///In the name of GOD
#pragma GCC optimize("O2")
#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
const ll MXN = 3e5 + 10;
const ll INF = 1e18;
ll n, m, sp, tp, up, vp;
ll dis[5][MXN], dp[5][MXN], val[MXN];
bool mark[MXN];
vector<ll> adj[MXN], Ver;
vector<pair<ll, ll>> G[MXN];
priority_queue<pair<ll, ll>, vector<pair<ll, ll>>, greater<pair<ll, ll>>> pq;
void DIJ(ll f, ll src){
for(int i = 1; i <= n; i ++){
dis[f][i] = INF, mark[i] = 0;
}
dis[f][src] = 0, pq.push({0, src});
while(!pq.empty()){
ll u, d; tie(d, u) = pq.top();
pq.pop();
if(mark[u]) continue;
mark[u] = 1;
for(auto Pr : G[u]){
ll v, w; tie(v, w) = Pr;
if(!mark[v] && d + w < dis[f][v]){
dis[f][v] = d + w;
pq.push({dis[f][v], v});
}
}
}
}
void Build(ll f, ll src, ll base){
for(int i = 1; i <= n; i ++) adj[i].clear();
for(int i = 1; i <= n; i ++) val[i] = dis[base][i];
for(int u = 1; u <= n; u ++){
for(auto Pr : G[u]){
ll v, w; tie(v, w) = Pr;
if(dis[f][v] + w == dis[f][u]){
adj[u].push_back(v);
}
}
}
}
bool cmpf;
bool CMP(ll u, ll v){
return dis[cmpf][u] < dis[cmpf][v];
}
void Calc(ll f, ll base){
for(int i = 1; i <= n; i ++) dp[f][i] = INF;
cmpf = base;
sort(Ver.begin(), Ver.end(), CMP);
for(auto u : Ver){
dp[f][u] = val[u];
for(auto v : adj[u]){
dp[f][u] = min(dp[f][u], dp[f][v]);
}
}
}
int main(){
ios::sync_with_stdio(0);cin.tie(0); cout.tie(0);
cin >> n >> m >> sp >> tp >> up >> vp;
for(int i = 1; i <= m; i ++){
ll u, v, w; cin >> u >> v >> w;
G[u].push_back({v, w});
G[v].push_back({u, w});
Ver.push_back(i);
}
DIJ(0, sp), DIJ(1, tp), DIJ(2, up), DIJ(3, vp);
Build(0, sp, 2);//up
Calc(0, 0);
Build(0, sp, 3);//vp
Calc(1, 0);
Build(1, tp, 2);//up
Calc(2, 1);
Build(1, tp, 3);//vp
Calc(3, 1);
ll ans = dis[2][vp];
for(int x = 1; x <= n; x ++){
if(dis[0][x] + dis[1][x] > dis[0][tp]) continue;
ll now = dis[2][x] + min(dp[1][x], dp[3][x]);
ans = min(ans, now);
}
cout << ans << '\n';
return 0;
}
/*!
HE'S AN INSTIGATOR,
ENEMY ELIMINATOR,
AND WHEN HE KNOCKS YOU BETTER
YOU BETTER LET HIM IN.
*/
//! N.N
