#include <bits/stdc++.h>
#define ll long long
#define task "cities"
using namespace std;
const int N = 2e5 + 16;
int n, K, m, u, v;
ll w;
vector <int> critical;
struct edge {
int u, v;
ll w;
bool operator < (const edge &other) const {
return w < other.w;
}
};
edge edgeList[N];
/*
4 3 6
1 3 4
1 2 4
1 3 9
1 4 6
2 3 2
2 4 5
3 4 8
*/
/*
10 3 12
1 5 10
1 2 4
1 3 10
3 4 8
2 4 5
4 5 6
3 5 7
3 6 9
6 7 2
6 8 3
7 9 16
8 9 16
9 10 20
*/
namespace sub5 {
struct dsu {
int parent[N], sz[N];
void makeSet(int k) {
parent[k] = k;
sz[k] = 1;
}
int findSet(int k) {
if (k == parent[k]) {
return k;
}
int p = findSet(parent[k]);
parent[k] = p;
return p;
}
bool unionSet(int a, int b) {
a = findSet(a);
b = findSet(b);
if (a != b) {
if (sz[a] < sz[b]) {
swap(a, b);
}
parent[b] = a;
sz[a] += sz[b];
return true;
}
return false;
}
};
dsu g1;
vector <edge> need;
ll mst;
vector <int> adj[N];
int cnt, st[N], sparse[26][N << 2], h[N], f[N];
void dfs(int k, int p) {
sparse[0][++cnt] = k;
st[k] = cnt;
for (auto v : adj[k]) {
if (v == p) {
continue;
}
h[v] = h[k] + 1;
dfs(v, k);
sparse[0][++cnt] = k;
}
}
int lca(int u, int v) {
int l = st[u], r = st[v];
if (l > r) {
swap(l, r);
}
int k = __lg(r - l + 1);
if (h[sparse[k][l]] < h[sparse[k][r - (1 << k) + 1]]) {
return sparse[k][l];
}
return sparse[k][r - (1 << k) + 1];
}
void dpCalc(int k, int p) {
for (auto v : adj[k]) {
if (v == p) {
continue;
}
dpCalc(v, k);
f[k] += f[v];
}
}
void solve() {
sort(edgeList + 1, edgeList + 1 + m);
for (int i = 1; i <= n; i++) {
g1.makeSet(i);
}
for (int i = 1; i <= m; i++) {
u = edgeList[i].u;
v = edgeList[i].v;
w = edgeList[i].w;
if (g1.unionSet(u, v)) {
need.push_back({u, v, w});
mst += w;
adj[u].push_back(v);
adj[v].push_back(u);
}
}
dfs(1, 1);
for (int j = 1; j <= 20; j++) {
for (int i = 1; i + (1 << j) - 1 <= cnt; i++) {
if (h[sparse[j - 1][i]] < h[sparse[j - 1][i + (1 << (j - 1))]]) {
sparse[j][i] = sparse[j - 1][i];
}
else {
sparse[j][i] = sparse[j - 1][i + (1 << (j - 1))];
}
}
}
for (auto &x : need) {
if (h[x.u] > h[x.v]) {
swap(x.u, x.v);
}
}
for (int i = 0; i < critical.size(); i++) {
for (int j = i + 1; j < critical.size(); j++) {
u = critical[i];
v = critical[j];
f[u]++;
f[v]++;
f[lca(u, v)] -= 2;
}
}
dpCalc(1, 1);
for (auto x : need) {
if (f[x.v] == 0) {
mst -= x.w;
}
}
cout << mst;
}
}
int main() {
ios_base :: sync_with_stdio(false);
cin.tie(0);
cout.tie(0);
if (fopen(task".inp", "r")) {
freopen(task".inp", "r", stdin);
freopen(task".out", "w", stdout);
}
cin >> n >> K >> m;
for (int i = 1; i <= K; i++) {
cin >> u;
critical.push_back(u);
}
for (int i = 1; i <= m; i++) {
cin >> u >> v >> w;
edgeList[i] = {u, v, w};
}
sub5 :: solve();
return 0;
}
