#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 = 4500000000000000000LL;
// dp[i][0] = par -> child, dp[i][1] = child -> par
int n, m, s, t, u, V;
ll dp[100005][2];
vector<pair<int, int>> adj[100005];
vector<int> p[100005], child[100005];
vector<ll> distV, distU, dist;
bool vis[100005];
vector<ll> dijkstra(ll start){
vector<ll> ndist(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(ndist[now.se] < now.fi) continue;
for(auto v: adj[now.se]){
if(ndist[v.fi] < now.fi + v.se) continue;
ndist[v.fi] = now.fi + v.se;
pq.push({ndist[v.fi], v.fi});
}
}
return ndist;
}
ll dfs1(ll u){
if(dp[u][0] != -1) return dp[u][0];
dp[u][0] = distV[u];
for(auto v: p[u]){
dp[u][0] = min(dp[u][0], dfs1(v));
}
return dp[u][0];
}
ll dfs2(ll u){
if(dp[u][1] != -1) return dp[u][1];
dp[u][1] = distV[u];
for(auto v: child[u]){
dp[u][1] = min(dp[u][1], dfs2(v));
}
return dp[u][1];
}
int main(){
hitaf
cin >> n >> m;
cin >> s >> t;
cin >> u >> V;
for(int i = 1; i <= m; i++){
int x, y, w;
cin >> x >> y >> w;
adj[x].push_back({y, w});
adj[y].push_back({x,w});
}
dist = dijkstra(s);
distU = dijkstra(u);
distV = dijkstra(V);
return 0;
queue<int> 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] = -1;
dp[i][0] = -1;
}
ll ans = distU[V];
for(int i = 1; i <= n; i++){
if(!p[i].empty() || !child[i].empty()){
ans = min(ans, distU[i] + min(dfs1(i), dfs2(i)));
}
}
//for(auto x: child[7]) cout << x << " ";
//cout << endl;
cout << ans << endl;
return 0;
}
/*
7 1 2 9 0
*/
