#include "bits/stdc++.h"
using namespace std;
typedef long long ll;
typedef long double ld;
typedef vector<ll> vi;
typedef pair<ll, ll> pi;
#define FOR(i, j, k) for (ll i = j; i < (ll) k; ++i)
#define FORD(i, j, k) for (ll i = j; i >= (ll) k; --i)
#define nl "\n"
#define sp " "
#define all(x) (x).begin(), (x).end()
#define sc second
#define fr first
#define pb emplace_back
struct edge {
ll b, w;
};
const ll mxN = 1e5 + 5;
ll n, m;
vector<edge> adj[mxN];
vi distU, distV;
vi djik(ll x) {
vi dist(n + 1, 1e15);
bool vis[n + 1] = {};
priority_queue<pi> pq;
dist[x] = 0;
pq.emplace(0, x);
while(!pq.empty()) {
ll u = pq.top().sc;
pq.pop();
if(vis[u]) continue;
vis[u] = true;
for(auto [v, w] : adj[u]) {
if(dist[v] > dist[u] + w) {
dist[v] = dist[u] + w;
pq.emplace(-dist[v], v);
}
}
}
return dist;
}
ll solve(ll start, ll end) {
ll dp[2][100001];
bool visited[100001];
ll ds[100001];
fill(dp[0], dp[0] + 100001, LLONG_MAX / 2);
fill(dp[1], dp[1] + 100001, LLONG_MAX / 2);
fill(ds, ds + 100001, LLONG_MAX / 2);
fill(visited, visited + 100001, false);
priority_queue<pair<ll, pair<ll, ll>>> pq;
pq.push({0, {start, 0}});
dp[0][0] = dp[1][0] = LLONG_MAX/ 2;
while (!pq.empty()) {
ll c, node, par;
pair<ll, ll> p;
tie(c, p) = pq.top();
tie(node, par) = p;
pq.pop();
if (!visited[node]) {
visited[node] = true;
ds[node] = -c;
dp[0][node] = min(distU[node], dp[0][par]);
dp[1][node] = min(distV[node], dp[1][par]);
for (auto i : adj[node]) pq.push({c - i.w, {i.b, node}});
} else if (-c == ds[node]) {
if (min(distU[node], dp[0][par]) + min(distV[node], dp[1][par]) <= dp[0][node] + dp[1][node]) {
dp[0][node] = min(distU[node], dp[0][par]);
dp[1][node] = min(distV[node], dp[1][par]);
}
}
}
return dp[0][end] + dp[1][end];
}
void solve()
{
cin >> n >> m;
ll s, t;
cin >> s >> t;
ll u, v;
cin >> u >> v;
FOR(i, 0, m) {
ll a, b, c;
cin >> a >> b >> c;
edge curr;
curr.b = b;
curr.w = c;
adj[a].pb(curr);
curr.b = a;
adj[b].pb(curr);
}
distU = djik(u);
distV = djik(v);
ll ans = distU[v];
ll v1 = solve(s, t);
ll v2 = solve(t, s);
ans = min({ans, v1, v2});
cout << ans << nl;
}
signed main()
{
ios_base::sync_with_stdio(false);
cin.tie(NULL);
ll t = 1;
// cin >> t;
while (t--)
{
solve();
}
}
