#include <bits/stdc++.h>
#define MAX_N 801
#define UNVISITED 0
#define BEAR 1
#define BEE 2
using namespace std;
int n, s;
char grid[MAX_N][MAX_N];
int visited[MAX_N][MAX_N];
int beed[MAX_N][MAX_N];
bool check(int t) {
pair<int, int> mecho_pos;
pair<int, int> home_pos;
vector<pair<int, int>> hive_edges;
for(int i = 0; i < n; i++) {
for(int j = 0; j < n; j++) {
visited[i][j] = UNVISITED;
beed[i][j] = -69;
if(grid[i][j] == 'H') {
hive_edges.push_back({i, j});
}
if(grid[i][j] == 'M') {
mecho_pos = {i, j};
}
if(grid[i][j] == 'D') {
home_pos = {i, j};
}
}
}
queue<pair<int, int>> beeq;
vector<pair<int, int>> bees_edge;
for(auto iter : hive_edges) {
visited[iter.first][iter.second] = BEE;
beed[iter.first][iter.second] = 0;
beeq.push(iter);
}
while(!beeq.empty()) {
pair<int, int> curr = beeq.front();
beeq.pop();
if(beed[curr.first][curr.second] == t) {
bees_edge.push_back(curr);
continue;
}
if(visited[curr.first + 1][curr.second] == UNVISITED && (grid[curr.first + 1][curr.second] == 'G' || grid[curr.first + 1][curr.second] == 'M')) {
visited[curr.first + 1][curr.second] = BEE;
beed[curr.first + 1][curr.second] = beed[curr.first][curr.second] + 1;
beeq.push({curr.first + 1, curr.second});
}
if(visited[curr.first - 1][curr.second] == UNVISITED && (grid[curr.first - 1][curr.second] == 'G' || grid[curr.first - 1][curr.second] == 'M')) {
visited[curr.first - 1][curr.second] = BEE;
beed[curr.first - 1][curr.second] = beed[curr.first][curr.second] + 1;
beeq.push({curr.first - 1, curr.second});
}
if(visited[curr.first][curr.second + 1] == UNVISITED && (grid[curr.first][curr.second + 1] == 'G' || grid[curr.first][curr.second + 1] == 'M')) {
visited[curr.first][curr.second + 1] = BEE;
beed[curr.first][curr.second + 1] = beed[curr.first][curr.second] + 1;
beeq.push({curr.first, curr.second + 1});
}
if(visited[curr.first][curr.second - 1] == UNVISITED && (grid[curr.first][curr.second - 1] == 'G' || grid[curr.first][curr.second - 1] == 'M')) {
visited[curr.first][curr.second - 1] = BEE;
beed[curr.first][curr.second - 1] = beed[curr.first][curr.second] + 1;
beeq.push({curr.first, curr.second - 1});
}
}
if(visited[mecho_pos.first][mecho_pos.second] == BEE) {
return false;
}
set<pair<int, int>> mecho_edge;
mecho_edge.insert(mecho_pos);
bool found = false;
while(!found) {
if(mecho_edge.size() == 0) {
return false;
}
queue<pair<pair<int, int>, int>> q; // mecho queue
for(auto iter : mecho_edge) {
visited[iter.first][iter.second] = BEAR;
q.push({iter, 0});
}
mecho_edge.clear();
while(!q.empty()) {
pair<pair<int, int>, int> curr = q.front();
q.pop();
if(curr.first.first + 1 < n && visited[curr.first.first + 1][curr.first.second] == UNVISITED && (grid[curr.first.first + 1][curr.first.second] == 'G' || grid[curr.first.first + 1][curr.first.second] == 'D')){
if(curr.second == s - 1) {
visited[curr.first.first + 1][curr.first.second] = BEAR;
mecho_edge.insert({curr.first.first + 1, curr.first.second});
} else {
visited[curr.first.first + 1][curr.first.second] = BEAR;
q.push({{curr.first.first + 1, curr.first.second}, curr.second + 1});
}
}
if(curr.first.first - 1 >= 0 && visited[curr.first.first - 1][curr.first.second] == UNVISITED && (grid[curr.first.first - 1][curr.first.second] == 'G' || grid[curr.first.first - 1][curr.first.second] == 'D')){
if(curr.second == s - 1) {
visited[curr.first.first - 1][curr.first.second] = BEAR;
mecho_edge.insert({curr.first.first - 1, curr.first.second});
} else {
visited[curr.first.first - 1][curr.first.second] = BEAR;
q.push({{curr.first.first - 1, curr.first.second}, curr.second + 1});
}
}
if(curr.first.second + 1 < n && visited[curr.first.first][curr.first.second + 1] == UNVISITED && (grid[curr.first.first][curr.first.second + 1] == 'G' || grid[curr.first.first][curr.first.second + 1] == 'D')){
if(curr.second == s - 1) {
visited[curr.first.first][curr.first.second + 1] = BEAR;
mecho_edge.insert({curr.first.first, curr.first.second + 1});
} else {
visited[curr.first.first][curr.first.second + 1] = BEAR;
q.push({{curr.first.first, curr.first.second + 1}, curr.second + 1});
}
}
if(curr.first.second - 1 >= 0 && visited[curr.first.first][curr.first.second - 1] == UNVISITED && (grid[curr.first.first][curr.first.second - 1] == 'G' || grid[curr.first.first][curr.first.second - 1] == 'D')){
if(curr.second == s - 1) {
visited[curr.first.first][curr.first.second - 1] = BEAR;
mecho_edge.insert({curr.first.first, curr.first.second - 1});
} else {
visited[curr.first.first][curr.first.second - 1] = BEAR;
q.push({{curr.first.first, curr.first.second - 1}, curr.second + 1});
}
}
}
if(visited[home_pos.first][home_pos.second] == BEAR) {
found = true;
break;
}
vector<pair<int, int>> tmpedge;
for(auto iter : bees_edge) {
if(iter.first + 1 < n && visited[iter.first + 1][iter.second] == UNVISITED && grid[iter.first + 1][iter.second] == 'G') {
visited[iter.first + 1][iter.second] = true;
tmpedge.push_back({iter.first + 1, iter.second});
}
if(iter.first - 1 >= 0 && visited[iter.first - 1][iter.second] == UNVISITED && grid[iter.first - 1][iter.second] == 'G') {
visited[iter.first - 1][iter.second] = true;
tmpedge.push_back({iter.first - 1, iter.second});
}
if(iter.second + 1 < n && visited[iter.first][iter.second + 1] == UNVISITED && grid[iter.first][iter.second + 1] == 'G') {
visited[iter.first][iter.second + 1] = true;
tmpedge.push_back({iter.first, iter.second + 1});
}
if(iter.second - 1 >= 0 && visited[iter.first][iter.second - 1] == UNVISITED && grid[iter.first][iter.second - 1] == 'G') {
visited[iter.first][iter.second - 1] = true;
tmpedge.push_back({iter.first, iter.second - 1});
}
}
bees_edge.clear();
bees_edge = tmpedge;
}
if(found) {
return true;
} else {
return false;
}
}
int main() {
cin >> n >> s;
for(int i = 0; i < n; i++) {
string tmp;
cin >> tmp;
for(int j = 0; j < n; j++) {
grid[i][j] = tmp[j];
}
}
int l = 0, r = 2 * n;
int ans = -1;
// true true true ... (true) false false
while(l <= r) {
int mid = l + (r - l) / 2;
if(check(mid)) {
ans = mid;
l = mid + 1;
} else {
r = mid - 1;
}
}
cout << ans;
return 0;
}
