#include using namespace std; #define rep(i, n) for (int i = 0; i < (n); i++) #define per(i, n) for (int i = (n) - 1; i >= 0; i--) #define rep2(i, l, r) for (int i = (l); i < (r); i++) #define per2(i, l, r) for (int i = (r) - 1; i >= (l); i--) #define each(e, v) for (auto &e : v) #define MM << " " << #define pb push_back #define eb emplace_back #define all(x) begin(x), end(x) #define rall(x) rbegin(x), rend(x) #define sz(x) (int)x.size() using ll = long long; using pii = pair; using pil = pair; using pli = pair; using pll = pair; template using minheap = priority_queue, greater>; template using maxheap = priority_queue; template bool chmax(T &x, const T &y) { return (x < y) ? (x = y, true) : false; } template bool chmin(T &x, const T &y) { return (x > y) ? (x = y, true) : false; } template int flg(T x, int i) { return (x >> i) & 1; } int pct(int x) { return __builtin_popcount(x); } int pct(ll x) { return __builtin_popcountll(x); } int topbit(int x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); } int topbit(ll x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); } int botbit(int x) { return (x == 0 ? -1 : __builtin_ctz(x)); } int botbit(ll x) { return (x == 0 ? -1 : __builtin_ctzll(x)); } template void print(const vector &v, T x = 0) { int n = v.size(); for (int i = 0; i < n; i++) cout << v[i] + x << (i == n - 1 ? '\n' : ' '); if (v.empty()) cout << '\n'; } template void printn(const vector &v, T x = 0) { int n = v.size(); for (int i = 0; i < n; i++) cout << v[i] + x << '\n'; } template void err_print(const vector &v, T x = 0) { int n = v.size(); for (int i = 0; i < n; i++) cerr << v[i] + x << ' '; cerr << endl; } template int lb(const vector &v, T x) { return lower_bound(begin(v), end(v), x) - begin(v); } template int ub(const vector &v, T x) { return upper_bound(begin(v), end(v), x) - begin(v); } template void rearrange(vector &v) { sort(begin(v), end(v)); v.erase(unique(begin(v), end(v)), end(v)); } template vector id_sort(const vector &v, bool greater = false) { int n = v.size(); vector ret(n); iota(begin(ret), end(ret), 0); sort(begin(ret), end(ret), [&](int i, int j) { return greater ? v[i] > v[j] : v[i] < v[j]; }); return ret; } template void reorder(vector &a, const vector &ord) { int n = a.size(); vector b(n); for (int i = 0; i < n; i++) b[i] = a[ord[i]]; swap(a, b); } template T floor(T x, T y) { assert(y != 0); if (y < 0) x = -x, y = -y; return (x >= 0 ? x / y : (x - y + 1) / y); } template T ceil(T x, T y) { assert(y != 0); if (y < 0) x = -x, y = -y; return (x >= 0 ? (x + y - 1) / y : x / y); } template pair operator+(const pair &p, const pair &q) { return make_pair(p.first + q.first, p.second + q.second); } template pair operator-(const pair &p, const pair &q) { return make_pair(p.first - q.first, p.second - q.second); } template istream &operator>>(istream &is, pair &p) { S a; T b; is >> a >> b; p = make_pair(a, b); return is; } template ostream &operator<<(ostream &os, const pair &p) { return os << p.first << ' ' << p.second; } struct io_setup { io_setup() { ios_base::sync_with_stdio(false); cin.tie(NULL); cout << fixed << setprecision(15); cerr << fixed << setprecision(15); } } io_setup; constexpr int inf = (1 << 30) - 1; constexpr ll INF = (1LL << 60) - 1; // constexpr int MOD = 1000000007; constexpr int MOD = 998244353; template struct Li_Chao_Tree { struct Line { T a, b; Line(const T &a, const T &b) : a(a), b(b) {} T get(const T &x) const { return a * x + b; } }; struct Node { Node *lch, *rch; Line l; Node(const Line &l) : lch(NULL), rch(NULL), l(l) {} Node(const T &a, const T &b) : lch(NULL), rch(NULL), l(a, b) {} }; Node *root; const T INF_T = numeric_limits::max() / 2; Li_Chao_Tree() : root(NULL) {} ~Li_Chao_Tree() { rec_delete(root); } void rec_delete(Node *now) { if (!now) return; rec_delete(now->lch), rec_delete(now->rch); delete now; } Node *add_line(const Line &k, Node *now, const T &l, const T &r) { if (!now) return new Node(k); T l1 = now->l.get(l), l2 = k.get(l); T r1 = now->l.get(r), r2 = k.get(r); if (l1 <= l2 && r1 <= r2) return now; if (l1 >= l2 && r1 >= r2) { now->l = k; return now; } T m = (l + r - 1) / 2; T m1 = now->l.get(m), m2 = k.get(m); if (m1 > m2) { if (l1 <= l2) { now->lch = add_line(now->l, now->lch, l, m); } else { now->rch = add_line(now->l, now->rch, m + 1, r); } now->l = k; } else { if (l1 >= l2) { now->lch = add_line(k, now->lch, l, m); } else { now->rch = add_line(k, now->rch, m + 1, r); } } return now; } // 直線 y = ax+b を追加 void add_line(const T &a, const T &b) { Line k(is_min ? a : -a, is_min ? b : -b); root = add_line(k, root, min_x, max_x); } Node *add_segment(const T &s, const T &t, const Line &k, Node *now, const T &l, const T &r) { if (r < s || t < l) return now; if (s <= l && r <= t) return add_line(k, now, l, r); T m = (l + r - 1) / 2; if (!now) now = new Node(0, INF_T); now->lch = add_segment(s, t, k, now->lch, l, m); now->rch = add_segment(s, t, k, now->rch, m + 1, r); return now; } // [l,r) に直線 y = ax+b を追加 void add_segment(const T &l, const T &r, const T &a, const T &b) { Line k(is_min ? a : -a, is_min ? b : -b); root = add_segment(l, r - 1, k, root, min_x, max_x); } T query(const T &x, Node *now, const T &l, const T &r) const { if (!now) return INF_T; if (l == r) return now->l.get(x); T m = (l + r - 1) / 2; if (x <= m) return min(now->l.get(x), query(x, now->lch, l, m)); return min(now->l.get(x), query(x, now->rch, m + 1, r)); } T query(const T &x) const { T ret = query(x, root, min_x, max_x); return is_min ? ret : -ret; } }; void solve() { int N, M; cin >> N >> M; vector W(N); rep(i, N) cin >> W[i]; vector> es(N); rep(i, M) { int u, v; ll w; cin >> u >> v >> w; u--, v--; es[u].eb(v, w), es[v].eb(u, w); } auto dijkstra = [&](int s) { vector d(N, INF); minheap que; que.emplace(d[s] = 0, s); while (!empty(que)) { auto [t, i] = que.top(); que.pop(); if (t > d[i]) continue; for (auto [e, l] : es[i]) { if (chmin(d[e], d[i] + l)) que.emplace(d[e], e); } } return d; }; auto d1 = dijkstra(0), d2 = dijkstra(N - 1); ll ans = d1[N - 1]; Li_Chao_Tree lct; rep(i, N) lct.add_line(W[i], d1[i]); rep(i, N) { ll tmp = lct.query(W[i]) + d2[i]; chmin(ans, tmp); } cout << ans << '\n'; // Li_Chao_Tree lct; // set s; // rep2(i, 0, N) s.emplace(W[i], i); // vector d(N, INF); // minheap que; // que.emplace(d[0] = 0, 0); // auto add = [&]() { // if (empty(s)) return; // auto [w, i] = *begin(s); // ll tmp = lct.query(w); // if (chmin(d[i], tmp)) que.emplace(d[i], i); // }; // while (!empty(que)) { // auto [t, i] = que.top(); // que.pop(); // if (t > d[i]) continue; // lct.add_line(W[i], d[i]); // s.erase(pli(W[i], i)); // add(); // for (auto [e, l] : es[i]) { // if (chmin(d[e], t + l)) que.emplace(d[e], e); // } // } // cout << d[N - 1] << '\n'; } int main() { int T = 1; // cin >> T; while (T--) solve(); }