#include <bits/stdc++.h>
#define all(v) begin(v), end(v)
#define siz(v) (int)(v).size()
#define ii pair<int, int>
#define ill pair<int, long long>
#define lli pair<long long, int>
#define fi first
#define se second
using namespace std;
template<class X, class Y> bool maximize(X &x, const Y &y){return x < y ? x = y, 1: 0;}
template<class X, class Y> bool minimize(X &x, const Y &y){return x > y ? x = y, 1: 0;}
const int MAXN = 1e5 + 5;
const long long inf = 1e18 + 234;
struct E{
int u, v, w;
E(int _u = 0, int _v = 0, int _w = 0):
u(_u), v(_v), w(_w) {};
int other(int x){
return u ^ v ^ x;
}
};
int numNode, numEdge, in[MAXN], S, T, U, V;
long long distS[MAXN], distT[MAXN], distU[MAXN], distV[MAXN], dpU[MAXN], dpV[MAXN];
vector<int> adj[MAXN], nadj[MAXN];
E edge[MAXN << 1];
void input(){
cin >> numNode >> numEdge;
cin >> S >> T >> U >> V;
for(int i = 1; i <= numEdge; i++){
int u, v, w; cin >> u >> v >> w;
adj[u].push_back(i);
adj[v].push_back(i);
edge[i] = E(u, v, w);
}
}
void dijsktra(long long *dist, const int &source){
priority_queue<lli, vector<lli>, greater<lli> > q;
memset(dist, 0x3f, (numNode + 1) * sizeof(long long));
q.push(lli(dist[source] = 0, source));
while(q.size()){
long long len = q.top().fi;
int u = q.top().se;
q.pop();
if (len > dist[u]) continue;
for(int id: adj[u]){
int v = edge[id].other(u);
if (minimize(dist[v], dist[u] + edge[id].w))
q.push(lli(dist[v], v));
}
}
}
bool valid(int u, int v, int w){
if (distS[u] + w + distT[v] == distS[T]) return 1;
return 0;
}
void addEdge(int u, int v){
nadj[u].push_back(v);
in[v]++;
}
void solve(){
dijsktra(distS, S); dijsktra(distT, T);
dijsktra(distU, U); dijsktra(distV, V);
for(int i = 1; i <= numEdge; i++){
int u = edge[i].u, v = edge[i].v, w = edge[i].w;
if (valid(u, v, w)) addEdge(u, v);
if (valid(v, u, w)) addEdge(v, u);
}
memset(dpU, 0x3f, sizeof dpU);
memset(dpV, 0x3f, sizeof dpV);
long long res = inf;
queue<int> q;
for(int u = 1; u <= numNode; u++) if (!in[u]) q.push(u);
while(q.size()){
int u = q.front();
q.pop();
minimize(dpU[u], distU[u]);
minimize(dpV[u], distV[u]);
minimize(res, dpU[u] + distV[u]);
minimize(res, dpV[u] + distU[u]);
for(int v: nadj[u]){
minimize(dpU[v], dpU[u]);
minimize(dpV[v], dpV[u]);
if (--in[v] == 0){
q.push(v);
}
}
}
cout << res << '\n';
}
int main(){
ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0);
#define task "test"
if (fopen(task".inp","r")){
freopen(task".inp", "r", stdin);
freopen(task".out", "w", stdout);
}
input();
solve();
}
