#include<bits/stdc++.h>
using namespace std;
#define int long long
int n, m, s, t, u, v, ans;
vector<vector<pair<int, int>>> adj;
vector<int> dist_u, dist_v;
vector<bool> visited;
void get_dist(int start, vector<int>& dist){
dist.resize(n+1, 1e18);
dist[start]=0;
fill(visited.begin(), visited.end(), false);
priority_queue<pair<int, int>> pq;
pq.push({dist[start], start});
while(!pq.empty()){
int a = pq.top().second;
int c = -pq.top().first;
pq.pop();
if(visited[a])continue;
visited[a]=true;
for(auto x : adj[a]){
if(dist[a]+x.second < dist[x.first]){
dist[x.first] = dist[a]+x.second;
pq.push({-dist[x.first], x.first});
}
}
}
}
signed main(){
cin >> n >> m >> s >> t >> u >> v;
adj.resize(n+1);
visited.resize(n+1);
for(int i = 0; i < m; i++){
int a, b, c;
cin >> a >> b >> c;
adj[a].push_back({b,c});
adj[b].push_back({a,c});
}
get_dist(u, dist_u);
get_dist(v, dist_v);
ans = dist_u[v];
int a = s, b=t;
for(int o = 0; o < 2; o++){
vector<int> dist_a, dp_c, dp_d;
dist_a.resize(n+1, 1e18);
dp_c.resize(n+1, 1e18);
dp_d.resize(n+1, 1e18);
dist_a[a]=0;
fill(visited.begin(), visited.end(), false);
priority_queue<pair<int, pair<int, int>>> pq;
pq.push({0, {a, 0}});
while (!pq.empty())
{
int c = -pq.top().first;
int d = pq.top().second.first;
int e = pq.top().second.second;
pq.pop();
if(!visited[d]){
visited[d]=true;
dp_c[d]=min(dp_c[e],dist_u[d]);
dp_d[d]=min(dp_d[e],dist_v[d]);
for(auto x : adj[d]){
if(dist_a[d] + x.second <= dist_a[x.first]){
dist_a[x.first]=dist_a[d]+x.second;
pq.push({-dist_a[x.first], {x.first, d}});
}
}
}
else{
if(c==dist_a[d] && (min(dp_c[e],dist_u[d]) + min(dp_d[e], dist_v[d]) <= dp_c[d]+dp_d[d])){
dp_c[d]=min(dp_c[e],dist_u[d]);
dp_d[d]=min(dp_d[e], dist_v[d]);
}
}
}
ans = min(ans, dp_c[b] + dp_d[b]);
a=t;b=s;
}
cout << ans << "\n";
}
