#include <bits/stdc++.h>
using namespace std;
#define int long long
#define ull unsigned long long
#define ld long double
#define pii pair<int, int>
#define fi first
#define se second
#define __builtin_popcount __builtin_popcountll
#define all(x) (x).begin(), (x).end()
#define BIT(x, i) (((x) >> (i)) & 1)
#define MASK(x) ((1ll << (x)))
#define debug(a, l, r) for (int _i = (l); _i <= (r); ++_i) cout << (a)[_i] << ' '; cout << '\n';
const int MAXN = 1e5 + 5;
const int INF = 1e18 + 5;
int n, m, s, t, x, y;
int dx[MAXN], dy[MAXN];
vector<pii> adj[MAXN];
void dijkstra(int source, int dist[]) {
for (int i = 1; i <= n; ++i) dist[i] = INF;
dist[source] = 0;
priority_queue<pii, vector<pii>, greater<pii>> pq;
pq.push({0, source});
while (!pq.empty()) {
int cost = pq.top().fi, u = pq.top().se;
pq.pop();
if (cost > dist[u]) continue;
for (auto &e : adj[u]) {
int v = e.fi, w = e.se;
if (dist[v] > dist[u] + w) {
dist[v] = dist[u] + w;
pq.push({dist[v], v});
}
}
}
}
int dp_dag(int start, int des) {
vector<int> dist(n + 5, INF);
dist[start] = 0;
priority_queue<pii, vector<pii>, greater<pii>> pq;
pq.push({0, start});
while (!pq.empty()) {
int cost = pq.top().fi, u = pq.top().se;
pq.pop();
if (cost > dist[u]) continue;
for (auto &e : adj[u]) {
int v = e.fi, w = e.se;
if (dist[v] > dist[u] + w) {
dist[v] = dist[u] + w;
pq.push({dist[v], v});
}
}
}
vector<int> nodes(n + 5, 0);
iota(begin(nodes) + 1, begin(nodes) + n + 1, 1);
sort(begin(nodes) + 1, begin(nodes) + n + 1, [&] (int x, int y) {
return (dist[x] < dist[y]);
});
// debug(dist, 1, n);
// debug(nodes, 1, n);
vector<vector<int>> dp(2, vector<int>(n + 5, INF));
vector<bool> vis(n + 5, 0);
dp[0][start] = dx[start];
dp[1][start] = dx[start] + dy[start];
vis[start] = 1;
for (int i = 1; i <= n; ++i) {
int u = nodes[i];
// dp[0][u] = min(dp[0][u], dx[u]);
// dp[1][u] = min(dp[1][u], dp[0][u] + dy[u]);
for (auto &e : adj[u]) {
int v = e.fi, w = e.se;
if (dist[v] == dist[u] + w) {
if (!vis[v]) {
dp[0][v] = min(dx[v], dp[0][u]);
dp[1][v] = min(dp[0][v] + dy[v], dp[1][u]);
vis[v] = 1;
} else {
dp[0][v] = min(dp[0][v], dp[0][u]);
dp[1][v] = min({dp[1][v], dp[0][v] + dy[v], dp[1][u]});
}
}
}
}
return dp[1][des];
}
void solve() {
cin >> n >> m;
cin >> s >> t >> x >> y;
for (int i = 1; i <= m; ++i) {
int u, v, w; cin >> u >> v >> w;
adj[u].push_back({v, w});
adj[v].push_back({u, w});
}
dijkstra(x, dx);
dijkstra(y, dy);
cout << min(dp_dag(s, t), dp_dag(t, s));
}
signed main() {
#ifdef NCTHANH
freopen("input.txt", "r", stdin);
freopen("output.txt", "w", stdout);
#endif
ios_base::sync_with_stdio(0);
cin.tie(nullptr); cout.tie(nullptr);
solve();
return 0;
}
