// URL: https://yukicoder.me/problems/no/19 import std.algorithm, std.array, std.container, std.math, std.range, std.typecons, std.string; version(unittest) {} else void main() { int N; io.getV(N); int[] L, S; io.getC(N, L, S); L[] *= 2; --S[]; auto uf = new UnionFind(N); foreach (i, Si; S) uf.unite(cast(int)i, Si); auto groups = uf.groups, r = 0; foreach (group; uf.groups) { auto za = Zaatsu!int(group); auto g = Graph(cast(int)group.length); foreach (u; group) g.addEdge(za.comp(S[u]), za.comp(u)); auto scc = g.stronglyConnectedComponentsKosaraju.comps; r += L.indexed(group).sum/2 + L.indexed(za.uncomp(scc[0])).minElement/2; } io.put!`{floatFormat: "%.1f"}`(cast(double)r/2); } class UnionFind { int n; this(int n) { this.n = this.s = n; p = new int[](n); p[] = s; cf = n; cn = new size_t[](n); cn[] = 1; } bool unite(int u, int v) { auto pu = subst(u), pv = subst(v); if (pu != pv) { p[pv] = pu; --cf; cn[pu] += cn[pv]; return true; } else { return false; } } bool isSame(int u, int v) { return subst(u) == subst(v); } size_t countForests() { return cf; } size_t countNodes(int u) { return cn[subst(u)]; } auto groups() { auto g = new int[][](n); foreach (i; 0..n) g[subst(i)] ~= i; return g.filter!(l => !l.empty); } private { int[] p; int s; size_t cf; size_t[] cn; int subst(int i) { return p[i] == s ? i : (p[i] = subst(p[i])); } } } struct Zaatsu(T) { const size_t n; this(U...)(U v) { T[] d; foreach (w; v) d ~= w.array; auto u = d.sort.uniq; n = u.walkLength; c2 = new T[](n); foreach (i, ui; u.enumerate(0)) { c1[ui] = i; c2[i] = ui; } } int comp(T v) { return c1[v]; } auto comp(R)(R v) if (isInputRange!R) { return v.map!(w => c1[w]); } T uncomp(int v) { return c2[v]; } auto uncomp(R)(R v) if (isInputRange!R) { return v.map!(w => c2[w]); } private { int[T] c1; T[] c2; } } struct Graph { alias Node = int; Node n; Node[][] g; alias g this; this(Node n) { this.n = n; g = new Node[][](n); } void addEdge(Node u, Node v) { g[u] ~= v; } void addEdgeB(Node u, Node v) { g[u] ~= v; g[v] ~= u; } } struct GraphW(W = int, W i = 10^^9) { alias Node = int, Wt = W, inf = i; struct Edge { Node src, dst; Wt wt; alias cap = wt; } Node n; Edge[][] g; alias g this; this(Node n) { this.n = n; g = new Edge[][](n); } void addEdge(Node u, Node v, Wt w) { g[u] ~= Edge(u, v, w); } void addEdgeB(Node u, Node v, Wt w) { g[u] ~= Edge(u, v, w); g[v] ~= Edge(v, u, w); } } struct GraphM(W = int, W i = 10^^9) { alias Node = int, Wt = W, inf = i; Node n; Wt[][] g; alias g this; this(int n) { this.n = n; g = new Wt[][](n, n); } static GraphM!(W, i) init(Node n) { auto g = GraphM!(W, i)(n); foreach (i; 0..n) { g[i][] = inf; g[i][i] = 0; } return g; } } struct StronglyConnectedComponentsKosaraju(Graph) { alias Node = Graph.Node; Graph g; alias g this; Node[][] comps; this(Graph g) { this.g = g; auto rdj = Graph(n), visited = new bool[](n); foreach (u; 0..n) foreach (v; g[u]) rdj.addEdge(v, u); auto dfs(Node s, Graph adj) { auto q = SList!Node(s); visited[s] = true; Node[] comp; while (!q.empty) { auto u = q.front; q.removeFront(); foreach (v; adj[u]) if (!visited[v]) { visited[v] = true; q.insertFront(v); } comp ~= u; } comp.reverse(); return comp; } Node[] ord; foreach (u; 0..n) if (!visited[u]) ord ~= dfs(u, g); visited[] = false; foreach_reverse (u; ord) if (!visited[u]) comps ~= dfs(u, rdj); } } StronglyConnectedComponentsKosaraju!Graph stronglyConnectedComponentsKosaraju(Graph)(Graph g) { return StronglyConnectedComponentsKosaraju!Graph(g); } struct StronglyConnectedComponentsGabow(Graph) { alias Node = Graph.Node; Graph g; alias g this; Node[][] comps; this(Graph g) { this.g = g; Node[] i = new Node[](n); auto s = SList!Node(), b = SList!Node(), ns = Node(0); void dfs(Node u) { b.insert(i[u] = ns); s.insert(u); ++ns; foreach (v; g[u]) { if (!i[v]) dfs(v); else while (i[v] < b.front) b.removeFront; } if (i[u] == b.front) { comps ~= [[]]; b.removeFront; while (i[u] < ns) { comps[$-1] ~= s.front; i[s.front] = n + cast(Node)comps.length; s.removeFront; --ns; } } } foreach (u; 0..n) if (!i[u]) dfs(u); } } StronglyConnectedComponentsGabow!Graph stronglyConnectedComponentsGabow(Graph)(Graph g) { return StronglyConnectedComponentsGabow!Graph(g); } auto io = IO!()(); import std.stdio; struct IO(alias IN = stdin, alias OUT = stdout) { import std.conv, std.format, std.meta, std.traits; auto getV(T...)(ref T v) { foreach (ref w; v) get(w); } auto getA(T)(size_t n, ref T v) if (hasAssignableElements!T) { v = new T(n); foreach (ref w; v) get(w); } auto getC(T...)(size_t n, ref T v) if (allSatisfy!(hasAssignableElements, T)) { foreach (ref w; v) w = new typeof(w)(n); foreach (i; 0..n) foreach (ref w; v) get(w[i]); } auto getM(T)(size_t r, size_t c, ref T v) if (hasAssignableElements!T && hasAssignableElements!(ElementType!T)) { v = new T(r); foreach (ref w; v) getA(c, w); } template getS(E...) { auto getS(T)(size_t n, ref T v) { v = new T(n); foreach (ref w; v) foreach (e; E) mixin("get(w."~e~");"); } } auto put(alias conf = "{}", T...)(T v) { import core.stdc.stdlib; mixin(" const PutConf c = "~conf~"; foreach (i, w; v) { putA!c(w); if (i < v.length-1) OUT.write(c.delimiter); } static if (c.newline) OUT.writeln; static if (c.flush) OUT.flush(); static if (c.exit) exit(0); "); } auto putB(alias conf = "{}", S, T)(bool c, S t, T f) { if (c) put(t); else put(f); } auto putRaw(T...)(T v) { OUT.write(v); OUT.writeln; } private { dchar[] buf; auto sp = (new dchar[](0)).splitter; void nextLine() { IN.readln(buf); sp = buf.splitter; } auto get(T)(ref T v) { if (sp.empty) nextLine(); v = sp.front.to!T; sp.popFront(); } auto putR(alias c, T)(T v) { auto w = v; while (!w.empty) { putA!c(w.front); w.popFront(); if (!w.empty) OUT.write(c.delimiter); } } auto putA(alias c, T)(T v) { static if (isInputRange!T && !isSomeString!T) putR!c(v); else if (isFloatingPoint!T) OUT.write(format(c.floatFormat, v)); else OUT.write(v); } } } const struct PutConf { bool newline = true; bool flush; bool exit; string floatFormat = "%.10f"; string delimiter = " "; }