#include<bits/stdc++.h>
#define Size(x) ((int)(x).size())
#define MASK(i) (1LL<<(i))
#define bit(mask, i) (((mask) >> (i)) & 1)
#define pii pair<long long,int>
using namespace std;
const long long inf = 1e18 + 7;
const int mod = 1e9 + 7;
const int N = 1e5 + 5;
template<class T1, class T2>
bool Min(T1 &a, T2 b){
if(a > b){ a = b; return true;}
return false;
}
struct Edge{
int u,v,w;
};
vector<Edge> edge;
vector<long long> minDistU, minDistV, minDistS, minDistT;
int s, t, u, v, n, m;
vector<pair<int,int>> graph[N];
vector<int> new_graph[N], inew_graph[N];
long long dpU[N], dpV[N], idpU[N], idpV[N];
void dijkstra(int s, vector<long long> &minDist){
minDist.resize(n+1, inf);
minDist[s] = 0;
priority_queue<pii, vector<pii>, greater<pii>> pq;
pq.push({minDist[s], s});
while(!pq.empty()){
int u = pq.top().second;
long long du = pq.top().first;
pq.pop();
if(du != minDist[u]) continue;
for(pair<int, int> child : graph[u]){
int v = child.first, w = child.second;
if(Min(minDist[v], minDist[u] + w)){
pq.push({minDist[v], v});
}
}
}
}
void dfs(int p){
dpU[p] = minDistU[p];
dpV[p] = minDistV[p];
for(int c : inew_graph[p]){
dfs(c);
dpU[p] = min(dpU[p], dpU[c]);
dpV[p] = min(dpV[p], dpV[c]);
}
}
void dfs2(int p){
idpU[p] = minDistU[p];
idpV[p] = minDistV[p];
for(int c : new_graph[p]){
dfs2(c);
idpU[p] = min(idpU[p], idpU[c]);
idpV[p] = min(idpV[p], idpV[c]);
}
}
void solve(){
cin >> n >> m;
cin >> s >> t;
cin >> u >> v;
for(int i = 1; i <= m; i++){
int u, v, w;
cin >> u >> v >> w;
graph[u].push_back({v, w});
graph[v].push_back({u, w});
edge.push_back({u, v, w});
}
dijkstra(s, minDistS);
dijkstra(t, minDistT);
dijkstra(u, minDistU);
dijkstra(v, minDistV);
for(int i = 0; i < m; i++){
int u = edge[i].u, v = edge[i].v, w = edge[i].w;
if(minDistS[u] + minDistT[v] + w == minDistS[t]){
new_graph[u].push_back(v);
inew_graph[v].push_back(u);
}
if(minDistS[v] + minDistT[u] + w == minDistS[t]){
new_graph[v].push_back(u);
inew_graph[u].push_back(v);
}
}
dfs(t);
dfs2(s);
long long res = minDistU[v];
for(int u = 1; u <= n; u++){
for(int v : new_graph[u]){
res = min(res, dpU[u] + idpV[v]);
res = min(res, dpV[u] + idpU[v]);
}
}
cout << res << '\n';
}
int main(){
// freopen("cbarn2.in", "r", stdin);
// freopen("cbarn2.out", "w", stdout);
ios_base::sync_with_stdio(false);
cin.tie(0);
solve();
return 0;
}
