#include <bits/stdc++.h>
using namespace std;
template <class X, class Y>
bool chkmin(X &a, const Y &b){
return a > b ? a = b, 1 : 0;
}
#define eb emplace_back
#define all(v) (v).begin(), (v).end()
using ll = long long;
struct edge{
int v; ll w;
edge(){}
edge(int v, ll w): v(v), w(w){}
bool operator < (const edge &o) const {
return w > o.w;
}
};
const int N = 1e5 + 5;
ll dp[N], dis_s[N], dis_t[N];
ll dis_x[N], dis_y[N];
vector <edge> adj[N];
priority_queue <edge> pq;
void dijkstra(int s, ll res[]){
res[s] = 0; pq.emplace(s, 0);
while (!pq.empty()){
edge cur = pq.top(); pq.pop();
if (res[cur.v] < cur.w) continue;
for (auto nxt : adj[cur.v])
if (chkmin(res[nxt.v], cur.w + nxt.w))
pq.emplace(nxt.v, res[nxt.v]);
}
}
int main(){
ios_base::sync_with_stdio(false);
cin.tie(0); cout.tie(0);
int n, m, s, t, x, y;
cin >> n >> m >> s >> t >> x >> y;
memset(dis_s, 0x3f, sizeof dis_s);
memset(dis_t, 0x3f, sizeof dis_t);
memset(dis_x, 0x3f, sizeof dis_x);
memset(dis_y, 0x3f, sizeof dis_y);
for (int i = 1; i <= m; i++){
int u, v; ll w; cin >> u >> v >> w;
adj[u].eb(v, w); adj[v].eb(u, w);
}
dijkstra(s, dis_s); dijkstra(t, dis_t);
dijkstra(x, dis_x); dijkstra(y, dis_y);
vector <int> in_st_path;
for (int i = 1; i <= n; i++)
if (dis_s[i] + dis_t[i] == dis_s[t])
in_st_path.eb(i);
sort(all(in_st_path), [&](int p, int q){
return dis_s[p] < dis_s[q];
});
for (int u : in_st_path) dp[u] = dis_x[u];
ll res = dis_x[y];
for (int u : in_st_path){
chkmin(res, dp[u] + dis_y[u]);
for (auto nxt : adj[u]){
if (dis_s[nxt.v] != dis_s[u] + nxt.w)
continue;
chkmin(dp[nxt.v], dp[u]);
}
}
for (int u : in_st_path) dp[u] = dis_y[u];
for (int u : in_st_path){
chkmin(res, dp[u] + dis_x[u]);
for (auto nxt : adj[u]){
if (dis_s[nxt.v] != dis_s[u] + nxt.w)
continue;
chkmin(dp[nxt.v], dp[u]);
}
}
cout << res << '\n';
}
