#include <iostream>
#include <sstream>
#include <iomanip>
#include <vector>
#include <string>
#include <map>
#include <set>
#include <algorithm>
#include <numeric>
#include <iterator>
#include <functional>
#include <complex>
#include <queue>
#include <stack>
#include <cmath>
#include <cassert>
#include <tuple>
using namespace std;
typedef long long LL;
typedef complex<double> CMP;
template<typename Vert=int, typename Flow=int, int NV=2048>
class MaxFlow
{
vector<int> G[NV];
Flow F[NV][NV];
public:
void addEdge( Vert s, Vert t, Flow f )
{
G[s].push_back(t);
G[t].push_back(s);
F[s][t] = f;
F[t][s] = 0;
}
Flow calc( Vert S, Vert D )
{
for( Flow total=0 ;; ) {
// Do BFS and compute the level for each node.
int LV[NV] = {0};
vector<int> Q(1, S);
for(int lv=1; !Q.empty(); ++lv) {
vector<int> Q2;
for(size_t i=0; i!=Q.size(); ++i) {
const vector<int>& ne = G[Q[i]];
for(size_t j=0; j!=ne.size(); ++j)
if( F[Q[i]][ne[j]] && !LV[ne[j]] && ne[j]!=S )
LV[ne[j]]=lv, Q2.push_back(ne[j]);
}
Q.swap(Q2);
}
// Destination is now unreachable. Done.
if( !LV[D] )
return total;
// Iterating DFS.
bool blocked[NV] = {};
total += dinic_dfs( S, D, LV, 0x7fffffff, blocked );
}
}
private:
Flow dinic_dfs( int v, int D, int LV[], Flow flow_in, bool blocked[] )
{
Flow flow_out = 0;
for(size_t i=0; i!=G[v].size(); ++i) {
int u = G[v][i];
if( LV[v]+1==LV[u] && F[v][u] ) {
Flow f = min(flow_in-flow_out, F[v][u]);
if( u==D || !blocked[u] && (f=dinic_dfs(u,D,LV,f,blocked))>0 ) {
F[v][u] -= f;
F[u][v] += f;
flow_out += f;
if( flow_in == flow_out ) return flow_out;
}
}
}
blocked[v] = (flow_out==0);
return flow_out;
}
};
class BlockTheBlockPuzzle { public:
int minimumHoles(vector <string> board)
{
const int H = board.size();
const int W = board[0].size();
const int INF = 2500;
for(int gy=0; gy<H; ++gy)
for(int gx=0; gx<W; ++gx) if(board[gy][gx] == '$')
{
map<pair<int,int>, int> id;
for(int y=gy%3; y<H; y+=3)
for(int x=gx%3; x<W; x+=3)
{
int new_id = id.size();
id[make_pair(y,x)] = new_id;
}
int N = id.size();
MaxFlow<>* mf = new MaxFlow<>;
enum {IN, OUT};
int Goal;
vector<int> Start;
for(int y=gy%3; y<H; y+=3)
for(int x=gx%3; x<W; x+=3)if(board[y][x]!='H')
{
int v1 = id[make_pair(y,x)];
if(board[y][x]=='$')
Goal = v1;
if(board[y][x]=='b')
Start.push_back(v1);
int e = (board[y][x]=='.' ? 1 : INF);
mf->addEdge(v1*2+IN, v1*2+OUT, e);
//cerr << v1 << " -- " << e << " -- " << v1 << endl;
const int dy[] = {+1,0};
const int dx[] = {0,+1};
for(int d=0; d<2; ++d)
{
int Y = y+dy[d]*3;
int X = x+dx[d]*3;
if(0<=Y&&Y<H&&0<=X&&X<W&&board[Y][X]!='H')
{
int v2 = id[make_pair(Y,X)];
int y1=y+dy[d]*1;
int x1=x+dx[d]*1;
int y2=y+dy[d]*2;
int x2=x+dx[d]*2;
int e = INF;
if(board[y1][x1]!='b'&&board[y2][x2]!='b')
e = (board[y1][x1]=='.')+(board[y2][x2]=='.');
if(e) {
mf->addEdge(v1*2+OUT, v2*2+IN, e);
mf->addEdge(v2*2+OUT, v1*2+IN, e);
//cerr << v1 << " -- " << e << " -- " << v2 << endl;
}
}
}
}
for(int v: Start) {
//cerr << "S: " << v << endl;
mf->addEdge(v*2+OUT, N*2+IN, INF);
}
//cerr << "G: " << Goal << endl;
int ans = mf->calc(Goal*2+OUT, N*2+IN);
delete mf;
return ans>=INF ? -1 : ans;
}
return -1;
}
};
// BEGIN CUT HERE
#include <ctime>
double start_time; string timer()
{ ostringstream os; os << " (" << int((clock()-start_time)/CLOCKS_PER_SEC*1000) << " msec)"; return os.str(); }
template<typename T> ostream& operator<<(ostream& os, const vector<T>& v)
{ os << "{ ";
for(typename vector<T>::const_iterator it=v.begin(); it!=v.end(); ++it)
os << '\"' << *it << '\"' << (it+1==v.end() ? "" : ", "); os << " }"; return os; }
void verify_case(const int& Expected, const int& Received) {
bool ok = (Expected == Received);
if(ok) cerr << "PASSED" << timer() << endl; else { cerr << "FAILED" << timer() << endl;
cerr << "\to: \"" << Expected << '\"' << endl << "\tx: \"" << Received << '\"' << endl; } }
#define CASE(N) {cerr << "Test Case #" << N << "..." << flush; start_time=clock();
#define END verify_case(_, BlockTheBlockPuzzle().minimumHoles(board));}
int main(){
CASE(0)
string board_[] = {"b..$",
"....",
"HHHH",
"HHHH"};
vector <string> board(board_, board_+sizeof(board_)/sizeof(*board_));
int _ = 2;
END
CASE(1)
string board_[] = {"............H..",
"...............",
"...............",
"HHH$HHH.....H..",
"HHHHHHH........",
"HHHHHHHH.......",
"......b..H.....",
"...............",
"...............",
"...H..H..H.....",
"...............",
"...............",
"...............",
"...............",
"..............."};
vector <string> board(board_, board_+sizeof(board_)/sizeof(*board_));
int _ = 0;
END
CASE(2)
string board_[] = {"............H..",
"...............",
"...............",
"HHH$HHH........",
"HHHHHHH........",
"HHHHHHHH.......",
"......b..H.....",
"...............",
"...............",
"...H..H..H.....",
"...............",
"...............",
"...............",
"...............",
"..............."};
vector <string> board(board_, board_+sizeof(board_)/sizeof(*board_));
int _ = 1;
END
CASE(3)
string board_[] = {"b..$...",
"...H...",
".......",
"b..b..b",
"...H...",
".......",
"b..b..b"}
;
vector <string> board(board_, board_+sizeof(board_)/sizeof(*board_));
int _ = 4;
END
CASE(4)
string board_[] = {"b..b..b",
"..b..b.",
".......",
"b..$bbb",
".b.....",
"....b..",
"b..b..b"}
;
vector <string> board(board_, board_+sizeof(board_)/sizeof(*board_));
int _ = -1;
END
/*
CASE(5)
string board_[] = ;
vector <string> board(board_, board_+sizeof(board_)/sizeof(*board_));
int _ = ;
END
CASE(6)
string board_[] = ;
vector <string> board(board_, board_+sizeof(board_)/sizeof(*board_));
int _ = ;
END
*/
}
// END CUT HERE