#include // {{{ // https://codeforces.com/blog/entry/96344 #pragma GCC optimize("O2,unroll-loops") #pragma GCC target("avx2,bmi,bmi2,lzcnt,popcnt") using namespace std; template [[nodiscard]] static T MIN() { return std::numeric_limits::min(); } template [[nodiscard]] static T MAX() { return std::numeric_limits::max(); } template [[nodiscard]] static T sc(auto&& x) { return static_cast(x); } template [[nodiscard]] static T sz(auto&& x) { return static_cast(x.size()); } #define prln(...) std::println(__VA_ARGS__) #define pr(...) std::print(__VA_ARGS__) #ifdef LOCAL #define dbgln(...) std::println(__VA_ARGS__) #define dbg(...) std::print(__VA_ARGS__) #endif inline static void NO() { prln("NO"); } inline static void YES() { prln("YES"); } using ll = long long; using ld = long double; template using ve = std::vector; template using ar = std::array; template using pa = std::pair; template using tu = std::tuple; template using dq = std::deque; template using qu = std::queue; template using pq = std::priority_queue; template using st = std::stack; auto lb = [](auto... args) { return std::lower_bound(args...); }; auto ub = [](auto... args) { return std::upper_bound(args...); }; #define ff first #define ss second #define eb emplace_back #define pb push_back #define all(x) (x).begin(), (x).end() #define rall(x) (x).rbegin(), (x).rend() // }}} constexpr static ll MOD = 998244353; void solve() { int n, m; ld d; cin >> n >> m >> d; ll d_squared = ll(d * d + 0.5); // Round to nearest integer auto dist = [](pair p1, pair p2) { return (p1.first - p2.first) * (p1.first - p2.first) + (p1.second - p2.second) * (p1.second - p2.second); }; vector grid(n); for (int i = 0; i < n; ++i) { cin >> grid[i]; } reverse(grid.begin(), grid.end()); vector>> holds(n); for (int i = 0; i < n; ++i) { for (int j = 0; j < m; ++j) { if (grid[i][j] == 'X') { holds[i].emplace_back(j, i); } } } // Check if starting level has holds if (holds[0].empty()) { cout << "0\n"; return; } vector prev(holds[0].size(), 1); for (int level = 1; level < n; ++level) { if (holds[level].empty()) { cout << "0\n"; return; } vector dp1(holds[level].size(), 0); vector dp2(holds[level].size(), 0); // First pass: transition from previous level int l = 0, r = 0; ll total = 0; for (int i = 0; i < holds[level].size(); ++i) { auto& h = holds[level][i]; // Expand r to include holds with dist <= d_squared while (r < prev.size() && dist(holds[level - 1][r], h) <= d_squared) { total = (total + prev[r]) % MOD; r++; } // Shrink l to exclude holds with dist > d_squared while (l < r && dist(holds[level - 1][l], h) > d_squared) { total = (total - prev[l] + MOD) % MOD; l++; } dp1[i] = total; } // Second pass: same-level transitions (pairs) l = 0, r = 0; total = 0; for (int i = 0; i < holds[level].size(); ++i) { auto& h = holds[level][i]; // Expand r to include holds with dist <= d_squared while (r < holds[level].size() && dist(holds[level][r], h) <= d_squared) { total = (total + dp1[r]) % MOD; r++; } // Shrink l to exclude holds with dist > d_squared while (l < r && dist(holds[level][l], h) > d_squared) { total = (total - dp1[l] + MOD) % MOD; l++; } // Subtract dp1[i] to avoid self-pairing dp2[i] = (total - dp1[i] + MOD) % MOD; } // Combine dp1 and dp2 for (int i = 0; i < holds[level].size(); ++i) { dp1[i] = (dp1[i] + dp2[i]) % MOD; } prev = dp1; } ll ans = accumulate(prev.begin(), prev.end(), 0LL) % MOD; cout << ans << "\n"; } int main() { // {{{ cin.tie(nullptr)->sync_with_stdio(false); cin.exceptions(cin.failbit); int t = 1; cin >> t; while (t--) { solve(); } return 0; } // }}}