#include <bits/stdc++.h>
using namespace std;
#define ll long long
#define ff first
#define ss second
#define N 200005
#define MOD 1000000007
#define INF 0x3f3f3f3f3f3f3f3f
int s[N], e[N], d[N];
vector<int> adj[N];
priority_queue<pair<ll, int> > pq;
void dij(int v, ll* dis){
memset(dis, 0x3f3f, N);
dis[v] = 0;
pq.push({0, v});
while(!pq.empty()){
v = pq.top().ss;
if(pq.top().ff != -dis[v]){
pq.pop();
continue;
}
pq.pop();
for(int& x : adj[v]){
int u = s[x] ^ e[x] ^ v;
if(dis[u] > dis[v] + d[x]){
dis[u] = dis[v] + d[x];
pq.push({-dis[u], u});
}
}
}
}
ll dis[3][N];
ll dpmn[2][N];
ll res;
void dfs(int v){
if(dpmn[0][v] != INF) return;
for(int& x : adj[v]){
int u = s[x] ^ e[x] ^ v;
if(dis[2][u] == dis[2][v] - d[x]){
dfs(u);
dpmn[1][v] = min(dpmn[1][u], dpmn[1][v]);
dpmn[0][v] = min(dpmn[0][u], dpmn[0][v]);
}
}
res = min(res, dpmn[1][v] + dis[0][v]);
res = min(res, dpmn[0][v] + dis[1][v]);
dpmn[1][v] = min(dpmn[1][v], dis[1][v]);
dpmn[0][v] = min(dpmn[0][v], dis[0][v]);
}
int main(){
ios_base::sync_with_stdio(0);
cin.tie(0);
cout.tie(0);
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
int n, m;
int ss, tt, uu, vv;
cin>>n>>m>>ss>>tt>>uu>>vv;
for(int i = 1; i <= m; i++){
cin>>s[i]>>e[i]>>d[i];
adj[s[i]].push_back(i);
adj[e[i]].push_back(i);
}
memset(dpmn, 0x3f3f, sizeof dpmn);
dij(uu, dis[0]);
dij(vv, dis[1]);
dij(ss, dis[2]);
res = dis[1][uu];
dfs(tt);
cout<<res;
}
