06a6ad17f5 2020-09-10        kinaba: #include <iostream>
06a6ad17f5 2020-09-10        kinaba: #include <sstream>
06a6ad17f5 2020-09-10        kinaba: #include <iomanip>
06a6ad17f5 2020-09-10        kinaba: #include <vector>
06a6ad17f5 2020-09-10        kinaba: #include <string>
06a6ad17f5 2020-09-10        kinaba: #include <map>
06a6ad17f5 2020-09-10        kinaba: #include <set>
06a6ad17f5 2020-09-10        kinaba: #include <algorithm>
06a6ad17f5 2020-09-10        kinaba: #include <numeric>
06a6ad17f5 2020-09-10        kinaba: #include <iterator>
06a6ad17f5 2020-09-10        kinaba: #include <functional>
06a6ad17f5 2020-09-10        kinaba: #include <complex>
06a6ad17f5 2020-09-10        kinaba: #include <queue>
06a6ad17f5 2020-09-10        kinaba: #include <stack>
06a6ad17f5 2020-09-10        kinaba: #include <cmath>
06a6ad17f5 2020-09-10        kinaba: #include <cassert>
06a6ad17f5 2020-09-10        kinaba: #include <tuple>
06a6ad17f5 2020-09-10        kinaba: using namespace std;
06a6ad17f5 2020-09-10        kinaba: typedef long long LL;
06a6ad17f5 2020-09-10        kinaba: typedef complex<double> CMP;
06a6ad17f5 2020-09-10        kinaba: 
06a6ad17f5 2020-09-10        kinaba: struct UnionFind
06a6ad17f5 2020-09-10        kinaba: {
06a6ad17f5 2020-09-10        kinaba: 	vector<int> uf, sz;
06a6ad17f5 2020-09-10        kinaba: 	int nc;
06a6ad17f5 2020-09-10        kinaba: 
06a6ad17f5 2020-09-10        kinaba: 	UnionFind(int N) : uf(N), sz(N, 1), nc(N)
06a6ad17f5 2020-09-10        kinaba: 	{
06a6ad17f5 2020-09-10        kinaba: 		for (int i = 0; i<N; ++i) uf[i] = i;
06a6ad17f5 2020-09-10        kinaba: 	}
06a6ad17f5 2020-09-10        kinaba: 	int size()
06a6ad17f5 2020-09-10        kinaba: 	{
06a6ad17f5 2020-09-10        kinaba: 		return nc;
06a6ad17f5 2020-09-10        kinaba: 	}
06a6ad17f5 2020-09-10        kinaba: 	int size(int a)
06a6ad17f5 2020-09-10        kinaba: 	{
06a6ad17f5 2020-09-10        kinaba: 		return sz[Find(a)];
06a6ad17f5 2020-09-10        kinaba: 	}
06a6ad17f5 2020-09-10        kinaba: 	int Find(int a)
06a6ad17f5 2020-09-10        kinaba: 	{
06a6ad17f5 2020-09-10        kinaba: 		return uf[a] == a ? a : uf[a] = Find(uf[a]);
06a6ad17f5 2020-09-10        kinaba: 	}
06a6ad17f5 2020-09-10        kinaba: 	// Semi-compression w.o. recursion.
06a6ad17f5 2020-09-10        kinaba: 	//{ while(uf[a] != a) a=uf[a]=uf[uf[a]]; return a; }
06a6ad17f5 2020-09-10        kinaba: 	bool Union(int a, int b)
06a6ad17f5 2020-09-10        kinaba: 	{
06a6ad17f5 2020-09-10        kinaba: 		a = Find(a);
06a6ad17f5 2020-09-10        kinaba: 		b = Find(b);
06a6ad17f5 2020-09-10        kinaba: 		if (a != b)
06a6ad17f5 2020-09-10        kinaba: 		{
06a6ad17f5 2020-09-10        kinaba: 			if (sz[a] >= sz[b]) swap(a, b);
06a6ad17f5 2020-09-10        kinaba: 			uf[a] = b;
06a6ad17f5 2020-09-10        kinaba: 			sz[b] += sz[a];
06a6ad17f5 2020-09-10        kinaba: 			--nc;
06a6ad17f5 2020-09-10        kinaba: 		}
06a6ad17f5 2020-09-10        kinaba: 		return (a != b);
06a6ad17f5 2020-09-10        kinaba: 	}
06a6ad17f5 2020-09-10        kinaba: };
06a6ad17f5 2020-09-10        kinaba: 
06a6ad17f5 2020-09-10        kinaba: static const unsigned MODVAL = 1000000007;
06a6ad17f5 2020-09-10        kinaba: struct mint
06a6ad17f5 2020-09-10        kinaba: {
06a6ad17f5 2020-09-10        kinaba: 	unsigned val;
06a6ad17f5 2020-09-10        kinaba: 	mint() :val(0) {}
06a6ad17f5 2020-09-10        kinaba: 	mint(int      x) :val(x%MODVAL) {}
06a6ad17f5 2020-09-10        kinaba: 	mint(unsigned x) :val(x%MODVAL) {}
06a6ad17f5 2020-09-10        kinaba: 	mint(LL       x) :val(x%MODVAL) {}
06a6ad17f5 2020-09-10        kinaba: };
06a6ad17f5 2020-09-10        kinaba: mint& operator+=(mint& x, mint y) { return x = x.val + y.val; }
06a6ad17f5 2020-09-10        kinaba: mint& operator-=(mint& x, mint y) { return x = x.val - y.val + MODVAL; }
06a6ad17f5 2020-09-10        kinaba: mint& operator*=(mint& x, mint y) { return x = LL(x.val)*y.val; }
06a6ad17f5 2020-09-10        kinaba: mint operator+(mint x, mint y) { return x += y; }
06a6ad17f5 2020-09-10        kinaba: mint operator-(mint x, mint y) { return x -= y; }
06a6ad17f5 2020-09-10        kinaba: mint operator*(mint x, mint y) { return x *= y; }
06a6ad17f5 2020-09-10        kinaba: 
06a6ad17f5 2020-09-10        kinaba: mint POW(mint x, LL e) { mint v = 1; for (; e; x *= x, e >>= 1) if (e & 1) v *= x; return v; }
06a6ad17f5 2020-09-10        kinaba: 
06a6ad17f5 2020-09-10        kinaba: class TheSocialNetwork { public:
06a6ad17f5 2020-09-10        kinaba: 	int minimumCut(int n, int m, vector <int> u, vector <int> v, vector <int> l)
06a6ad17f5 2020-09-10        kinaba: 	{
06a6ad17f5 2020-09-10        kinaba: 		vector<tuple<int, int, int>> e;
06a6ad17f5 2020-09-10        kinaba: 		for (int i = 0; i < m; ++i)
06a6ad17f5 2020-09-10        kinaba: 			e.emplace_back(l[i], u[i]-1, v[i]-1);
06a6ad17f5 2020-09-10        kinaba: 		sort(e.begin(), e.end());
06a6ad17f5 2020-09-10        kinaba: 
06a6ad17f5 2020-09-10        kinaba: 		vector<bool> use(m, false);
06a6ad17f5 2020-09-10        kinaba: 		for (int k = e.size() - 1; k >= 0; --k) {
06a6ad17f5 2020-09-10        kinaba: 			use[k] = true;
06a6ad17f5 2020-09-10        kinaba: 			if (is_connected(n, m, use, e))
06a6ad17f5 2020-09-10        kinaba: 				use[k] = false;
06a6ad17f5 2020-09-10        kinaba: 		}
06a6ad17f5 2020-09-10        kinaba: 
06a6ad17f5 2020-09-10        kinaba: 		mint ans = 0;
06a6ad17f5 2020-09-10        kinaba: 		for (int i = 0; i < m; ++i) if (!use[i])
06a6ad17f5 2020-09-10        kinaba: 			ans += POW(2, get<0>(e[i]));
06a6ad17f5 2020-09-10        kinaba: 		return ans.val;
06a6ad17f5 2020-09-10        kinaba: 	}
06a6ad17f5 2020-09-10        kinaba: 
06a6ad17f5 2020-09-10        kinaba: 	bool is_connected(int n, int m, const vector<bool>& use, const vector<tuple<int, int, int>>& e) {
06a6ad17f5 2020-09-10        kinaba: 		UnionFind uf(n);
06a6ad17f5 2020-09-10        kinaba: 		for (int i = 0; i < m; ++i) if (use[i])
06a6ad17f5 2020-09-10        kinaba: 			uf.Union(get<1>(e[i]), get<2>(e[i]));
06a6ad17f5 2020-09-10        kinaba: 		return uf.size() == 1;
06a6ad17f5 2020-09-10        kinaba: 
06a6ad17f5 2020-09-10        kinaba: 	}
06a6ad17f5 2020-09-10        kinaba: };
06a6ad17f5 2020-09-10        kinaba: 
06a6ad17f5 2020-09-10        kinaba: // BEGIN CUT HERE
06a6ad17f5 2020-09-10        kinaba: #include <ctime>
06a6ad17f5 2020-09-10        kinaba: double start_time; string timer()
06a6ad17f5 2020-09-10        kinaba:  { ostringstream os; os << " (" << int((clock()-start_time)/CLOCKS_PER_SEC*1000) << " msec)"; return os.str(); }
06a6ad17f5 2020-09-10        kinaba: template<typename T> ostream& operator<<(ostream& os, const vector<T>& v)
06a6ad17f5 2020-09-10        kinaba:  { os << "{ ";
06a6ad17f5 2020-09-10        kinaba:    for(typename vector<T>::const_iterator it=v.begin(); it!=v.end(); ++it)
06a6ad17f5 2020-09-10        kinaba:    os << '\"' << *it << '\"' << (it+1==v.end() ? "" : ", "); os << " }"; return os; }
06a6ad17f5 2020-09-10        kinaba: void verify_case(const int& Expected, const int& Received) {
06a6ad17f5 2020-09-10        kinaba:  bool ok = (Expected == Received);
06a6ad17f5 2020-09-10        kinaba:  if(ok) cerr << "PASSED" << timer() << endl;  else { cerr << "FAILED" << timer() << endl;
06a6ad17f5 2020-09-10        kinaba:  cerr << "\to: \"" << Expected << '\"' << endl << "\tx: \"" << Received << '\"' << endl; } }
06a6ad17f5 2020-09-10        kinaba: #define CASE(N) {cerr << "Test Case #" << N << "..." << flush; start_time=clock();
06a6ad17f5 2020-09-10        kinaba: #define END	 verify_case(_, TheSocialNetwork().minimumCut(n, m, u, v, l));}
06a6ad17f5 2020-09-10        kinaba: int main(){
06a6ad17f5 2020-09-10        kinaba: 
06a6ad17f5 2020-09-10        kinaba: CASE(0)
06a6ad17f5 2020-09-10        kinaba: 	int n = 6;
06a6ad17f5 2020-09-10        kinaba: 	int m = 6;
06a6ad17f5 2020-09-10        kinaba: 	int u_[] = {1, 2, 3, 4, 5, 6}	;
06a6ad17f5 2020-09-10        kinaba: 	  vector <int> u(u_, u_+sizeof(u_)/sizeof(*u_));
06a6ad17f5 2020-09-10        kinaba: 	int v_[] = {2, 3, 4, 5, 6, 1};
06a6ad17f5 2020-09-10        kinaba: 	  vector <int> v(v_, v_+sizeof(v_)/sizeof(*v_));
06a6ad17f5 2020-09-10        kinaba: 	int l_[] = {1, 7, 3, 4, 6, 12};
06a6ad17f5 2020-09-10        kinaba: 	  vector <int> l(l_, l_+sizeof(l_)/sizeof(*l_));
06a6ad17f5 2020-09-10        kinaba: 	int _ = 10;
06a6ad17f5 2020-09-10        kinaba: END
06a6ad17f5 2020-09-10        kinaba: CASE(1)
06a6ad17f5 2020-09-10        kinaba: 	int n = 5;
06a6ad17f5 2020-09-10        kinaba: 	int m = 7;
06a6ad17f5 2020-09-10        kinaba: 	int u_[] = {1, 1, 1, 2, 2, 3, 3};
06a6ad17f5 2020-09-10        kinaba: 	  vector <int> u(u_, u_+sizeof(u_)/sizeof(*u_));
06a6ad17f5 2020-09-10        kinaba: 	int v_[] = {5, 3, 2, 5, 3, 5, 4};
06a6ad17f5 2020-09-10        kinaba: 	  vector <int> v(v_, v_+sizeof(v_)/sizeof(*v_));
06a6ad17f5 2020-09-10        kinaba: 	int l_[] = {1, 8, 2, 3, 4, 6, 9};
06a6ad17f5 2020-09-10        kinaba: 	  vector <int> l(l_, l_+sizeof(l_)/sizeof(*l_));
06a6ad17f5 2020-09-10        kinaba: 	int _ = 28;
06a6ad17f5 2020-09-10        kinaba: END
06a6ad17f5 2020-09-10        kinaba: CASE(2)
06a6ad17f5 2020-09-10        kinaba: 	int n = 7;
06a6ad17f5 2020-09-10        kinaba: 	int m = 6;
06a6ad17f5 2020-09-10        kinaba: 	int u_[] = {1, 1, 2, 2, 3, 3};
06a6ad17f5 2020-09-10        kinaba: 	  vector <int> u(u_, u_+sizeof(u_)/sizeof(*u_));
06a6ad17f5 2020-09-10        kinaba: 	int v_[] = {2, 3, 4, 5, 6, 7};
06a6ad17f5 2020-09-10        kinaba: 	  vector <int> v(v_, v_+sizeof(v_)/sizeof(*v_));
06a6ad17f5 2020-09-10        kinaba: 	int l_[] = {7, 11, 6, 9, 20, 15};
06a6ad17f5 2020-09-10        kinaba: 	  vector <int> l(l_, l_+sizeof(l_)/sizeof(*l_));
06a6ad17f5 2020-09-10        kinaba: 	int _ = 64;
06a6ad17f5 2020-09-10        kinaba: END
06a6ad17f5 2020-09-10        kinaba: CASE(3)
06a6ad17f5 2020-09-10        kinaba: 	int n = 8;
06a6ad17f5 2020-09-10        kinaba: 	int m = 11;
06a6ad17f5 2020-09-10        kinaba: 	int u_[] = {1, 1, 2, 2, 3, 3, 3, 4, 5, 5, 7};
06a6ad17f5 2020-09-10        kinaba: 	  vector <int> u(u_, u_+sizeof(u_)/sizeof(*u_));
06a6ad17f5 2020-09-10        kinaba: 	int v_[] = {2, 8, 3, 5, 4, 6, 7, 5, 6, 8, 8};
06a6ad17f5 2020-09-10        kinaba: 	  vector <int> v(v_, v_+sizeof(v_)/sizeof(*v_));
06a6ad17f5 2020-09-10        kinaba: 	int l_[] = {2, 3, 1, 6, 11, 8, 9, 10, 7, 4, 5};
06a6ad17f5 2020-09-10        kinaba: 	  vector <int> l(l_, l_+sizeof(l_)/sizeof(*l_));
06a6ad17f5 2020-09-10        kinaba: 	int _ = 12;
06a6ad17f5 2020-09-10        kinaba: END
06a6ad17f5 2020-09-10        kinaba: CASE(4)
06a6ad17f5 2020-09-10        kinaba: 	int n = 13;
06a6ad17f5 2020-09-10        kinaba: 	int m = 56;
06a6ad17f5 2020-09-10        kinaba: 	int u_[] = {1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 8, 8, 8, 9, 9, 9, 9, 10, 10, 10, 11, 11, 12};
06a6ad17f5 2020-09-10        kinaba: 	  vector <int> u(u_, u_+sizeof(u_)/sizeof(*u_));
06a6ad17f5 2020-09-10        kinaba: 	int v_[] = {3, 4, 5, 7, 9, 12, 13, 3, 5, 8, 9, 10, 12, 13, 5, 6, 8, 9, 10, 11, 12, 5, 6, 7, 9, 11, 13, 7, 8, 9, 11, 12, 7, 8, 9, 10, 13, 8, 9, 10, 11, 12, 13, 9, 11, 12, 10, 11, 12, 13, 11, 12, 13, 12, 13, 13};
06a6ad17f5 2020-09-10        kinaba: 	  vector <int> v(v_, v_+sizeof(v_)/sizeof(*v_));
06a6ad17f5 2020-09-10        kinaba: 	int l_[] = {82, 240, 395, 1041, 1165, 1274, 1540, 1650, 1904, 2306, 2508, 3162, 3380, 3637, 3778, 3913, 3971, 4101, 4148, 4218, 4394, 4434, 5107, 6147, 6280, 6337, 6461, 6490, 7056, 8024, 8373, 8924, 8961, 9058, 9304, 9359, 10899, 11049, 11090, 11174, 11269, 11356, 11547, 11808, 12566, 12591, 13322, 13447, 13667, 13672, 15013, 15319, 16153, 16447, 16454, 16470};
06a6ad17f5 2020-09-10        kinaba: 	  vector <int> l(l_, l_+sizeof(l_)/sizeof(*l_));
06a6ad17f5 2020-09-10        kinaba: 	int _ = 504663883;
06a6ad17f5 2020-09-10        kinaba: END
06a6ad17f5 2020-09-10        kinaba: /*
06a6ad17f5 2020-09-10        kinaba: CASE(5)
06a6ad17f5 2020-09-10        kinaba: 	int n = ;
06a6ad17f5 2020-09-10        kinaba: 	int m = ;
06a6ad17f5 2020-09-10        kinaba: 	int u_[] = ;
06a6ad17f5 2020-09-10        kinaba: 	  vector <int> u(u_, u_+sizeof(u_)/sizeof(*u_));
06a6ad17f5 2020-09-10        kinaba: 	int v_[] = ;
06a6ad17f5 2020-09-10        kinaba: 	  vector <int> v(v_, v_+sizeof(v_)/sizeof(*v_));
06a6ad17f5 2020-09-10        kinaba: 	int l_[] = ;
06a6ad17f5 2020-09-10        kinaba: 	  vector <int> l(l_, l_+sizeof(l_)/sizeof(*l_));
06a6ad17f5 2020-09-10        kinaba: 	int _ = ;
06a6ad17f5 2020-09-10        kinaba: END
06a6ad17f5 2020-09-10        kinaba: CASE(6)
06a6ad17f5 2020-09-10        kinaba: 	int n = ;
06a6ad17f5 2020-09-10        kinaba: 	int m = ;
06a6ad17f5 2020-09-10        kinaba: 	int u_[] = ;
06a6ad17f5 2020-09-10        kinaba: 	  vector <int> u(u_, u_+sizeof(u_)/sizeof(*u_));
06a6ad17f5 2020-09-10        kinaba: 	int v_[] = ;
06a6ad17f5 2020-09-10        kinaba: 	  vector <int> v(v_, v_+sizeof(v_)/sizeof(*v_));
06a6ad17f5 2020-09-10        kinaba: 	int l_[] = ;
06a6ad17f5 2020-09-10        kinaba: 	  vector <int> l(l_, l_+sizeof(l_)/sizeof(*l_));
06a6ad17f5 2020-09-10        kinaba: 	int _ = ;
06a6ad17f5 2020-09-10        kinaba: END
06a6ad17f5 2020-09-10        kinaba: */
06a6ad17f5 2020-09-10        kinaba: }
06a6ad17f5 2020-09-10        kinaba: // END CUT HERE