#include <bits/stdc++.h>
#define fi first
#define se second
#define int long long
using namespace std;
using ii = pair<int,int>;
const int N = 1e5+5;
int n,m,s,t,u,v,a,b,c,ans = 0;
int d[N][3],dp[N][3];
bool vis[N];
vector <ii> adj[N];
void D(int u,int type){
priority_queue<ii,vector<ii>,greater<ii>> pq;
pq.push({0,u});
d[u][type] = 0;
while (!pq.empty()){
int u = pq.top().se;
int kc = pq.top().fi;
pq.pop();
if (kc > d[u][type]) continue;
for (ii it : adj[u]){
int v = it.fi;
int kcv = it.se;
if (d[v][type] > d[u][type] + kcv){
d[v][type] = d[u][type] + kcv;
pq.push({d[v][type],v});
}
}
}
}
void trace(int u){
dp[u][0] = d[u][1];
dp[u][1] = d[u][2];
vis[u] = 1;
for (ii it : adj[u]){
int v = it.fi;
int kcv = it.se;
if (d[v][0] == d[u][0] - kcv){
if (!vis[v]) trace(v);
dp[u][0] = min(dp[u][0],dp[v][0]);
dp[u][1] = min(dp[u][1],dp[v][1]);
}
}
ans = min({ans,dp[u][0] + d[u][2],dp[u][1] + d[u][1]});
}
signed main(){
ios_base::sync_with_stdio(false);
cin.tie(NULL); cout.tie(NULL);
cin >> n >> m >> s >> t >> u >> v;
for (int i = 1; i <= m; i++){
cin >> a >> b >> c;
adj[a].push_back({b,c});
adj[b].push_back({a,c});
}
memset(d,0x3f,sizeof d);
D(s,0);
D(u,1);
D(v,2);
ans = d[v][1];
trace(t);
cout << ans;
return 0;
}
