#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;
class CandidatesSelection { public:
string possible(vector <string> score, vector <int> result)
{
return solve(score, result) ? "Possible" : "Impossible";
}
bool solve(vector <string> score, vector <int> result)
{
const int N = score.size();
const int S = score[0].size();
// po[a][b] : bitmask of skill set that makes a<b.
vector<vector<LL>> po(N, vector<LL>(N));
for(int a=0; a<N; ++a)
for(int b=0; b<N; ++b) if(a!=b)
{
LL mask = 0;
for(int s=0; s<S; ++s)
if(score[a][s] <= score[b][s])
mask |= 1LL<<s;
if(a<b)
mask |= 1LL<<S;
po[a][b] = mask;
}
vector<vector<int>> now(1, result);
function<bool(LL,vector<vector<int>>)> rec;
rec = [&](LL used, vector<vector<int>> obl) {
LL pos = ~0LL;
for(auto& oi: obl)
for(int i=0; i+1<oi.size(); ++i)
pos &= po[oi[i]][oi[i+1]];
if(pos & (1LL<<S)) // original order is enough.
return true;
bool changed = false;
for(int s=0; s<S; ++s) if(pos & ~used & (1LL<<s)) {
vector<vector<int>> next;
for(auto& oi: obl) {
vector<int> cur;
for(int o: oi) {
if(!cur.empty() && score[cur.back()][s] < score[o][s]) {
changed = true;
if(cur.size()>=2)
next.push_back(cur);
cur.clear();
}
cur.push_back(o);
}
if(cur.size()>=2)
next.push_back(cur);
}
obl = std::move(next);
}
return changed && rec(used|pos, obl);
};
return rec(0, now);
}
};
// 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 string& Expected, const 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(_, CandidatesSelection().possible(score, result));}
int main(){
CASE(0)
string score_[] = {"CC", "AA", "BB"};
vector <string> score(score_, score_+sizeof(score_)/sizeof(*score_));
int result_[] = {1,2,0};
vector <int> result(result_, result_+sizeof(result_)/sizeof(*result_));
string _ = "Possible";
END
CASE(1)
string score_[] = {"BAB", "ABB", "AAB", "ABA"};
vector <string> score(score_, score_+sizeof(score_)/sizeof(*score_));
int result_[] = {2,0,1,3};
vector <int> result(result_, result_+sizeof(result_)/sizeof(*result_));
string _ = "Possible";
END
CASE(2)
string score_[] = {"BAB", "ABB", "AAB", "ABA"};
vector <string> score(score_, score_+sizeof(score_)/sizeof(*score_));
int result_[] = {0, 1, 3, 2};
vector <int> result(result_, result_+sizeof(result_)/sizeof(*result_));
string _ = "Impossible";
END
CASE(3)
string score_[] = {"AAA", "ZZZ"};
vector <string> score(score_, score_+sizeof(score_)/sizeof(*score_));
int result_[] = {1, 0};
vector <int> result(result_, result_+sizeof(result_)/sizeof(*result_));
string _ = "Impossible";
END
CASE(4)
string score_[] = {"ZZZ", "AAA"};
vector <string> score(score_, score_+sizeof(score_)/sizeof(*score_));
int result_[] = {0, 1};
vector <int> result(result_, result_+sizeof(result_)/sizeof(*result_));
string _ = "Possible";
END
CASE(5)
string score_[] = {"ZYYYYX","YXZYXY","ZZZZXX","XZXYYX","ZZZYYZ","ZZXXYZ","ZYZZXZ","XZYYZX"};
vector <string> score(score_, score_+sizeof(score_)/sizeof(*score_));
int result_[] = {3,7,1,0,2,5,6,4};
vector <int> result(result_, result_+sizeof(result_)/sizeof(*result_));
string _ = "Possible";
END
/*
CASE(6)
string score_[] = ;
vector <string> score(score_, score_+sizeof(score_)/sizeof(*score_));
int result_[] = ;
vector <int> result(result_, result_+sizeof(result_)/sizeof(*result_));
string _ = ;
END
CASE(7)
string score_[] = ;
vector <string> score(score_, score_+sizeof(score_)/sizeof(*score_));
int result_[] = ;
vector <int> result(result_, result_+sizeof(result_)/sizeof(*result_));
string _ = ;
END
*/
}
// END CUT HERE