#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>
using namespace std;
typedef long long LL;
typedef complex<double> CMP;
LL comb(LL n, LL k)
{
k = min(k, n-k);
LL c = 1;
for(LL i=0; i<k; ++i)
c *= n-i, c /= i+1;
return c;
}
class StarsInGraphs { public:
int starnum(LL n, LL C)
{
if( n<=2 )
return -1;
LL sum = 0;
for(LL k=3; k<=n; ++k)
{
sum += comb(n,k);
if( sum > C )
return -1;
}
return (int) sum;
}
int starryPaths(vector <string> adjacencyMatrix, int C)
{
const int N = adjacencyMatrix.size();
vector<int> sn;
for(int i=0; i<N; ++i)
sn.push_back( starnum(count(adjacencyMatrix[i].begin(), adjacencyMatrix[i].end(), '1'), C) );
vector<int> v;
for(int i=0; i<N; ++i)
if( sn[i] > 0 )
v.push_back(i);
for(int step=0 ;; ++step)
{
if( v.empty() )
return step;
if( step >= 3*N )
break; // infinite
vector<int> v2;
for(int u=0; u<N; ++u)
for(int i=0; i<v.size(); ++i)
if( adjacencyMatrix[v[i]][u]=='1' && sn[v[i]] <= sn[u] )
{v2.push_back(u); break;}
v.swap(v2);
}
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(_, StarsInGraphs().starryPaths(adjacencyMatrix, C));}
int main(){
CASE(0)
string adjacencyMatrix_[] = {"01110",
"10111",
"00000",
"00000",
"00000"};
vector <string> adjacencyMatrix(adjacencyMatrix_, adjacencyMatrix_+sizeof(adjacencyMatrix_)/sizeof(*adjacencyMatrix_));
int C = 1000;
int _ = 2;
END
CASE(1)
string adjacencyMatrix_[] = {"01011",
"00111",
"10011",
"00000",
"00000"};
vector <string> adjacencyMatrix(adjacencyMatrix_, adjacencyMatrix_+sizeof(adjacencyMatrix_)/sizeof(*adjacencyMatrix_));
int C = 1;
int _ = -1;
END
CASE(2)
string adjacencyMatrix_[] = {"0111",
"0000",
"0000",
"0000"};
vector <string> adjacencyMatrix(adjacencyMatrix_, adjacencyMatrix_+sizeof(adjacencyMatrix_)/sizeof(*adjacencyMatrix_));
int C = 1;
int _ = 1;
END
CASE(3)
string adjacencyMatrix_[] = {"01111",
"00000",
"00000",
"00000",
"00000"};
vector <string> adjacencyMatrix(adjacencyMatrix_, adjacencyMatrix_+sizeof(adjacencyMatrix_)/sizeof(*adjacencyMatrix_));
int C = 4;
int _ = 0;
END
CASE(4)
string adjacencyMatrix_[] = {"010001100",
"001001100",
"000101110",
"000010111",
"000001111",
"010000000",
"000110000",
"000100001",
"100001000"};
vector <string> adjacencyMatrix(adjacencyMatrix_, adjacencyMatrix_+sizeof(adjacencyMatrix_)/sizeof(*adjacencyMatrix_));
int C = 10;
int _ = 5;
END
CASE(5)
string adjacencyMatrix_[] = {"00","00"};
vector <string> adjacencyMatrix(adjacencyMatrix_, adjacencyMatrix_+sizeof(adjacencyMatrix_)/sizeof(*adjacencyMatrix_));
int C = 9999999;
int _ = 0;
END
CASE(6)
string adjacencyMatrix_[] = {"0111","1011","1101","1110"};
vector <string> adjacencyMatrix(adjacencyMatrix_, adjacencyMatrix_+sizeof(adjacencyMatrix_)/sizeof(*adjacencyMatrix_));
int C = 9999;
int _ = -1;
END
}
// END CUT HERE