1; for (int j = W - 1; j >= 0; j--) { mask -= (1 << j); if (A[0][j] == '?') { dp[0][0][mask] = (num * 8) % MOD; num = (num * 9) % MOD; } } auto tail = [&](const int i, const int j) { return (j == 0 ? A[i][W - 1] : A[i + 1][j - 1]); }; for (int i = 0; i < H; i++) { for (int j = 0; j < W; j++) { if (i == 0 and j == 0) { continue; } if (i == H - 1 and j > 0) { break; } if (j == 1) { for (int mask = 0; mask < maximum / 2; mask++) { for (int l = 0; l < 2; l++) { const int MASK = mask; const int PREVMASK = mask * 2 + l; const bool above = (bool)l and fromAbove(i, j); dp[i][j][MASK + (1 << (W - 1))] += (not above ? 0 : prev(dp, i, j)[PREVMASK]); dp[i][j][MASK + (1 << (W - 1))] %= MOD; dp[i][j][MASK] += (not above ? prev(dp, i, j)[PREVMASK] * (tail(i, j) == '?' ? 9 : 1) : prev(dp, i, j)[PREVMASK] * (tail(i, j) == '?' ? 8 : 0)); dp[i][j][MASK] %= MOD; } } } else { for (int mask = 0; mask < maximum / 4; mask++) { for (int k = 0; k < 2; k++) { for (int l = 0; l < 2; l++) { const int MASK = mask + k * (1 << (W - 2)); const int PREVMASK = mask * 2 + k * (1 << (W - 1)) + l; const bool left = (bool)k and fromLeft(i, j); const bool above = (bool)l and fromAbove(i, j); dp[i][j][MASK + (1 << (W - 1))] += (not left and not above ? 0 : prev(dp, i, j)[PREVMASK]); dp[i][j][MASK + (1 << (W - 1))] %= MOD; dp[i][j][MASK] += (not left and not above ? prev(dp, i, j)[PREVMASK] * (tail(i, j) == '?' ? 9 : 1) : prev(dp, i, j)[PREVMASK] * (tail(i, j) == '?' ? 8 : 0)); dp[i][j][MASK] %= MOD; } } } } } } ll ans = 0; for (int i = 0; i < maximum; i++) { if (i & (1 << (W - 1))) { ans += dp[H - 1][0][i]; ans %= MOD; } } cout << ans << endl; return 0; }