/* -*- coding: utf-8 -*- * * 1917.cc: No.1917 LCMST - yukicoder */ #include #include #include using namespace std; /* constant */ const int MAX_N = 1000000; const int MAX_A = 100000; /* typedef */ typedef long long ll; typedef vector vi; struct Edge { int u, v; ll w; Edge() {} Edge(int _u, int _v, ll _w): u(_u), v(_v), w(_w) {} bool operator<(const Edge &e) const { return w < e.w; } }; typedef vector ve; struct UFT { int links[MAX_N], ranks[MAX_N], sizes[MAX_N]; UFT() {} void init(int n) { for (int i = 0; i < n; i++) links[i] = i, ranks[i] = sizes[i] = 1; } int root(int i) { int i0 = i; while (links[i0] != i0) i0 = links[i0]; return (links[i] = i0); } int rank(int i) { return ranks[root(i)]; } int size(int i) { return sizes[root(i)]; } bool same(int i, int j) { return root(i) == root(j); } int merge(int i0, int i1) { int r0 = root(i0), r1 = root(i1), mr; if (r0 == r1) return r0; if (ranks[r0] == ranks[r1]) { links[r1] = r0; sizes[r0] += sizes[r1]; ranks[r0]++; mr = r0; } else if (ranks[r0] > ranks[r1]) { links[r1] = r0; sizes[r0] += sizes[r1]; mr = r0; } else { links[r0] = r1; sizes[r1] += sizes[r0]; mr = r1; } return mr; } }; /* global variables */ int as[MAX_N]; vi vs[MAX_A + 1]; UFT uft; /* subroutines */ /* main */ int main() { int n; scanf("%d", &n); for (int i = 0; i < n; i++) scanf("%d", as + i); sort(as, as + n); ll sum = 0; int k = 0; for (int i = 0; i < n;) { int j = i; while (i < n && as[j] == as[i]) i++; as[k++] = as[j]; sum += (ll)as[j] * (i - j - 1); } for (int i = 0; i < k; i++) { int ai = as[i]; for (int p = 1; p * p <= ai; p++) if (ai % p == 0) { vs[p].push_back(i); int q = ai / p; if (q != p) vs[q].push_back(i); } } int maxa = as[k - 1]; ve es; for (int d = 1; d <= maxa; d++) { vi &vd = vs[d]; if (vd.size() > 1) { int u = vd[0]; for (int i = 1; i < vd.size(); i++) es.push_back(Edge(u, vd[i], (ll)as[u] * as[vd[i]] / d)); } } sort(es.begin(), es.end()); uft.init(k); for (auto e: es) if (! uft.same(e.u, e.v)) { uft.merge(e.u, e.v); sum += e.w; } printf("%lld\n", sum); return 0; }