#include <bits/stdc++.h>
using namespace std;

typedef long long ll;

int n;
vector<int> vcost;
vector<vector<pair<int, int> > > edges;

vector<pair<pair<int,int>, int> > order;

void dfs(int v, int p) {
	for (size_t j = 0; j < edges[v].size(); j++) {
		int w = edges[v][j].first;
		if (w == p) continue;
		order.push_back(make_pair(make_pair(w, v), edges[v][j].second));
		dfs(w, v);
	}
}

vector<vector<pair<ll, int> > > best;

void prop_edge(int v, int w, int c) {
	// 保证两个末端不同
	for (int j = 0; j < 2; j++) {
		if (best[v][j].second == best[w][0].second) {
			swap(best[w][0], best[w][1]);
		}
		best[w][1] = min(best[w][1], make_pair(best[v][j].first + c, best[v][j].second));
		if (best[w][0] > best[w][1]) {
			swap(best[w][0], best[w][1]);
		}
	}
}

int main() {
	ios::sync_with_stdio(0), cin.tie(0);
	cin >> n;
	vcost.resize(n);
	for (int i = 0; i < n; i++) cin >> vcost[i];
	edges.resize(n);
	for (int i = 0; i < n-1; i++) {
		int a, b, c;
		cin >> a >> b >> c;
		a--; b--;
		edges[a].push_back(make_pair(b, c));
		edges[b].push_back(make_pair(a, c));
	}
	order.reserve(n-1);
	dfs(0, -1);

	ll total = 0;
	vector<vector<int> > cc_edges(n);
	vector<int> vis(n);
	vector<int> which_cc(n);
	vector<int> cc;
	cc.reserve(n);
	best.assign(n, vector<pair<ll, int> >(2));
	vector<pair<ll, int> > cc_best;
	cc_best.reserve(n);
	vector<vector<int> > ccs;
	ccs.reserve(n);
	while (true) {
		fill(vis.begin(), vis.end(), 0);
		fill(which_cc.begin(), which_cc.end(), -1);
		ccs.clear();
		for (int i = 0; i < n; i++) {
			if (vis[i]) continue;
			cc.clear();
			cc.push_back(i);
			vis[i] = 1;
			for (int s = 0; s < int(cc.size()); s++) {
				int v = cc[s];
				for (size_t j = 0; j < cc_edges[v].size(); j++) {
					int w = cc_edges[v][j];
					if (!vis[w]) {
						vis[w] = 1;
						cc.push_back(w);
					}
				}
			}
			for (size_t j = 0; j < cc.size(); j++) {
				which_cc[cc[j]] = int(ccs.size());
			}
			ccs.push_back(cc);
		}
		if (ccs.size() == 1) break;
		for (int v = 0; v < n; v++) {
			best[v][0] = make_pair(vcost[v], which_cc[v]);
			best[v][1] = make_pair(1e18, -1);
		}
		for (int i = n-2; i >= 0; i--) {
			pair<pair<int, int>, int>& e = order[i];
			prop_edge(e.first.first, e.first.second, e.second);
		}
		for (int i = 0; i < n-1; i++) {
			pair<pair<int, int>, int>& e = order[i];
			prop_edge(e.first.second, e.first.first, e.second);
		}
		cc_best.resize(ccs.size());
		fill(cc_best.begin(), cc_best.end(), make_pair(1e18, -1));
		for (int v = 0; v < n; v++) {
			for (int j = 0; j < 2; j++) {
				if (best[v][j].second != which_cc[v]) {
					cc_best[which_cc[v]] = min(cc_best[which_cc[v]], 
											   make_pair(best[v][j].first + vcost[v], best[v][j].second));
				}
			}
		}
		for (int k = 0; k < int(ccs.size()); k++) {
			int l = cc_best[k].second;
			if (cc_best[l].second == k && l < k) continue;
			total += cc_best[k].first;
			cc_edges[ccs[k].front()].push_back(ccs[l].front());
			cc_edges[ccs[l].front()].push_back(ccs[k].front());
		}
	}
	cout << total << '\n';
}