#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
#define MAXN 100100
#define RNG(i, n) for(int i=0;i<n;i++)
struct Edge{
int u, w;
Edge() : u(0), w(0) {}
Edge(int u, int w) : u(u), w(w) {}
};
struct Data {
ll dist;
ll mu, mv;
Data() : dist(0), mu(0), mv(0) {}
Data(ll dist, ll mu, ll mv) : dist(dist), mu(mu), mv(mv) {}
};
ll du[MAXN];
ll dv[MAXN];
vector<Edge> adj[MAXN];
bool visited[MAXN];
Data dist[MAXN];
int n;
void basicDjikstra(int u, ll *d) {
RNG(i, n) d[i]=LONG_LONG_MAX;
memset(visited, 0, sizeof(visited));
d[u]=0;
priority_queue<pair<ll, int>> pq;
pq.push({0, u});
while(!pq.empty()) {
pair<ll, int> pr=pq.top();
pq.pop();
int v=pr.second;
if(visited[v]) continue;
visited[v]=true;
ll curd=d[v];
for(auto e : adj[v]) {
int u=e.u;
int w=e.w;
ll newd=curd+w;
if(newd<d[u]) {
d[u]=newd;
pq.push({-newd, u});
}
}
}
}
int main() {
int m, s, t, u, v;
cin >> n >> m;
cin >> s >> t;
cin >> u >> v;
s--;
t--;
u--;
v--;
RNG(i, m) {
int a, b, c;
cin >> a >> b >> c;
a--;
b--;
adj[a].push_back(Edge(b, c));
adj[b].push_back(Edge(a, c));
}
basicDjikstra(u, du);
basicDjikstra(v, dv);
RNG(i, n) dist[i].dist=LONG_LONG_MAX;
memset(visited, 0, sizeof(visited));
dist[s].mu=du[s];
dist[s].mv=dv[s];
priority_queue<pair<ll, int>> pq;
pq.push({0, s});
dist[s].dist=0;
while(!pq.empty()) {
pair<ll, int> pr=pq.top();
pq.pop();
int v=pr.second;
if(visited[v]) continue;
visited[v]=true;
ll curd=dist[v].dist;
for(auto e : adj[v]) {
int to=e.u;
int w=e.w;
ll newd=curd+w;
if(newd<dist[to].dist) {
dist[to].dist=newd;
dist[to].mu=min(du[to], dist[v].mu);
dist[to].mv=min(dv[to], dist[v].mv);
pq.push({-newd, to});
} else if(newd==dist[to].dist) {
if(dist[v].mu+dist[v].mv<dist[to].mu+dist[to].mv) {
dist[to].mu=dist[v].mu;
dist[to].mv=dist[v].mv;
}
}
}
}
ll ans=dv[u];
ll mu=dist[t].mu;
ll mv=dist[t].mv;
//cout << ans << endl;
//cout << mu << endl;
//cout << mv << endl;
ans=min(ans, mu+mv);
cout << ans << endl;
}
