#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 <cstring>
#ifdef __GNUC__
#include <ext/hash_map>
#define unordered_map __gnu_cxx::hash_map
#else
#include <unordered_map>
#endif
using namespace std;
typedef long long LL;
typedef complex<double> CMP;
typedef int vert;
typedef vert edge;
typedef vector<edge> edges;
typedef vector<edges> graph;
bool augment( graph& G, int v, vector<vert>& matchTo, bool visited[] )
{
for(int i=0; i<G[v].size(); ++i) {
vert u = G[v][i];
if( visited[u] ) continue;
visited[u] = true;
if( matchTo[u]<0 || augment(G, matchTo[u], matchTo, visited) )
{ matchTo[v]=u, matchTo[u]=v; return true; }
}
return false;
}
template<int NV>
int biMatch( graph& G, int L ) // [0,L):left, [L,?):right
// only left->right edges are used during computation
{
vector<vert> matchTo(G.size(), -1);
int ans = 0;
for(vert v=0; v<L; ++v) {
bool visited[NV] = {};
if( augment(G, v, matchTo, visited) )
++ans;
}
return ans;
}
class P8XMatrixRecovery { public:
int H, W;
vector <string> solve(vector <string> rows, vector <string> columns)
{
H = rows.size();
W = rows[0].size();
for(int y=0; y<H; ++y)
for(int x=0; x<W; ++x)
if( rows[y][x] == '?' ) {
rows[y][x] = '0';
if( !can(rows, columns) )
rows[y][x] = '1';
}
return rows;
}
bool can(const vector<string>& rows, const vector<string>& columns)
{
graph G(W*2);
for(int x1=0; x1<W; ++x1) {
string left;
for(int y=0; y<H; ++y)
left += rows[y][x1];
for(int x2=0; x2<W; ++x2)
if( match(left, columns[x2]) )
G[x1].push_back(x2+W);
}
return biMatch<60>(G, W) == W;
}
bool match( const string& l, const string& r )
{
for(int i=0; i<l.size(); ++i)
if( l[i]!=r[i] && l[i]!='?' && r[i]!='?' )
return false;
return true;
}
};
// 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 vector <string>& Expected, const vector <string>& 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(_, P8XMatrixRecovery().solve(rows, columns));}
int main(){
CASE(0)
string rows_[] = {"10?"
,"?11"};
vector <string> rows(rows_, rows_+sizeof(rows_)/sizeof(*rows_));
string columns_[] = {"01"
,"10"
,"1?"}
;
vector <string> columns(columns_, columns_+sizeof(columns_)/sizeof(*columns_));
string __[] = {"101", "011" };
vector <string> _(__, __+sizeof(__)/sizeof(*__));
END
CASE(1)
string rows_[] = {"0"
,"?"
,"1"};
vector <string> rows(rows_, rows_+sizeof(rows_)/sizeof(*rows_));
string columns_[] = {"0?1"};
vector <string> columns(columns_, columns_+sizeof(columns_)/sizeof(*columns_));
string __[] = {"0", "0", "1" };
vector <string> _(__, __+sizeof(__)/sizeof(*__));
END
CASE(2)
string rows_[] = {"10"
,"01"};
vector <string> rows(rows_, rows_+sizeof(rows_)/sizeof(*rows_));
string columns_[] = {"10"
,"01"};
vector <string> columns(columns_, columns_+sizeof(columns_)/sizeof(*columns_));
string __[] = {"10", "01" };
vector <string> _(__, __+sizeof(__)/sizeof(*__));
END
CASE(3)
string rows_[] = {"??0"
,"11?"
,"?01"
,"1?1"};
vector <string> rows(rows_, rows_+sizeof(rows_)/sizeof(*rows_));
string columns_[] = {"1???"
,"?111"
,"0?1?"};
vector <string> columns(columns_, columns_+sizeof(columns_)/sizeof(*columns_));
string __[] = {"010", "110", "101", "101" };
vector <string> _(__, __+sizeof(__)/sizeof(*__));
END
CASE(4)
string rows_[] = {
"??????????????????????????????",
"??????????????????????????????",
"??????????????????????????????",
"??????????????????????????????",
"??????????????????????????????",
"??????????????????????????????",
"??????????????????????????????",
"??????????????????????????????",
"??????????????????????????????",
"??????????????????????????????",
"??????????????????????????????",
"??????????????????????????????",
"??????????????????????????????",
"??????????????????????????????",
"??????????????????????????????",
"??????????????????????????????",
"??????????????????????????????",
"??????????????????????????????",
"??????????????????????????????",
"??????????????????????????????",
"??????????????????????????????",
"??????????????????????????????",
"??????????????????????????????",
"??????????????????????????????",
"??????????????????????????????",
"??????????????????????????????",
"??????????????????????????????",
"??????????????????????????????",
"??????????????????????????????",
"??????????????????????????????",
};
vector <string> rows(rows_, rows_+sizeof(rows_)/sizeof(*rows_));
string columns_[] = {
"??????????????????????????????",
"??????????????????????????????",
"??????????????????????????????",
"??????????????????????????????",
"??????????????????????????????",
"??????????????????????????????",
"??????????????????????????????",
"??????????????????????????????",
"??????????????????????????????",
"??????????????????????????????",
"??????????????????????????????",
"??????????????????????????????",
"??????????????????????????????",
"??????????????????????????????",
"??????????????????????????????",
"??????????????????????????????",
"??????????????????????????????",
"??????????????????????????????",
"??????????????????????????????",
"??????????????????????????????",
"??????????????????????????????",
"??????????????????????????????",
"??????????????????????????????",
"??????????????????????????????",
"??????????????????????????????",
"??????????????????????????????",
"??????????????????????????????",
"??????????????????????????????",
"??????????????????????????????",
"??????????????????????????????",
};
vector <string> columns(columns_, columns_+sizeof(columns_)/sizeof(*columns_));
string __[] = {"?"};
vector <string> _(__, __+sizeof(__)/sizeof(*__));
END
CASE(5)
string rows_[] = {"?"};
vector <string> rows(rows_, rows_+sizeof(rows_)/sizeof(*rows_));
string columns_[] = {"?"};
vector <string> columns(columns_, columns_+sizeof(columns_)/sizeof(*columns_));
string __[] = {"0"};
vector <string> _(__, __+sizeof(__)/sizeof(*__));
END
CASE(6)
string rows_[] = {"??","??"};
vector <string> rows(rows_, rows_+sizeof(rows_)/sizeof(*rows_));
string columns_[] = {"00","11"};
vector <string> columns(columns_, columns_+sizeof(columns_)/sizeof(*columns_));
string __[] = {"01","01"};
vector <string> _(__, __+sizeof(__)/sizeof(*__));
END
CASE(7)
string rows_[] = {"0??", "?0?"};
vector <string> rows(rows_, rows_+sizeof(rows_)/sizeof(*rows_));
string columns_[] = {"01", "00", "10"};
vector <string> columns(columns_, columns_+sizeof(columns_)/sizeof(*columns_));
string __[] = {"001", "100"};
vector <string> _(__, __+sizeof(__)/sizeof(*__));
END
}
// END CUT HERE