#include <bits/stdc++.h>
using namespace std;
/*
#pragma GCC optimize("O3")
#include <bitset>
#pragma GCC target("avx2")*/
#define fi first
#define se second
#define int long long
typedef long long ll;
typedef long double ld;
mt19937 rnd(chrono::high_resolution_clock::now().time_since_epoch().count());
int inf = 1e15;
int n, k, m;
vector<vector<pair<int,int>>> g;
struct dsu {
vector<int> par;
vector<int> sz;
void init(int siz) {
par.resize(siz);
sz.resize(siz);
for (int i = 0; i < siz; i++) {
par[i] = i;
sz[i] = 1;
}
}
int get_par(int v) {
if (par[v] == v)
return v;
int ans = get_par(par[v]);
par[v] = ans;
return ans;
}
void merg(int v, int u) {
v = get_par(v);
u = get_par(u);
if (v == u)
return;
if (sz[u] > sz[v]) {
swap(v, u);
}
sz[v] += sz[u];
par[u] = v;
}
};
pair<vector<int>, vector<int>> dijktra(int st) {
vector<int> dist(n, inf);
vector<int> par(n, -1);
dist[st] = 0;
set<pair<int, int>> q = {{0, st}};
while(!q.empty()) {
auto pa = *q.begin();
q.erase(q.begin());
int d = pa.fi, v = pa.se;
for (auto [u, w] : g[v]) {
if (dist[u] > dist[v] + w) {
par[u] = v;
q.erase({dist[u], u});
dist[u] = dist[v] + w;
q.insert({dist[u], u});
}
}
}
return {dist, par};
}
int K = 200;
signed main() {
ios_base::sync_with_stdio(false);
cin.tie(NULL);
cin >> n >> k >> m;
vector<int> a(k);
g.resize(n);
for (int i = 0; i < k; i++) {
cin >> a[i];
a[i]--;
}
for (int i = 0; i < m; i++) {
int v, u, w;
cin >> v >> u >> w;
g[v - 1].push_back({u - 1, w});
g[u - 1].push_back({v - 1, w});
}
if (n <= 20) {
int mini = inf;
for (int ma = 0; ma < (1 << n); ma++) {
bool ok = 1;
for (auto el: a) {
if (((ma >> el) & 1) == 0) {
ok = 0;
}
}
if (!ok)
continue;
vector<int> ind;
map<int, int> mp;
for (int i = 0; i < n; i++) {
if ((ma >> i) & 1) {
mp[i] = ind.size();
ind.push_back(i);
}
}
int siz = ind.size();
dsu dsu;
dsu.init(siz);
vector<vector<int>> edg;
for (int i = 0; i < n; i++) {
if (((ma >> i) & 1) == 1) {
for (auto [u, w]: g[i]) {
if ((ma >> u) & 1) {
edg.push_back({w, mp[i], mp[u]});
}
}
}
}
sort(edg.begin(), edg.end());
int sum = 0;
int comp = siz;
for (int i = 0; i < edg.size(); i++) {
auto s = edg[i];
if (dsu.get_par(s[1]) != dsu.get_par(s[2])) {
comp--;
sum += s[0];
dsu.merg(s[1], s[2]);
}
}
if (comp == 1) {
mini = min(mini, sum);
}
}
cout << mini << '\n';
return 0;
}
vector<vector<int>> di, pars;
for (auto el: a) {
auto spa = dijktra(el);
di.push_back(spa.fi);
pars.push_back(spa.se);
}
int mini = inf;
if (k <= 3) {
for (int i = 0; i < n; i++) {
int val = 0;
for (int j = 0; j < k; j++) {
val += di[j][i];
}
mini = min(mini, val);
}
cout << mini << '\n';
}else if (k == 4) {
vector<vector<int>> stuff;
for (int i = 0; i < n; i ++) {
for (int blo = 0; blo < k; blo++) {
int val = 0;
for (int j = 0; j < k; j++) {
if (j == blo)
continue;
val += di[j][i];
}
stuff.push_back({val, i, blo});
}
}
sort(stuff.begin(), stuff.end());
for (int i = 0; i < 300; i++) {
auto s = stuff[i];
int val = s[0];
int cen = s[1];
int blo = s[2];
vector<int> cov;
for (int j = 0; j < k; j++) {
if (j == blo)
continue;
int cur = cen;
while (cur != -1) {
cov.push_back(cur);
cur = pars[j][cur];
}
}
int mbl = inf;
for (auto pos : cov) {
mbl = min(mbl, di[blo][pos]);
}
val += mbl;
mini = min(mini, val);
}
cout << mini << '\n';
return 0;
} else {
vector<vector<int>> stuff;
vector<vector<int>> nst;
for (int i = 0; i < n; i ++) {
for (int bl1 = 0; bl1 < k; bl1++) {
for (int bl2 = 0; bl2 < k; bl2++) {
int val = 0;
for (int j = 0; j < k; j++) {
if (j == bl1 || j == bl2)
continue;
val += di[j][i];
}
stuff.push_back({val, i, bl1, bl2});
}
}
sort(stuff.begin(), stuff.end());
nst.clear();
for (int j = 0; j < min(K, (int)stuff.size()); j++) {
nst.push_back(stuff[j]);
}
stuff = nst;
}
vector<vector<int>> stu;
for (int i = 0; i < K; i++) {
auto s= stuff[i];
int val = s[0];
int cen = s[1];
int bl1 = s[2];
int bl2 = s[3];
vector<int> cov;
for (int j = 0; j < k; j++) {
if (j == bl1 || j == bl2)
continue;
int cur = cen;
while (cur != -1) {
cov.push_back(cur);
cur = pars[j][cur];
}
}
for (auto pos : cov) {
int nval = val + di[bl1][pos];
stu.push_back({nval, cen, bl1, bl2, pos});
}
sort(stu.begin(), stu.end());
nst.clear();
for (int j = 0; j < min(K, (int)stu.size()); j++) {
nst.push_back(stu[j]);
}
stu = nst;
}
for (int i = 0; i < K; i++) {
auto s=stu[i];
int val = s[0];
int cen = s[1];
int bl1 = s[2];
int bl2 = s[3];
int bp = s[4];
vector<int> cov;
for (int j = 0; j < k; j++) {
if (j == bl1 || j == bl2)
continue;
int cur = cen;
while (cur != -1) {
cov.push_back(cur);
cur = pars[j][cur];
}
}
int cur = bp;
while (cur != -1) {
cov.push_back(cur);
cur = pars[bl1][cur];
}
int mbl = inf;
for (auto pos : cov) {
if (di[bl2][pos] < mbl) {
mbl = di[bl2][pos];
}
}
val += mbl;
mini = min(mini, val);
}
cout << mini << '\n';
}
}
