#pragma GCC optimize ("O3") #pragma GCC target ("avx") #include "bits/stdc++.h" // define macro "/D__MAI" using namespace std; typedef long long int ll; #define xprintf(fmt,...) fprintf(stderr,fmt,__VA_ARGS__) #define debugv(v) {printf("L%d %s > ",__LINE__,#v);for(auto e:v){cout< ",__LINE__,#m);for(int x=0;x<(w);x++){cout<<(m)[x]<<" ";}cout<\n",__LINE__,#m);for(int y=0;y<(h);y++){for(int x=0;x<(w);x++){cout<<(m)[y][x]<<" ";}cout< ostream& operator <<(ostream &o, const pair p) { o << "(" << p.first << ":" << p.second << ")"; return o; } template inline size_t argmin(iterator begin, iterator end) { return distance(begin, min_element(begin, end)); } template inline size_t argmax(iterator begin, iterator end) { return distance(begin, max_element(begin, end)); } template T& maxset(T& to, const T& val) { return to = max(to, val); } template T& minset(T& to, const T& val) { return to = min(to, val); } mt19937_64 randdev(8901016); inline ll rand_range(ll l, ll h) { return uniform_int_distribution(l, h)(randdev); } #ifdef __MAI #define getchar_unlocked getchar #define putchar_unlocked putchar #endif #ifdef __VSCC #define getchar_unlocked _getchar_nolock #define putchar_unlocked _putchar_nolock #endif namespace { #define isvisiblechar(c) (0x21<=(c)&&(c)<=0x7E) class MaiScanner { public: template void input_integer(T& var) { var = 0; T sign = 1; int cc = getchar_unlocked(); for (; cc<'0' || '9'>(int& var) { input_integer(var); return *this; } inline MaiScanner& operator>>(long long& var) { input_integer(var); return *this; } inline MaiScanner& operator>>(string& var) { int cc = getchar_unlocked(); for (; !isvisiblechar(cc); cc = getchar_unlocked()); for (; isvisiblechar(cc); cc = getchar_unlocked()) var.push_back(cc); return *this; } template void in(IT begin, IT end) { for (auto it = begin; it != end; ++it) *this >> *it; } }; } MaiScanner scanner; class unionfind { public: vector data; unionfind(int size) : data(size, -1) { } bool union_set(int x, int y) { x = root(x); y = root(y); if (x != y) { if (data[y] < data[x]) swap(x, y); data[x] += data[y]; data[y] = x; } return x != y; } inline bool find_set(int x, int y) { return root(x) == root(y); } inline int root(int x) { return data[x] < 0 ? x : data[x] = root(data[x]); } inline int size(int x) { return -data[root(x)]; } }; class DGraph { public: size_t n; vector> vertex_to; vector> vertex_from; DGraph(size_t n) :n(n), vertex_to(n), vertex_from(n) {} void connect(int from, int to) { vertex_to[from].emplace_back(to); vertex_from[to].emplace_back(from); } void resize(size_t _n) { n = _n; vertex_to.resize(_n); vertex_from.resize(_n); } }; int strongly_connected_components(const DGraph& graph, unionfind& result) { stack s; int size = graph.n; vector num(size), low(size); vector flg(size); int count = 0; int n_components = graph.n; function dfs = [&](int idx) { low[idx] = num[idx] = ++count; s.push(idx); flg[idx] = true; for (int w : graph.vertex_to[idx]) { if (num[w] == 0) { dfs(w); low[idx] = min(low[idx], low[w]); } else if (flg[w]) { // ? low[idx] = min(low[idx], num[w]); } } if (low[idx] == num[idx]) { while (!s.empty()) { int w = s.top(); s.pop(); flg[w] = false; if (idx == w) break; n_components -= result.union_set(idx, w); } } }; for (int i = 0; i < graph.n; ++i) { if (num[i] == 0) dfs(i); } return n_components; } class scc_DGraph { public: const DGraph& orig; DGraph sccg; vector ori2scc; vector> scc2ori; scc_DGraph(const DGraph& g) :orig(g), sccg(1), ori2scc(g.n, -1) { build(); } void build() { unionfind uf(orig.n); strongly_connected_components(orig, uf); int n_vtx = 0; for (int i = 0; i < orig.n; ++i) { int r = uf.root(i); if (ori2scc[r] == -1) { ori2scc[r] = n_vtx++; scc2ori.emplace_back(); } ori2scc[i] = ori2scc[r]; scc2ori[ori2scc[i]].push_back(i); } sccg.resize(n_vtx); for (int i = 0; i < orig.n; ++i) { for (int to : orig.vertex_to[i]) { if (ori2scc[i] == ori2scc[to]) continue; sccg.connect(ori2scc[i], ori2scc[to]); } } } inline const vector& vertex_to(int v) const { return sccg.vertex_to[v]; } inline const vector& vertex_from(int v) const { return sccg.vertex_from[v]; } inline int size() const { return sccg.n; } }; ll m, n, kei; pair stages[110]; int main() { scanner >> n; DGraph graph(n); repeat(i, n) { int l, s; scanner >> l >> s; l *= 2; --s; stages[i] = make_pair(l, s); if (s != i) { graph.connect(s, i); } } scc_DGraph scc(graph); // 強連結成分の難易度は,「強連結成分の難易度の総和/2 + 強連結成分内の最も簡単な難易度/2」 // 制約(入次数が高々1)より,強連結成分は弱連結成分でもある // つまり,弱連結成分は,サイクルか根付き木のどちらか. // もしかして,サイクル検出だけで十分?SCC要らない? int result = 0; for (auto& lis : scc.scc2ori) { if (lis.size() >= 2) { int easy = 1e9; int sum = 0; for (int u : lis) { int d = stages[u].first; sum += d; minset(easy, d); } result += sum / 2 + easy / 2; } else if (lis.size() == 1) { int u = lis[0]; int d = stages[u].first; if (graph.vertex_from[u].size() == 0) { // 入次数が0 result += d; } else { result += d / 2; } } } cout << ((double)result) / 2 << endl; return 0; }