#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>
using namespace std;
typedef long long LL;
typedef long double LD;
typedef complex<double> CMP;
const int dy[] = {-1,+1,0,0};
const int dx[] = {0,0,-1,+1};
template<typename T>
class IdGen
{
map<T, int> v2id_;
vector<T> id2v_;
public:
int v2id(const T& v) {
if( !v2id_.count(v) ) { v2id_[v] = size(); id2v_.push_back(v); }
return v2id_[v];
}
const T& id2v(int i) const { return id2v_[i]; }
int size() const { return id2v_.size(); }
};
template<typename Vert, typename Flow, int NV=2048>
class MaxFlow
{
IdGen<Vert> idgen;
vector<int> G[NV];
Flow F[NV][NV];
public:
void addEdge( Vert s_, Vert t_, Flow f )
{
const int s = idgen.v2id(s_), t = idgen.v2id(t_);
G[s].push_back(t);
G[t].push_back(s);
F[s][t] = f;
F[t][s] = 0;
}
Flow calc( Vert s_, Vert t_ )
{
const int S = idgen.v2id(s_), D = idgen.v2id(t_);
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 Block3Checkers { public:
int blockThem(vector <string> board)
{
int H = board.size();
int W = board[0].size();
for(int y=0; y<H; ++y)
for(int x=0; x<W; ++x)
if(board[y][x] == 'A') {
for(int d=0; d<4; ++d) {
int xx = x+dx[d];
int yy = y+dy[d];
if(0<=xx&&xx<W&&0<=yy&&yy<H&&board[yy][xx]=='A')
return 100;
}
}
vector<pair<int,int> > ps, as;
for(int y=0; y<H; ++y)
for(int x=0; x<W; ++x)
if(board[y][x]=='.')
ps.push_back(make_pair(y,x));
else if(board[y][x]=='A')
as.push_back(make_pair(y,x));
vector<vector<int> > rf;
if(ok(board,as,rf))
return 0;
for(int i=0; i<ps.size(); ++i) {
int y = ps[i].first;
int x = ps[i].second;
board[y][x] = 'N';
if(ok(board,as,rf))
return 1;
board[y][x] = '.';
}
int best = 6;
for(int i=0; i<ps.size(); ++i)
for(int k=i+1; k<ps.size(); ++k) {
int y1 = ps[i].first;
int x1 = ps[i].second;
int y2 = ps[k].first;
int x2 = ps[k].second;
board[y1][x1] = 'N';
board[y2][x2] = 'N';
if(ok(board,as,rf))
return 2;
if(rf[as[0].first][as[0].first] == (1<<0))
best = min(best, 2+split(board, as[1], as[2]));
if(rf[as[1].first][as[1].first] == (1<<1))
best = min(best, 2+split(board, as[2], as[0]));
if(rf[as[2].first][as[2].first] == (1<<2))
best = min(best, 2+split(board, as[0], as[1]));
board[y1][x1] = '.';
board[y2][x2] = '.';
}
return best;
}
bool ok(const vector<string>& B, vector<pair<int,int> >& as, vector<vector<int> >& rf)
{
int H = B.size();
int W = B[0].size();
rf.assign(H, vector<int>(W, 0));
for(int i=0; i<as.size(); ++i)
{
int ay = as[i].first;
int ax = as[i].second;
rf[ay][ax] |= (1<<i);
queue<pair<int,int> > q;
q.push(as[i]);
while(!q.empty()) {
int y = q.front().first;
int x = q.front().second;
q.pop();
for(int d=0; d<4; ++d) {
int yy = y+dy[d];
int xx = x+dx[d];
if(0<=yy&&yy<H&&0<=xx&&xx<W&&B[y][x]!='N'&&!(rf[yy][xx]&(1<<i))) {
rf[yy][xx] |= 1<<i;
q.push(make_pair(yy,xx));
}
}
}
}
for(int i=0; i<as.size(); ++i)
if(rf[as[i].first][as[i].second] != (1<<i))
return false;
return true;
}
int split(const vector<string>& B, pair<int,int> S, pair<int,int> D)
{
int OUT = 0, IN = 1;
typedef pair<int, pair<int,int> > Vert;
MaxFlow<Vert, int>* mf = new MaxFlow<Vert,int>;
int H = B.size();
int W = B[0].size();
for(int y=0; y<H; ++y)
for(int x=0; x<W; ++x)
if(B[y][x] != 'N') {
pair<int,int> p(y,x);
for(int d=0; d<4; ++d) {
int xx = x+dx[d];
int yy = y+dy[d];
if(0<=xx&&xx<W&&0<=yy&&yy<H&&B[yy][xx]!='N')
mf->addEdge(make_pair(OUT, p), make_pair(IN, make_pair(yy,xx)), 1);
}
if(p!=S && p!=D)
mf->addEdge(make_pair(IN, p), make_pair(OUT, p), 1);
}
int m = mf->calc(make_pair(OUT,S), make_pair(IN,D));
delete mf;
return m;
}
};
// 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(_, Block3Checkers().blockThem(board));}
int main(){
CASE(0)
string board_[] = {"A......A",
"...N.N..",
".NNN.NN.",
"NNNN.N.N",
"N.NN.NNN",
".NNN.NNN",
"NNN...NN",
".NN.A..N"};
vector <string> board(board_, board_+sizeof(board_)/sizeof(*board_));
int _ = 1;
END
CASE(1)
string board_[] = {".....A",
"......",
"......",
"NNNNNN",
"A.....",
"A....."};
vector <string> board(board_, board_+sizeof(board_)/sizeof(*board_));
int _ = 100;
END
CASE(2)
string board_[] = {"A.N",
"NNA",
"AN."};
vector <string> board(board_, board_+sizeof(board_)/sizeof(*board_));
int _ = 0;
END
CASE(3)
string board_[] = {"......NA",
".NNNN.N.",
".N......",
"....NNNN",
"........",
".N..NNN.",
"......N.",
"A.N....A"}
;
vector <string> board(board_, board_+sizeof(board_)/sizeof(*board_));
int _ = 3;
END
/*
CASE(4)
string board_[] = ;
vector <string> board(board_, board_+sizeof(board_)/sizeof(*board_));
int _ = ;
END
CASE(5)
string board_[] = ;
vector <string> board(board_, board_+sizeof(board_)/sizeof(*board_));
int _ = ;
END
*/
}
// END CUT HERE