#ifdef DEBUG #define _GLIBCXX_DEBUG #else #pragma GCC target("avx2") #pragma GCC optimize("Ofast,unroll-loops") #endif #include using namespace std; #if __has_include() #include using mint = atcoder::modint998244353; istream& operator>>(istream& is, mint& a) { int t; is >> t; a = t; return is; } ostream& operator<<(ostream& os, mint a) { return os << a.val(); } #endif #define rep(i, n) for (int i = 0; i < n; i++) #define per(i, n) for (int i = n - 1; i >= 0; i--) #define ALL(a) a.begin(), a.end() #define vec vector #undef long #define long long long template ostream& operator<<(ostream& os, vector a) { const int n = a.size(); rep(i, n) os << a[i] << " \n"[i + 1 == n]; return os; } template ostream& operator<<(ostream& os, array a) { rep(i, n) os << a[i] << " \n"[i + 1 == n]; return os; } template istream& operator>>(istream& is, vector& a) { for (T& i : a) is >> i; return is; } template bool chmin(T& x, T y) { if (x > y) { x = y; return true; } return false; } template bool chmax(T& x, T y) { if (x < y) { x = y; return true; } return false; } template void operator++(vector& a) { for (T& i : a) ++i; } template void operator--(vector& a) { for (T& i : a) --i; } template void operator++(vector& a, int) { for (T& i : a) i++; } template void operator--(vector& a, int) { for (T& i : a) i--; } #undef endl #define endl '\n' 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); } }; constexpr int INF = 1e5 + 2; mint ten[12]; mint a_val[INF], a_len[INF]; struct mint_int { mint val; int size; mint_int() : val(0), size(0) {} mint_int(mint val, int size) : val(val), size(size) {} }; mint_int merge(mint_int x, mint_int y) { return mint_int(x.val + y.val, x.size + y.size); } mint_int e() { return mint_int(0, 0); } mint_int put_edge(mint_int x, int) { return x; } mint_int put_vertex(mint_int x, int idx) { return mint_int((x.size + 1) * a_val[idx] + x.val * a_len[idx], x.size + 1); } void solve() { ten[0] = 1; for (int i = 1; i < 12; i++) ten[i] = 10 * ten[i - 1]; int n; cin >> n; rep(i, n) { string s; cin >> s; a_val[i] = stol(s); a_len[i] = ten[s.size()]; } RerootingDP cd(n); rep(i, n - 1) { int u, v; cin >> u >> v; u--, v--; cd.add_edge(u, v, v, u); } cd.build(); mint ans = 0; for (auto [val, idx] : cd.reroot()) ans += val; cout << ans << endl; } int main() { // srand((unsigned)time(NULL)); cin.tie(nullptr); ios::sync_with_stdio(false); // cout << fixed << setprecision(40); solve(); return 0; }