#include <bits/stdc++.h>
using namespace std;
const int MAX_N = 805;
int n, s;
char c[MAX_N][MAX_N];
vector<vector<int>> vis(MAX_N, vector<int>(MAX_N, INT_MAX)); // bee_time
pair<int, int> st, ed; // Start 'M' and end 'D' positions
int dx[4] = {0, 0, 1, -1};
int dy[4] = {1, -1, 0, 0};
// BFS to compute when bees reach each cell
void compute_bee_times() {
queue<pair<int, int>> q;
for (int i = 0; i < n; i++) {
for (int j = 0; j < n; j++) {
if (c[i][j] == 'H') {
q.push({i, j});
vis[i][j] = 0;
}
}
}
while (!q.empty()) {
auto [x, y] = q.front();
q.pop();
for (int d = 0; d < 4; d++) {
int nx = x + dx[d];
int ny = y + dy[d];
if (nx >= 0 && nx < n && ny >= 0 && ny < n &&
(c[nx][ny] == 'G' || c[nx][ny] == 'M') && vis[nx][ny] == INT_MAX) {
vis[nx][ny] = vis[x][y] + 1;
q.push({nx, ny});
}
}
}
}
// Check if Mecho can reach 'D' starting at minute k+1
bool check(int k) {
if (vis[st.first][st.second] <= k) return false; // Caught at 'M'
vector<pair<int, int>> current_positions;
queue<array<int, 3>> q; // (x, y, dist)
vector<vector<bool>> local_vis(n, vector<bool>(n, false));
q.push({st.first, st.second, 0});
local_vis[st.first][st.second] = true;
// Positions reachable at the end of minute k+1
while (!q.empty()) {
auto [x, y, dist] = q.front();
q.pop();
if (dist > s) continue;
if (vis[x][y] > k + 1) {
current_positions.push_back({x, y});
}
for (int d = 0; d < 4; d++) {
int nx = x + dx[d];
int ny = y + dy[d];
if (nx >= 0 && nx < n && ny >= 0 && ny < n &&
c[nx][ny] != 'T' && c[nx][ny] != 'H' && !local_vis[nx][ny]) {
local_vis[nx][ny] = true;
q.push({nx, ny, dist + 1});
}
}
}
int t = k + 1;
while (!current_positions.empty()) {
if (find(current_positions.begin(), current_positions.end(), ed) !=
current_positions.end()) {
return true;
}
t++;
vector<pair<int, int>> next_positions;
q = queue<array<int, 3>>();
local_vis.assign(n, vector<bool>(n, false));
// Start BFS from all current positions
for (auto [x, y] : current_positions) {
if (!local_vis[x][y]) {
q.push({x, y, 0});
local_vis[x][y] = true;
}
}
// Positions reachable by the end of minute t
while (!q.empty()) {
auto [x, y, dist] = q.front();
q.pop();
if (dist > s) continue;
if (vis[x][y] > t) {
next_positions.push_back({x, y});
}
for (int d = 0; d < 4; d++) {
int nx = x + dx[d];
int ny = y + dy[d];
if (nx >= 0 && nx < n && ny >= 0 && ny < n &&
c[nx][ny] != 'T' && c[nx][ny] != 'H' && !local_vis[nx][ny]) {
local_vis[nx][ny] = true;
q.push({nx, ny, dist + 1});
}
}
}
current_positions = next_positions;
}
return false;
}
int main() {
ios::sync_with_stdio(false);
cin.tie(nullptr);
cin >> n >> s;
for (int i = 0; i < n; i++) {
for (int j = 0; j < n; j++) {
cin >> c[i][j];
if (c[i][j] == 'M') st = {i, j};
if (c[i][j] == 'D') ed = {i, j};
}
}
compute_bee_times();
int lo = 0, hi = n * n; // Maximum reasonable k
int ans = -1;
while (lo <= hi) {
int mid = lo + (hi - lo) / 2;
if (check(mid)) {
ans = mid;
lo = mid + 1;
} else {
hi = mid - 1;
}
}
cout << ans << "\n";
return 0;
}
