#include #define all(v) v.begin(), v.end() #define rall(v) v.rbegin(), v.rend() #define rep(i,n) for(int i=0;i<(int)(n);i++) #define codefor int test;cin>>test;while(test--) #define INT(...) int __VA_ARGS__;in(__VA_ARGS__) #define LL(...) ll __VA_ARGS__;in(__VA_ARGS__) #define vector2d(type,name,h,...) vector>name(h,vector(__VA_ARGS__)) #define vector3d(type,name,h,w,...) vector>>name(h,vector>(w,vector(__VA_ARGS__))) using namespace std; using ll = long long; template using rpriority_queue = priority_queue, greater>; template istream& operator>>(istream& is, vector& vec) {for(T& x : vec)is >> x;return is;} template ostream& operator<<(ostream& os, const vector& vec) {if(vec.empty())return os;os << vec[0];for(auto it = vec.begin(); ++it!= vec.end();)os << ' ' << *it;return os;} void in(){} template void in(Head& head, Tail&... tail){cin >> head;in(tail...);} void out(){cout << '\n';} templatevoid out(const T& a){cout << a << '\n';} template void out(const Head& head,const Tail&... tail){cout << head << ' ';out(tail...);} const int INF = 1 << 30; const long long INF2 = 1ll << 60; template void chmax(T &a,const T b){if(b>a)a=b;} template void chmin(T &a,const T b){if(b> g; vector> parent; vector depth; LCA_tree() : _n(0) {} LCA_tree(int n) : _n(n), g(n),depth(n) { MAX_LOG_V = 1; while(_n >> MAX_LOG_V) MAX_LOG_V++; parent.resize(MAX_LOG_V, vector(_n)); } void merge(int u, int v){ g[u].push_back(v); g[v].push_back(u); } void dfs(int v,int p,int d){ parent[0][v]=p; depth[v]=d; for(int i=0;idepth[v])swap(u,v); for(int i=0;i>i&1)v=parent[i][v]; } if(u==v)return u; for(int i=MAX_LOG_V-1;i>=0;i--){ if(parent[i][u]!=parent[i][v]){ u=parent[i][u]; v=parent[i][v]; } } return parent[0][u]; } //パスの辺数 int dist(int u,int v){ int lcav=lca(u,v); if(lcav==-1)return depth[u]+depth[v]; return depth[u]+depth[v]-2*depth[lcav]; } //頂点wが頂点u,vのパス上に存在するか int on_path(int u,int v,int w){ return (dist(u,w)+dist(v,w)==dist(u,v)); } }; template struct mcf_graph { public: mcf_graph() {} mcf_graph(int n) : _n(n), g(n) {} int add_edge(int from, int to, Cap cap, Cost cost) { assert(0 <= from && from < _n); assert(0 <= to && to < _n); int m = int(pos.size()); pos.push_back({from, int(g[from].size())}); g[from].push_back(_edge{to, int(g[to].size()), cap, cost}); g[to].push_back(_edge{from, int(g[from].size()) - 1, 0, -cost}); return m; } struct edge { int from, to; Cap cap, flow; Cost cost; }; edge get_edge(int i) { int m = int(pos.size()); assert(0 <= i && i < m); auto _e = g[pos[i].first][pos[i].second]; auto _re = g[_e.to][_e.rev]; return edge{ pos[i].first, _e.to, _e.cap + _re.cap, _re.cap, _e.cost, }; } std::vector edges() { int m = int(pos.size()); std::vector result(m); for (int i = 0; i < m; i++) { result[i] = get_edge(i); } return result; } std::pair flow(int s, int t) { return flow(s, t, std::numeric_limits::max()); } std::pair flow(int s, int t, Cap flow_limit) { return slope(s, t, flow_limit).back(); } std::vector> slope(int s, int t) { return slope(s, t, std::numeric_limits::max()); } std::vector> slope(int s, int t, Cap flow_limit) { assert(0 <= s && s < _n); assert(0 <= t && t < _n); assert(s != t); std::vector dual(_n, 0), dist(_n); std::vector pv(_n), pe(_n); std::vector vis(_n); auto dual_ref = [&]() { std::fill(dist.begin(), dist.end(), std::numeric_limits::max()); std::fill(pv.begin(), pv.end(), -1); std::fill(pe.begin(), pe.end(), -1); std::fill(vis.begin(), vis.end(), false); struct Q { Cost key; int to; bool operator<(Q r) const { return key > r.key; } }; std::priority_queue que; dist[s] = 0; que.push(Q{0, s}); while (!que.empty()) { int v = que.top().to; que.pop(); if (vis[v]) continue; vis[v] = true; if (v == t) break; for (int i = 0; i < int(g[v].size()); i++) { auto e = g[v][i]; if (vis[e.to] || !e.cap) continue; Cost cost = e.cost - dual[e.to] + dual[v]; if (dist[e.to] - dist[v] > cost) { dist[e.to] = dist[v] + cost; pv[e.to] = v; pe[e.to] = i; que.push(Q{dist[e.to], e.to}); } } } if (!vis[t]) { return false; } for (int v = 0; v < _n; v++) { if (!vis[v]) continue; dual[v] -= dist[t] - dist[v]; } return true; }; Cap flow = 0; Cost cost = 0, prev_cost = -1; std::vector> result; result.push_back({flow, cost}); while (flow < flow_limit) { if (!dual_ref()) break; Cap c = flow_limit - flow; for (int v = t; v != s; v = pv[v]) { c = std::min(c, g[pv[v]][pe[v]].cap); } for (int v = t; v != s; v = pv[v]) { auto& e = g[pv[v]][pe[v]]; e.cap -= c; g[v][e.rev].cap += c; } Cost d = -dual[s]; flow += c; cost += c * d; if (prev_cost == d) { result.pop_back(); } result.push_back({flow, cost}); prev_cost = cost; } return result; } std::vector detail_slope(int s, int t){ std::vector> ori = slope(s, t); std::vector ans(ori.back().first + 1); Cap x = 0, nx; Cost y = 0, ny; for(int i = 1; i < ori.size(); i++){ std::tie(nx, ny) = ori[i]; Cost d = (ny - y) / (nx - x); while(x != nx){ ++x, y+= d; ans[x] = y; } } return ans; } private: int _n; struct _edge { int to, rev; Cap cap; Cost cost; }; std::vector> pos; std::vector> g; }; template< typename T > T hungarian(vector> &A) { const T infty = numeric_limits< T >::max(); const int N = (int) A.size(); const int M = (int) A[0].size(); vector< int > P(M), way(M); vector< T > U(N, 0), V(M, 0), minV; vector< bool > used; for(int i = 1; i < N; i++) { P[0] = i; minV.assign(M, infty); used.assign(M, false); int j0 = 0; while(P[j0] != 0) { int i0 = P[j0], j1 = 0; used[j0] = true; T delta = infty; for(int j = 1; j < M; j++) { if(used[j]) continue; T curr = A[i0][j] - U[i0] - V[j]; if(curr < minV[j]) minV[j] = curr, way[j] = j0; if(minV[j] < delta) delta = minV[j], j1 = j; } for(int j = 0; j < M; j++) { if(used[j]) U[P[j]] += delta, V[j] -= delta; else minV[j] -= delta; } j0 = j1; } do { P[j0] = P[way[j0]]; j0 = way[j0]; } while(j0 != 0); } return -V[0]; } int main(){ ios::sync_with_stdio(false); cin.tie(0); INT(n, m); vector> A(n, vector(n, INF2)); int u, v; vector c(n); for(int i = 0; i < m; i++){ cin >> u >> v; u--, v--; A[u][v] = A[v][u] = 1; } in(c); for(int i = 0; i < n; i++) A[i][i] = 0; for(int k = 0; k < n; k++){ for(int i = 0; i < n; i++){ for(int j = 0; j < n; j++){ chmin(A[i][j], A[i][k] + A[k][j]); } } } int cnt = count(all(c), 1); if(cnt & 1){ out(-1); return 0; } //cerr << "enter" << '\n'; mcf_graph g(2 * n + 2); //cnt /= 2; //cerr << cnt * 2 << '\n'; int s = 2 * n, t = s + 1; for(int i = 0; i < n; i++){ if(c[i]){ g.add_edge(s, i, 1, 0); g.add_edge(i + n, t, 1, 0); } for(int j = 0; j < n; j++){ if(i == j) continue; if(c[i] && c[j]){ if(A[i][j] == INF2) continue; g.add_edge(i, j + n, 1, A[i][j]); } } } auto p = g.flow(s, t); if(p.first != cnt){ out(-1); return 0; } ll S = 0; for(int i = 0; i < n; i++){ if(c[i]) S |= 1ll << i; } map mp; function dfs = [&](ll S){ if(S == 0) return 0ll; if(mp.find(S) != mp.end())return mp[S]; ll res = INF2; for(int i = 0; i < n; i++){ if(~S >> i & 1) continue; for(int j = i + 1; j < n; j++){ if(~S >> j & 1) continue; chmin(res, dfs(S ^ (1ll << i) ^ (1ll << j)) + A[i][j]); } break; } return mp[S] = res; }; out(dfs(S)); }