#include <bits/stdc++.h>
using namespace std;
#define N 100005
#define int long long
#define oo 1e18
#define fi first
#define se second
typedef pair<int, int> ii;
/*
1 --> s
2 --> t
3 --> u
4 --> v
*/
int n, m, d[5][N], s, t, u, v, dp1[3][N], dp2[3][N], in1[N], in2[N];
vector<ii> adj[N];
vector<int> ddj[N], djj2[N];
void ditra(int typ, int s){
for (int i = 1; i <= n; i++){
d[typ][i] = oo;
}
d[typ][s] = 0;
priority_queue<ii, vector<ii>, greater<ii>> q;
q.push({0, s});
while (!q.empty()){
int u = q.top().se;
int du = q.top().fi;
q.pop();
if (du != d[typ][u]) continue;
for (auto x : adj[u]){
int v = x.fi;
int dv = x.se;
if (d[typ][v] > du + dv){
d[typ][v] = du + dv;
q.push({d[typ][v], v});
}
}
}
}
signed main(){
ios_base::sync_with_stdio(0);
cin.tie(NULL);
cin >> n >> m;
cin >> s >> t;
cin >> u >> v;
for (int i = 1; i <= m; i++){
int u, v, w;
cin >> u >> v >> w;
adj[u].push_back({v, w});
adj[v].push_back({u, w});
}
ditra(1, s);
ditra(2, t);
ditra(3, u);
ditra(4, v);
for (int i = 1; i <= n; i++){
dp1[1][i] = dp2[1][i] = d[3][i];
dp1[2][i] = dp2[2][i] = d[4][i];
}
queue<int> q;
q.push(s);
for (int i = 1; i <= n; i++){
for (auto x : adj[i]){
int v = x.fi;
int w = x.se;
if (d[1][i] + w + d[2][v] == d[2][s]){
ddj[i].push_back(v);
in1[v]++;
in2[i]++;
djj2[v].push_back(i);
}
}
}
while (!q.empty()){
int u = q.front();
q.pop();
for (auto x : ddj[u]){
in1[x]--;
dp1[1][x] = min(dp1[1][x], dp1[1][u]);
dp1[2][x] = min(dp1[2][x], dp1[2][u]);
if (!in1[x]) q.push(x);
}
}
int res = d[3][v];
q.push(t);
while (!q.empty()){
int u = q.front();
q.pop();
res = min(res, dp2[1][u] + dp1[2][u]);
res = min(res, dp2[2][u] + dp1[1][u]);
for (auto x : djj2[u]){
in2[x]--;
dp2[1][x] = min(dp2[1][x], dp2[1][u]);
dp2[2][x] = min(dp2[2][x], dp2[2][u]);
if (!in2[x]) q.push(x);
}
}
cout << res;
return 0;
}
