// From https://usaco.guide/problems/ioi-2009mecho/solution
#include <bits/stdc++.h>
using namespace std;
#define pii pair<int, int>
#define MAX_N 800
vector<string> field(MAX_N);
int n, s;
int dx[4] = {-1, 0, 1, 0};
int dy[4] = {0, -1, 0, 1};
int mechox, mechoy, home_x, home_y;
vector<vector<bool>> bees_visited(MAX_N, vector<bool>(MAX_N));
vector<vector<int>> bees_time(MAX_N, vector<int>(MAX_N));
bool valid_sq(int x, int y) {
return x >= 0 && x < n && y >= 0 && y < n && (field[x][y] == 'G' || field[x][y] == 'M');
}
bool mecho_reached(int mecho_dis, int bees_dis){
return mecho_dis / s < bees_dis;
}
bool ok(int eating_time) {
vector<vector<bool>> mecho_visited(n, vector<bool>(n));
vector<vector<int>> mecho_time(n, vector<int>(n));
// move Mecho
queue<pii> q;
q.push({mechox, mechoy});
mecho_visited[mechox][mechoy] = true;
if (bees_time[mechox][mechoy] <= eating_time) {
q.pop();
}
while (!q.empty()) {
int x = q.front().first, y = q.front().second;
q.pop();
for (int i = 0; i < 4; i++) {
int nx = x + dx[i], ny = y + dy[i];
/*
* check if mecho reaces node[x][y] before the bees
* divide the time mecho takes to reach a node by s, since
* mecho walks s steps at a time.
* substract the eating time from the time taken for the
* bees to reach the node, because that time was used by
* mecho for eating
*/
if (valid_sq(nx, ny) && !mecho_visited[nx][ny] &&
mecho_reached(mecho_time[x][y] + 1, bees_time[nx][ny]
- eating_time)) {
mecho_visited[nx][ny] = true;
q.push({nx, ny});
mecho_time[nx][ny] = mecho_time[x][y] + 1;
}
}
}
// check if mecho reached a node surrounding his cave before the bees
for (int i = 0; i < 4; i++) {
int nx = home_x + dx[i], ny = home_y + dy[i];
if (valid_sq(nx, ny) && mecho_reached(mecho_time[nx][ny],
bees_time[nx][ny] - eating_time) && mecho_visited[nx][ny]) {
return true;
}
}
return false;
}
int bs(int lo, int hi) {
if (lo > hi) {
return -1;
}
int mid = (lo + hi) / 2;
if (!ok(mid)) {
return bs(lo, mid - 1);
}
else if (mid < hi && ok(mid + 1)) {
return bs(mid + 1, hi);
}
else {
return mid;
}
}
int main() {
cin >> n >> s;
for (int i = 0; i < n; i++) {
cin >> field[i];
}
vector<pii> hives;
// find x and y coordinates for for Mecho, the bees and the cave
for (int i = 0; i < n; i++) {
for (int j = 0; j < n; j++) {
if (field[i][j] == 'M') {
mechox = i;
mechoy = j;
} else if (field[i][j] == 'H') {
hives.push_back({i, j});
} else if (field[i][j] == 'D') {
home_x = i;
home_y = j;
}
}
}
// move bees
queue<pii> q;
for (auto i : hives) {
q.push({i.first, i.second});
bees_visited[i.first][i.second] = true;
}
while (!q.empty()) {
int x = q.front().first, y = q.front().second;
q.pop();
for (int i = 0; i < 4; i++) {
int nx = x + dx[i], ny = y + dy[i];
if (valid_sq(nx, ny) && !bees_visited[nx][ny]) {
bees_time[nx][ny] = bees_time[x][y] + 1;
q.push({nx, ny});
bees_visited[nx][ny] = true;
}
}
}
// binary search on waiting time
cout << bs(0, n * n) << "\n";
}
