#include #include using namespace std; using mint = atcoder::modint998244353; //https://trap.jp/post/1702/ template struct RerootingDP { struct edge { int to, idx, xdi; }; RerootingDP(int n_ = 0) : n(n_), inner_edge_id(0) { es.resize(2 * n - 2); start.resize(2 * n - 2); if (n == 1) es_build(); } void add_edge(int u, int v, int idx, int xdi) { start[inner_edge_id] = u; es[inner_edge_id] = { v,idx,xdi }; inner_edge_id++; start[inner_edge_id] = v; es[inner_edge_id] = { u,xdi,idx }; inner_edge_id++; if (inner_edge_id == 2 * n - 2) { es_build(); } } vector build(int root_ = 0) { root = root_; vector subdp(n); subdp[0] = put_vertex(e(), 0); outs.resize(n); vector geta(n + 1, 0); for (int i = 0; i < n; i++) geta[i + 1] = start[i + 1] - start[i] - 1; geta[root + 1]++; for (int i = 0; i < n; i++) geta[i + 1] += geta[i]; auto dfs = [&](auto sfs, int v, int f) -> void { E val = e(); for (int i = start[v]; i < start[v + 1]; i++) { if (es[i].to == f) { swap(es[start[v + 1] - 1], es[i]); } if (es[i].to == f) continue; sfs(sfs, es[i].to, v); E nval = put_edge(subdp[es[i].to], es[i].idx); outs[geta[v]++] = nval; val = merge(val, nval); } subdp[v] = put_vertex(val, v); }; dfs(dfs, root, -1); return subdp; } vector reroot() { vector reverse_edge(n); reverse_edge[root] = e(); vector answers(n); auto dfs = [&](auto sfs, int v) -> void { int le = outs_start(v); int ri = outs_start(v + 1); int siz = ri - le; vector rui(siz + 1); rui[siz] = e(); for (int i = siz - 1; i >= 0; i--) { rui[i] = merge(outs[le + i], rui[i + 1]); } answers[v] = put_vertex(merge(rui[0], reverse_edge[v]), v); E lui = e(); for (int i = 0; i < siz; i++) { V rdp = put_vertex(merge(merge(lui, rui[i + 1]), reverse_edge[v]), v); reverse_edge[es[start[v] + i].to] = put_edge(rdp, es[start[v] + i].xdi); lui = merge(lui, outs[le + i]); sfs(sfs, es[start[v] + i].to); } }; dfs(dfs, root); return answers; } private: int n, root, inner_edge_id; vector outs; vector es; vector start; int outs_start(int v) { int res = start[v] - v; if (root < v) res++; return res; } void es_build() { vector nes(2 * n - 2); vector nstart(n + 2, 0); for (int i = 0; i < 2 * n - 2; i++) nstart[start[i] + 2]++; for (int i = 0; i < n; i++) nstart[i + 1] += nstart[i]; for (int i = 0; i < 2 * n - 2; i++) nes[nstart[start[i] + 1]++] = es[i]; swap(es, nes); swap(start, nstart); } }; vector C; vector A; struct S { mint sum, subsize; S(mint a = 0, mint b = 0) : sum(a), subsize(b) {} }; S merge(S a, S b) { return S(a.sum + b.sum, a.subsize + b.subsize); } S e() { return S(); } S put_edge(S v, int i) { return v; } S put_vertex(S e, int v) { mint subsize = e.subsize + 1; mint sum = e.sum * mint(10).pow(A[v].size()) + C[v] * subsize; return S(sum, subsize); } int main() { int N; cin >> N; A.resize(N); C.resize(N); for (int i = 0; i < N; i++) { cin >> A[i]; C[i] = stoll(A[i]); } RerootingDP g(N); for (int i = 0; i < N - 1; i++) { int u, v; cin >> u >> v; u--; v--; g.add_edge(u, v, i, i); } g.build(); mint ans = 0; for (auto v : g.reroot()) { ans += v.sum; } cout << ans.val() << endl; }