#include <bits/stdc++.h>
#define maxn 100010
using namespace std;
typedef long long ll;
typedef pair<ll, int> pl;
int n, m, s, t, u, v;
vector<pl> graph[maxn];
vector<ll> dist;
vector<ll> du(maxn, 1ll << 50), dv(maxn, 1ll << 50);
vector<int> prv[maxn], nxt[maxn];
priority_queue< pl, vector<pl>, greater<pl> > pq;
vector<int> ind(maxn);
bool in[maxn];
void dijkstra(int x, bool z){
dist.assign(maxn, 1ll << 50);
dist[x] = 0;
pq.push(make_pair(0, x));
while(! pq.empty()){
pl p = pq.top(); pq.pop();
int y = p.second; ll d = p.first;
if (d > dist[y]) continue;
for (int i = 0; i < graph[y].size(); i ++){
int to = graph[y][i].second;
ll w = graph[y][i].first;
if (w + d < dist[to]){
dist[to] = w + d;
pq.push(make_pair(dist[to], to));
if (z){
nxt[y].clear();
if (y != t) nxt[y].push_back(to);
prv[to].clear();
if (to != s) prv[to].push_back(y);
}
} else if (w + d == dist[to] && z){
if (y != t) nxt[y].push_back(to);
if (to != s) prv[to].push_back(y);
}
}
}
}
void bfs(vector<ll> &dp1, vector<ll> &dp2, int st){
queue<int> que;
que.push(st);
dp1[st] = dv[st];
dp2[st] = du[st];
while(! que.empty()){
int p = que.front(); que.pop();
in[p] = true;
int sz = (st == s ? nxt[p].size() : prv[p].size());
for (int i = 0; i < sz; i ++){
int to = (st == s ? nxt[p][i] : prv[p][i]);
dp1[to] = min(dp1[to], min(dp1[p], dv[to]));
dp2[to] = min(dp2[to], min(dp2[p], du[to]));
ind[to] --;
if (ind[to] == 0) que.push(to);
}
}
}
int main(){
cin >> n >> m >> s >> t >> u >> v;
s --; t --; u --; v --;
for (int i = 0; i < m; i ++){
int x, y; ll w;
cin >> x >> y >> w;
x --; y --;
graph[x].push_back(make_pair(w, y));
graph[y].push_back(make_pair(w, x));
}
dijkstra(s, true);
dijkstra(u, false);
du = dist;
dijkstra(v, false);
dv = dist;
ll ans = dv[u];
vector<ll> dp_fv(maxn, 1ll << 50), dp_bv(maxn, 1ll << 50), dp_fu(maxn, 1ll << 50), dp_bu(maxn, 1ll << 50);
for (int i = 0; i < n; i ++){
ind[i] = prv[i].size();
}
bfs(dp_fv, dp_fu, s);
for (int i = 0; i < n; i ++){
ind[i] = nxt[i].size();
}
bfs(dp_bv, dp_bu, t);
for (int i = 0; i < n; i ++){
if (in[i]){
ans = min(ans, dp_fu[i] + dp_bv[i]);
ans = min(ans, dp_fv[i] + dp_bu[i]);
}
}
cout << ans << endl;
}
