usaco replication third fail

#include <bits/stdc++.h>
using namespace std;

const int dr[4] = {-1, 0, 1, 0};
const int dc[4] = {0, 1, 0, -1};

const int MAXN = 1010;

int n, D;

bool wall[MAXN][MAXN];
int dist[MAXN][MAXN];
int firstiter[MAXN][MAXN];
bool vis[MAXN][MAXN][2];
bool vis2[MAXN][MAXN];
vector<pair<int, int>> queues[MAXN];

//vector<vector<bool>> wall, vis2;
//vector<vector<int>> dist, firstiter;
//vector<vector<pair<int, int>>> queues;

int main() {
    cin.tie(0)->sync_with_stdio(false);
//  #ifndef _DEBUG
//  freopen("dream.in", "r", stdin);
//  freopen("dream.out", "w", stdout);
//  #endif
//  wall.assign(MAXN, vector<bool>(MAXN));
//  dist.assign(MAXN, vector<int>(MAXN));
//  firstiter.assign(MAXN, vector<int>(MAXN));
//  vis2.assign(MAXN, vector<bool>(MAXN));
//  queues.assign(MAXN, vector<pair<int, int>>());
    cin >> n >> D;
    queue<pair<int, int>> q;
    queue<tuple<int, int, int>> q2;
    for (int r = 1; r <= n; ++r) {
        for (int c = 1; c <= n; ++c) {
            dist[r][c] = -1;
            vis[r][c][0] = vis[r][c][1] = false;
            firstiter[r][c] = -1;
            char ch;
            cin >> ch;
            if (ch == 'S') {
                ch = '.';
                q2.emplace(r, c, 0);
                vis[r][c][0] = true;
            }
            if (ch == '.') {
                wall[r][c] = false;
            } else {
                wall[r][c] = true;
                q.emplace(r, c);
                dist[r][c] = 0;
            }
        }
    }
    while (!q.empty()) {
        int r, c;
        tie(r, c) = q.front();
        q.pop();
        for (int dir = 0; dir < 4; ++dir) {
            int r1 = r + dr[dir];
            int c1 = c + dc[dir];
            if (dist[r1][c1] == -1) {
                dist[r1][c1] = dist[r][c] + 1;
                q.emplace(r1, c1);
            }
        }
    }
    while (!q2.empty()) {
        int r, c, t;
        tie(r, c, t) = q2.front();
        q2.pop();
        int par = t % 2;
        int iter = t / D;
        firstiter[r][c] = iter;
        if (t > 0 && t % D == 0) {
            // expand
            if (iter >= dist[r][c]) {
                // no space
                firstiter[r][c] = iter-1; // before expanding
                continue;
            }
        }
        for (int dir = 0; dir < 4; ++dir) {
            int r1 = r + dr[dir];
            int c1 = c + dc[dir];
            if (wall[r1][c1] || vis[r1][c1][1-par]) continue;
            if (iter >= dist[r1][c1]) continue;
            vis[r1][c1][1-par] = true;
            q2.emplace(r1, c1, t+1);
        }
    }
//  static int PAPA[MAXN][MAXN];
    int dpar = D % 2;
    for (int r = 1; r <= n; ++r) {
        for (int c = 1; c <= n; ++c) {
            vis2[r][c] = false;
            int maxiter = -1;
            if (vis[r][c][dpar]) {
                maxiter = max(maxiter, firstiter[r][c]);
                int x = dist[r][c]-1;
                for (int dir = 0; dir < 4; ++dir) {
                    int r1 = r + dc[dir];
                    int c1 = c + dc[dir];
                    if (!vis[r1][c1][1-dpar]) continue;
                    int x1 = dist[r1][c1]-1;
                    maxiter = max(maxiter, min(x, x1+1));
                }
            }
            if (vis[r][c][1-dpar]) {
                maxiter = max(maxiter, firstiter[r][c]);
                for (int dir = 0; dir < 4; ++dir) {
                    int r1 = r + dc[dir];
                    int c1 = c + dc[dir];
                    if (!vis[r1][c1][dpar]) continue;
                    int x1 = dist[r1][c1]-1;
                    maxiter = max(maxiter, x1);
                }
            }
            if (maxiter >= 0) {
                queues[maxiter].emplace_back(r, c);
            }
//          PAPA[r][c]=maxiter;
        }
    }
    int ans = 0;
    for (int iter = n; iter >= 0; --iter) {
        for (auto& cell : queues[iter]) {
            int r, c;
            tie(r, c) = cell;
            if (vis2[r][c]) continue;
            vis2[r][c] = true;
            ++ans; // #vis2
            if (iter == 0) continue;
            for (int dir = 0; dir < 4; ++dir) {
                int r1 = r + dr[dir];
                int c1 = c + dc[dir];
                if (!wall[r1][c1] && !vis2[r1][c1]) {
                    queues[iter-1].emplace_back(r1, c1);
                }
            }
        }
    }
    cout << ans << '\n';
//  cout<<"vis:\n";
//  for (int r = 1; r <= n; ++r) {
//      for (int c = 1; c <= n ; ++c) {
//          if (wall[r][c]) cout<<"#";
//          else if (vis2[r][c]) cout << "x";
//          else cout << ".";
//      }
//      cout<<"\n";
//  }
//  cout<<"dist:\n";
//  for (int r = 1; r <= n; ++r) {
//      for (int c = 1; c <= n; ++c) {
//          cout<<dist[r][c];
//      }
//      cout<<"\n";
//  }
//  cout<<"visparity:\n";
//  for (int r = 1; r <= n; ++r) {
//      for (int c = 1; c <= n; ++c) {
//          if(wall[r][c])cout<<"#";
//          else if (vis[r][c][0]&&vis[r][c][1])cout<<"2";
//          else if (vis[r][c][0])cout<<"0";
//          else if (vis[r][c][1])cout<<"1";
//          else cout<<".";;
//      }
//      cout<<"\n";
//  }
//  cout<<"maxiter:\n";
//  for (int r = 1; r <= n; ++r) {
//      for (int c = 1; c <= n; ++c) {
//          if(wall[r][c])cout<<"#";
//          else if (PAPA[r][c]==-1) cout << ".";
//          else cout<<PAPA[r][c];
//      }
//      cout<<"\n";
//  }
//  cout<<"firstiter:\n";
//  for (int r = 1; r <= n; ++r) {
//      for (int c = 1; c <= n; ++c) {
//          if(wall[r][c])cout<<"#";
//          else if (firstiter[r][c]==-1) cout << ".";
//          else cout<<firstiter[r][c];
//      }
//      cout<<"\n";
//  }
}