#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
#define endl '\n'
#define hitaf ios_base::sync_with_stdio(false); cin.tie(NULL);
#define fi first
#define se second
const ll MOD = 998244353;
const ll INF = 1e18;
// dp[i][0] = par -> child, dp[i][1] = child -> par
ll n, m, s, t, u, V, dp[100005][2];
vector<pair<ll, ll>> adj[100005];
vector<ll> p[100005], child[100005];
bool vis[100005];
vector<ll> dijkstra(ll start){
vector<ll> dist(n + 2, INF);
priority_queue<pair<ll, ll>, vector<pair<ll, ll>>, greater<pair<ll, ll>>> pq;
pq.push({0, start});
dist[start] = 0;
while(!pq.empty()){
auto now = pq.top();
pq.pop();
if(dist[now.se] < now.fi) continue;
for(auto v: adj[now.se]){
if(dist[v.fi] < now.fi + v.se) continue;
dist[v.fi] = now.fi + v.se;
pq.push({dist[v.fi], v.fi});
}
}
return dist;
}
void dfs1(ll u, vector<ll> distV){
if(dp[u][0] != INF) return;
dp[u][0] = distV[u];
for(auto v: p[u]){
dfs1(v, distV);
dp[u][0] = min(dp[u][0], dp[v][0]);
}
}
void dfs2(ll u, vector<ll> distV){
if(dp[u][1] != INF) return;
dp[u][1] = distV[u];
for(auto v: child[u]){
dfs2(v, distV);
dp[u][1] = min(dp[u][1], dp[v][1]);
}
}
int main(){
hitaf
cin >> n >> m;
cin >> s >> t;
cin >> u >> V;
for(int i = 1; i <= m; i++){
ll x, y, w;
cin >> x >> y >> w;
adj[x].push_back({y, w});
adj[y].push_back({x,w});
}
vector<ll> dist = dijkstra(s);
vector<ll> distU = dijkstra(u);
vector<ll> distV = dijkstra(V);
queue<ll> q;
q.push(t);
while(!q.empty()){
ll now = q.front();
q.pop();
for(auto v: adj[now]){
if(dist[v.fi] + v.se == dist[now]){
p[now].push_back(v.fi);
child[v.fi].push_back(now);
if(vis[v.fi]) continue;
vis[v.fi] = true;
q.push(v.fi);
}
}
}
for(int i = 1; i <= n; i++) dp[i][1] = dp[i][0] = INF;
ll ans = distU[V];
for(int i = 1; i <= n; i++){
dfs1(i, distV);
dfs2(i, distV);
}
for(int i = 1; i <= n; i++){
if(!p[i].empty() || !child[i].empty()){
ans = min(ans, distU[i] + min(dp[i][0], dp[i][1]));
}
}
//cout << dp[1][1] << endl;
cout << ans << endl;
}
/*
7 1 2 9 0
*/
