#include <bits/stdc++.h>
using namespace std;
#define N 100005
#define int long long
#define oo 1e18
#define se second
#define fi first
typedef pair<int, int> ii;
/*
1 --> s
2 --> t
3 --> u
4 --> v
*/
int n, d[5][N], m, s, t, u, v, dp[3][N];
vector<ii> adj[N];
vector<int> vex;
bool cmp (int& i, int& j){
return d[1][i] < d[1][j];
}
void ditra(int s, int typ){
for (int i = 1; i <= n; i++){
d[typ][i] = oo;
}
priority_queue<ii, vector<ii>, greater<ii>> q;
d[typ][s] = 0;
q.push({0, s});
while (!q.empty()){
int du = q.top().fi;
int u = q.top().se;
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] > dv + du){
d[typ][v] = dv + du;
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(s, 1);
ditra(t, 2);
ditra(u, 3);
ditra(v, 4);
for (int i = 1; i <= n; i++) {vex.push_back(i); dp[1][i] = d[3][i]; dp[2][i] = d[4][i];}
sort(vex.begin(), vex.end(), cmp);
int res = d[3][v];
for (auto x : vex){
for (auto xx : adj[x]){
int v = xx.fi;
int dv = xx.se;
if (d[1][x] + dv + d[2][v] == d[1][t]){
res = min(res, dp[1][x] + d[4][v]);
res = min(res, dp[2][x] + d[3][v]);
dp[1][v] = min(dp[1][v], dp[1][x]);
dp[2][v] = min(dp[2][v], dp[2][x]);
}
}
}
cout << res;
return 0;
}
