#include<bits/stdc++.h>
#define int long long
#define double long double
#define ii pair <int,int>
#define fi first
#define se second
#define endl '\n'
#define all(x) x.begin(), x.end()
#define rall(x) x.rbegin(), x.rend()
using namespace std;
const int maxN = 1e5 + 10;
vector <ii> adj[maxN];
int dist[5][maxN];
vector <int> path[5][maxN];
int mk[maxN];
int cntin[maxN];
void dickcha(int s, int type){
for (int i = 1; i < maxN; i++){
dist[type][i] = 1e18;
path[type][i].clear();
}
priority_queue <ii, vector <ii>, greater <ii>> q;
dist[type][s] = 0;
q.push({0,s});
while(q.size()){
ii t = q.top();
q.pop();
if (dist[type][t.se] != t.fi){
continue;
}
for (auto i: adj[t.se]){
if (dist[type][i.se] > t.fi + i.fi){
dist[type][i.se] = t.fi + i.fi;
path[type][i.se].clear();
path[type][i.se].push_back(t.se);
q.push({dist[type][i.se], i.se});
}
else if (dist[type][i.se] == t.fi + i.fi){
path[type][i.se].push_back(t.se);
}
}
}
}
void dfs(int nu){
cntin[nu]++;
mk[nu] = 1;
// cout << nu << endl;
for (auto i: path[0][nu]){
if (mk[i] == 0){
dfs(i);
}
}
}
int dp[maxN];
int n, m, s, t, S, T;
int solve(){
dickcha(S,1);
dickcha(T,2);
for (int i = 1; i <= n; i++){
mk[i] = 0;
}
dfs(t);
for (int i = 1; i <= n; i++){
dp[i] = 1e18;
}
queue <int> q;
q.push(t);
dp[t] = dist[2][t];
cntin[t]--;
while(q.size()){
int te = q.front();
// cout << te << " " << dp[te] << endl;
q.pop();
for (auto i: path[0][te]){
cntin[i]--;
dp[i] = min({dp[i],dist[2][i], dp[te]});
if (cntin[i] == 0){
q.push(i);
}
}
}
int res = dist[1][T];
for (int i = 1; i <= n; i++){
// cout << i << ": " << dp[i] << " " << dist[1][i] << endl;
res = min(res, dp[i] + dist[1][i]);
}
// cout << endl;
return res;
}
signed main(){
//freopen("input.INP", "r", stdin);
//freopen("output.OUT", "w", stdout);
if (fopen(".inp", "r")) {
freopen(".inp", "r", stdin);
freopen(".out", "w", stdout);
}
ios_base::sync_with_stdio(false);
cin.tie(NULL);
cout.tie(NULL);
cin >> n >> m;
cin >> s >> t >> S >> T;
for (int i = 1; i <= m; i++){
int a, b, w;
cin >> a >> b >> w;
adj[a].push_back({w,b});
adj[b].push_back({w,a});
}
dickcha(s,0);
int res = solve();
swap(T,S);
res = min(res,solve());
cout << res << endl;
return 0;
}
