#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<LD> CMP;
template<typename Vert, typename Flow, int NV=16>
class MaxFlow
{
vector<int> G[NV];
Flow F[NV][NV];
public:
void addEdge( Vert s, Vert t, Flow f )
{
G[s].push_back(t);
G[t].push_back(s);
F[s][t] = f;
F[t][s] = 0;
}
Flow calc( Vert S, Vert D )
{
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 CosmicBlocks { public:
vector<int> blockTypes;
int N, minWays, maxWays;
int getNumOrders(vector <int> blockTypes_, int minWays_, int maxWays_)
{
N = blockTypes_.size();
blockTypes = blockTypes_;
minWays = minWays_;
maxWays = maxWays_;
return try_all_latitude();
}
int try_all_latitude()
{
vector<int> lat;
return rec_assign_latitude(&lat, (1<<N)-1, 0x7fffffff);
}
int rec_assign_latitude(vector<int>* lat, int mask, int prev_lat_blocks)
{
if( mask == 0 )
return try_all_touching_releation(*lat);
int total = 0;
for(int m=1; m<=mask; ++m) if( (m&mask)==m ) {
int sum = 0;
for(int i=0; (1<<i)<=m; ++i) if(1<<i & m)
sum+=blockTypes[i];
if( prev_lat_blocks >= sum ) {
lat->push_back(m);
total += rec_assign_latitude(lat, mask&~m, sum);
lat->pop_back();
}
}
return total;
}
int try_all_touching_releation(const vector<int>& lat)
{
int total = 0;
vector<int> fst = elements(lat[0]);
vector< pair<int,int> > adj = adjacent_blocks(lat);
for(int m=0; m<(1<<adj.size()); ++m)
{
vector< vector<int> > up(N);
up.push_back(fst);
for(int i=0; (1<<i)<=m; ++i) if(1<<i & m)
up[adj[i].first].push_back(adj[i].second);
if( !possible(up) )
continue;
int ways = calc_ways(up);
if( minWays<=ways && ways<=maxWays )
++total;
}
return total;
}
vector<int> elements(int mask)
{
vector<int> result;
for(int i=0; (1<<i)<=mask; ++i) if(1<<i & mask)
result.push_back(i);
return result;
}
vector< pair<int,int> > adjacent_blocks(const vector<int>& lat)
{
vector< pair<int,int> > result;
for(int i=1; i<lat.size(); ++i)
for(int a=0; (1<<a)<=lat[i-1]; ++a) if(1<<a & lat[i-1])
for(int b=0; (1<<b)<=lat[i]; ++b) if(1<<b & lat[i])
result.push_back(make_pair(a,b));
return result;
}
int calc_ways(const vector< vector<int> >& up)
{
vector<int> governed(N);
for(int i=0; i<up.size(); ++i)
for(int k=0; k<up[i].size(); ++k)
governed[up[i][k]] ++;
// trivial check 2
for(int i=0; i<governed.size(); ++i)
if(governed[i] == 0)
return 0;
vector<int> memo(1<<N, -1);
return calc_ways_rec(N, (1<<N)-1, up, governed, memo);
}
int calc_ways_rec(int i, int mask, const vector< vector<int> >& up, vector<int>& governed,
vector<int>& memo)
{
if(mask == 0)
return 1;
if(memo[mask] != -1)
return memo[mask];
int sum = 0;
for(int k=0; k<up[i].size(); ++k) governed[up[i][k]]--;
{
for(int k=0; k<governed.size(); ++k)
if(!governed[k] && (mask & 1<<k))
sum += calc_ways_rec(k, mask &~ (1<<k), up, governed, memo);
}
for(int k=0; k<up[i].size(); ++k) governed[up[i][k]]++;
return memo[mask] = sum;
}
bool possible(const vector< vector<int> >& up)
{
static const int INF = 0x3fffffff;
int total = accumulate(blockTypes.begin(), blockTypes.end(), 0);
MaxFlow<int, int> mf;
vector<int> out = blockTypes, in = blockTypes;
for(int v=0; v<=N; ++v) {
for(int i=0; i<up[v].size(); ++i) {
int u = up[v][i];
mf.addEdge(v, N+1+u, INF);
if(v<N) {in[v] -= 1; if(in[v]<0) return false; }
out[u] -= 1; if(out[u]<0) return false;
total -= 1;
}
}
for(int v=0; v<=N; ++v)
if(v == N) {
mf.addEdge(N+1+N, v, INF);
} else {
mf.addEdge(N+1+N, v, in[v]);
mf.addEdge(N+1+v, N+1+N+1, out[v]);
}
return mf.calc(N+1+N, N+1+N+1) == total;
}
};
// 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(_, CosmicBlocks().getNumOrders(blockTypes, minWays, maxWays));}
int main(){
CASE(0)
int blockTypes_[] = {2,2,2};
vector <int> blockTypes(blockTypes_, blockTypes_+sizeof(blockTypes_)/sizeof(*blockTypes_));
int minWays = 1;
int maxWays = 1;
int _ = 6;
END
CASE(1)
int blockTypes_[] = {1,1,1,1,1,1};
vector <int> blockTypes(blockTypes_, blockTypes_+sizeof(blockTypes_)/sizeof(*blockTypes_));
int minWays = 720;
int maxWays = 720;
int _ = 1;
END
CASE(2)
int blockTypes_[] = {2,2};
vector <int> blockTypes(blockTypes_, blockTypes_+sizeof(blockTypes_)/sizeof(*blockTypes_));
int minWays = 1;
int maxWays = 2;
int _ = 3;
END
CASE(3)
int blockTypes_[] = {1,2};
vector <int> blockTypes(blockTypes_, blockTypes_+sizeof(blockTypes_)/sizeof(*blockTypes_));
int minWays = 1;
int maxWays = 2;
int _ = 2;
END
CASE(4)
int blockTypes_[] = {1};
vector <int> blockTypes(blockTypes_, blockTypes_+sizeof(blockTypes_)/sizeof(*blockTypes_));
int minWays = 1;
int maxWays = 1;
int _ = 1;
END
CASE(5)
int blockTypes_[] = {1,2,4,8};
vector <int> blockTypes(blockTypes_, blockTypes_+sizeof(blockTypes_)/sizeof(*blockTypes_));
int minWays = 5;
int maxWays = 30;
int _ = 27;
END
CASE(6)
int blockTypes_[] = {1,2,3,4,5,6};
vector <int> blockTypes(blockTypes_, blockTypes_+sizeof(blockTypes_)/sizeof(*blockTypes_));
int minWays = 1;
int maxWays = 720;
int _ = 4445;
END
CASE(7)
int blockTypes_[] = {7500,1000,7500,1000,7500};
vector <int> blockTypes(blockTypes_, blockTypes_+sizeof(blockTypes_)/sizeof(*blockTypes_));
int minWays = 8;
int maxWays = 88;
int _ = 448;
END
/*
CASE(8)
int blockTypes_[] = ;
vector <int> blockTypes(blockTypes_, blockTypes_+sizeof(blockTypes_)/sizeof(*blockTypes_));
int minWays = ;
int maxWays = ;
int _ = ;
END
CASE(9)
int blockTypes_[] = ;
vector <int> blockTypes(blockTypes_, blockTypes_+sizeof(blockTypes_)/sizeof(*blockTypes_));
int minWays = ;
int maxWays = ;
int _ = ;
END
*/
}
// END CUT HERE