//Huyduocdithitp
#include <bits/stdc++.h>
typedef long long ll;
#define endl '\n'
#define yes cout<<"YES"<<endl;
#define no cout<<"NO"<<endl;
#define fi first
#define se second
#define pii pair<ll, ll>
#define inf 1e18
#define faster ios_base::sync_with_stdio(false);cin.tie(NULL);cout.tie(NULL);
#define MP make_pair
#define TASK "ghuy4g"
#define start if(fopen(TASK".inp","r")){freopen(TASK".inp","r",stdin);freopen(TASK".out","w",stdout);}
#define LOG 19
#define N 100005
using namespace std;
ll n, m, s, t, x, y, d[4][N], ans = inf;
vector<pair<int, ll>> adj[N];
vector<int> adj2[N];
ll minx[N], miny[N];
bool vst[N];
void dijsktra(ll st, ll id) {
for (int i = 1; i <= n; i ++) {
d[id][i] = inf;
}
d[id][st] = 0;
priority_queue<pii, vector<pii>, greater<pii>> pq;
pq.push({d[id][st], st});
while (pq.size()) {
auto c = pq.top().fi;
auto u = pq.top().se;
pq.pop();
if (c > d[id][u]) continue;
for (auto v : adj[u]) {
if (d[id][v.fi] > c + v.se) {
d[id][v.fi] = c + v.se;
pq.push({c + v.se, v.fi});
}
}
}
}
void trace(ll u, ll id) {
for (auto v : adj[u]) {
if (d[id - 0][u] + v.se + d[1 - id][v.fi] == d[0][t]) {
adj2[u].push_back(v.fi);
trace(v.fi, id);
}
}
}
void dfs2(ll u) {
minx[u] = inf, miny[u] = inf, vst[u] = 1;
for (auto v : adj2[u]) {
if (vst[v]) {
ans = min(ans, d[2][u] + miny[v]);
ans = min(ans, d[3][u] + minx[v]);
continue;
}
dfs2(v);
ans = min(ans, d[2][u] + miny[v]);
ans = min(ans, d[3][u] + minx[v]);
minx[u] = min(minx[u], minx[v]);
miny[u] = min(miny[u], miny[v]);
}
minx[u] = min(minx[u], d[2][u]);
miny[u] = min(miny[u], d[3][u]);
}
signed main(void) {
faster;
cin >> n >> m >> s >> t >> x >> y;
for (int i = 1; i <= m; i ++) {
ll u, v, w;
cin >> u >> v >> w;
adj[u].push_back({v, w});
adj[v].push_back({u, w});
}
dijsktra(s, 0); dijsktra(t, 1); dijsktra(x, 2); dijsktra(y, 3);
trace(s, 0);
ans = d[2][y];
dfs2(s);
for (int i = 1; i <= n; i ++) {
vst[i] = 0;
adj2[i].clear();
}
trace(t, 1);
dfs2(t);
cout << ans;
return 0;
}
