#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;
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 FoxAndGemstone { public:
string isPossible(vector <string> bags)
{
set<char> gems;
for(auto& bag: bags)
for(char gem: bag)
gems.insert(gem);
vector<char> g(gems.begin(), gems.end());
do {
bool ok = false;
for(int x=0; x<bags.size(); ++x) {
bool fail = false;
for(int y=0; y<bags.size(); ++y) if(x!=y)
if(!surely_heavy(bags[x], bags[y], g))
fail=true;
if(!fail)
ok = true;
}
if(!ok)
return "Impossible";
} while(next_permutation(g.begin(), g.end()));
return "Possible";
}
// w[a] >= w[b] for sure
bool surely_heavy(const string& a, const string& b, vector<char> g)
{
if(a.size() < b.size())
return false;
graph G(a.size()+b.size());
for(int x=0; x<a.size(); ++x)
for(int y=0; y<b.size(); ++y)
if(find(g.begin(),g.end(),a[x]) >= find(g.begin(),g.end(),b[y]))
G[x].emplace_back(a.size()+y);
return biMatch<100>(G, a.size()) == b.size();
}
};
// 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(_, FoxAndGemstone().isPossible(bags));}
int main(){
CASE(0)
string bags_[] = {"AB", "AC"};
vector <string> bags(bags_, bags_+sizeof(bags_)/sizeof(*bags_));
string _ = "Possible";
END
CASE(1)
string bags_[] = {"A", "BC"};
vector <string> bags(bags_, bags_+sizeof(bags_)/sizeof(*bags_));
string _ = "Impossible";
END
CASE(2)
string bags_[] = {"A", "B", "C", "AB", "AC", "BC", "ABC"};
vector <string> bags(bags_, bags_+sizeof(bags_)/sizeof(*bags_));
string _ = "Possible";
END
CASE(3)
string bags_[] = {"AB","AC","AD","BC","BD","CD"};
vector <string> bags(bags_, bags_+sizeof(bags_)/sizeof(*bags_));
string _ = "Possible";
END
CASE(4)
string bags_[] = {"AB", "CD"};
vector <string> bags(bags_, bags_+sizeof(bags_)/sizeof(*bags_));
string _ = "Impossible";
END
CASE(5)
string bags_[] = {"A", "A", "A"};
vector <string> bags(bags_, bags_+sizeof(bags_)/sizeof(*bags_));
string _ = "Possible";
END
/*
CASE(6)
string bags_[] = ;
vector <string> bags(bags_, bags_+sizeof(bags_)/sizeof(*bags_));
string _ = ;
END
CASE(7)
string bags_[] = ;
vector <string> bags(bags_, bags_+sizeof(bags_)/sizeof(*bags_));
string _ = ;
END
*/
}
// END CUT HERE