#include<bits/stdc++.h>
#define f first
#define s second
#define int long long
#define pii pair<int,int>
using namespace std;
const int N = 2e5 + 5, inf = 1e16;
int t, d[4][N], n, m, mn[N][2], in[N], fix[N];
vector<int> adj[2][N];
vector<pii> V[N];
void dijkstra(int u,int t) {
for(int i = 1; i <= n; i++) d[t][i] = inf;
d[t][u] = 0;
priority_queue<pii,vector<pii>,greater<pii> > q;
q.push({0,u});
while(q.size()) {
int u = q.top().s;
int dist = q.top().f;
q.pop();
if(dist > d[t][u]) continue;
for(int i = 0; i < V[u].size(); i++) {
int v = V[u][i].f, c = V[u][i].s;
if(d[t][v] > d[t][u] + c) {
adj[t][v].clear();
adj[t][v].push_back(u);
d[t][v] = d[t][u] + c;
q.push({d[t][v],v});
}
else if(d[t][v] == d[t][u] + c) adj[t][v].push_back(u);
}
}
}
void dfs(int u) {
if(fix[u]) return;
fix[u] = 1;
for(int j = 0; j < adj[0][u].size(); j++) {
in[adj[0][u][j]]++;
dfs(adj[0][u][j]);
}
}
main(){
cin >> n >> m;
int s,t,u,v;
cin >> s >> t >> u >> v;
for(int i = 1; i <= m; i++) {
int u,v,c;
cin >> u >> v >> c;
V[u].push_back({v,c});
V[v].push_back({u,c});
}
dijkstra(u,1);
dijkstra(v,2);
dijkstra(s,0);
queue<int> q;
q.push(t);
dfs(t); // DAG
int ans = d[1][v];
for(int i = 1; i <= n; i++) {
for(int t = 0; t < 2; t++) mn[i][t] = inf;
}
while(q.size()) {
int u = q.front();
q.pop();
ans = min(ans, min(mn[u][0] + d[2][u], mn[u][1] + d[1][u]));
mn[u][0] = min(mn[u][0],d[1][u]);
mn[u][1] = min(mn[u][1], d[2][u]);
for(int i = 0; i < adj[0][u].size(); i++) {
in[adj[0][u][i]]--;
for(int t = 0; t < 2; t++)
mn[adj[0][u][i]][t] = min(mn[adj[0][u][i]][t], mn[u][t]);
if(!in[adj[0][u][i]]) q.push(adj[0][u][i]);
}
}
cout << ans;
}
