#include <bits/stdc++.h>
using namespace std;
#define pii pair<int, int>
#define fi first
#define se second
#define int long long
using ll = long long;
const ll inf = 1e18;
const int N = 1e5+5;
int n, m, s, t, u, v;
ll ds[N], du[N], dv[N], dpv[N], dpu[N], save[N], ans = inf;
bool chk[N];
vector <int> dag[N], tree[N];
vector <pii> g[N];
void dijkstra(int s, ll d[]) {
priority_queue <pii, vector<pii>, greater<pii>> pq;
d[s] = 0;
pq.push(make_pair(d[s], s));
while(pq.size()) {
pii u = pq.top(); pq.pop();
if(u.fi > d[u.se]) continue;
for(pii e:g[u.se]) {
if(d[e.fi] > d[u.se] + e.se) {
d[e.fi] = d[u.se] + e.se;
pq.push(make_pair(d[e.fi], e.fi));
}
}
}
}
void dfs(int u) {
chk[u] = true;
for(int v:dag[u]) if(!chk[v]) {
dfs(v);
if(save[v]) tree[u].emplace_back(v);
save[u] = save[u] | save[v];
}
}
void dag_dijkstra() {
queue <int> q;
q.push(s);
while(q.size()) {
int u = q.front(); q.pop();
if(chk[u]) continue;
chk[u] = true;
for(pii e:g[u]) {
if(ds[e.fi] == ds[u] + e.se) {
dag[u].emplace_back(e.fi);
q.push(e.fi);
}
}
}
memset(chk, 0, sizeof(chk));
save[t] = 1;
dfs(s);
}
void dfs_dp(int u) {
ll Minu = inf, Minv = inf;
for(int v:tree[u]) {
dfs_dp(v);
ans = min({ans, du[u] + dpv[v], dv[u] + dpu[v]});
Minu = min(Minu, dpu[v]);
Minv = min(Minv, dpv[v]);
}
dpu[u] = min(Minu, du[u]); dpv[u] = min(Minv, dv[u]);
}
void dynamic_programming() {
dfs_dp(s);
ans = min(ans, du[v]);
cout << ans;
}
signed main() {
ios_base::sync_with_stdio(0);
cin.tie(0); cout.tie(0);
if(fopen("test.inp", "r")) {
freopen("test.inp", "r", stdin);
freopen("test.out", "w", stdout);
}
cin >> n >> m >> s >> t >> u >> v;
for(int i = 1, a, b, c; i <= m; ++i) {
cin >> a >> b >> c;
g[a].emplace_back(b, c);
g[b].emplace_back(a, c);
}
memset(ds, 0x3f, sizeof(ds)); memset(du, 0x3f, sizeof(du)); memset(dv, 0x3f, sizeof(dv));
memset(dpv, 0x3f, sizeof(dpv)); memset(dpu, 0x3f, sizeof(dpu));
dijkstra(s, ds); dijkstra(u, du), dijkstra(v, dv);
dag_dijkstra();
dynamic_programming();
}
