#include <bits/stdc++.h>
using namespace std;
#define FOR(i, l, r) for(int i = (l); i <= (r); ++i)
#define FORD(i, r, l) for(int i = (r); i >= (l); --i)
#define REP(i, l, r) for(int i = (l); i < (r); ++i)
#define pb push_back
#define fi first
#define se second
#define el '\n'
#define ll long long
#define all(v) v.begin(), v.end()
#define compact(v) v.erase(unique(all(v)), end(v))
const int maxN = 1e5 + 5;
const int MOD = 1e9 + 7;
const ll INF = 1e18;
struct Edges {
int u, v;
ll cost;
Edges(int _u = 0, int _v = 0, ll _c = 0) : u(_u), v(_v), cost(_c) {}
} b[maxN];
int n, m, s, t, u, v;
vector< pair <int, ll> > adj[maxN];
vector < int > g[maxN];
ll dist[5][maxN], fu[maxN], fv[maxN], ans;
bool vis[maxN];
void dijk(int start, int type) {
priority_queue< pair<ll, int>, vector< pair<ll, int> >, greater< pair<ll, int> > > pq;
FOR(i, 1, n) dist[type][i] = INF;
dist[type][start] = 0;
pq.push(make_pair(0, start));
while(!pq.empty()) {
int u = pq.top().se;
ll cost = pq.top().fi;
pq.pop();
if (cost > dist[type][u]) continue;
for(pair <int, ll> s : adj[u]) {
int v = s.fi;
ll cost = s.se;
if (dist[type][v] > dist[type][u] + cost) {
dist[type][v] = dist[type][u] + cost;
pq.push(make_pair(dist[type][v], v));
}
}
}
}
void build(int u){
vis[u] = true;
for(auto [v, wv] : adj[u]){
if(dist[1][u] + wv + dist[2][v] == dist[1][t]){
g[u].pb(v);
if(!vis[v]) build(v);
}
}
}
void dfs(int start) {
fu[start] = dist[3][start];
fv[start] = dist[4][start];
vis[start] = 1;
for(int child : g[start]) {
if (vis[child] == false) {
dfs(child);
}
fu[start] = min(fu[start], fu[child]);
fv[start] = min(fv[start], fv[child]);
}
// cout << start << " " << dist[3][start] + fv[start] << " " << dist[4][start] + fu[start] << el;
ans = min(ans, dist[3][start] + fv[start]);
ans = min(ans, dist[4][start] + fu[start]);
}
void etoile() {
cin >> n >> m >> s >> t >> u >> v;
FOR(i, 1, m) {
int u, v;
ll c;
cin >> u >> v >> c;
adj[u].pb(make_pair(v, c));
adj[v].pb(make_pair(u, c));
b[i] = Edges(u, v, c);
}
dijk(s, 1);
dijk(t, 2);
dijk(u, 3);
dijk(v, 4);
// build dag
build(s);
memset(vis, 0, sizeof(vis));
ans = dist[3][v];
// FOR(i, 1, 4) {
// FOR(j, 1, n) {
// cout << dist[i][j] << el;
// }
// cout << el;
// }
dfs(s);
cout << ans << el;
}
signed main() {
ios_base::sync_with_stdio(false);
cin.tie(0);
#define cecilia "bus"
freopen(cecilia".inp", "r", stdin);
freopen(cecilia".out", "w", stdout);
etoile();
return 0;
}
/*
5 6
1 3
4 5
1 2 10
1 3 30
1 4 15
2 3 10
4 3 5
3 5 10
*/
