#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef pair<ll, ll> pll;
#define fastio ios::sync_with_stdio(false), cin.tie(0)
#define pb push_back
#define eb emplace_back
const int maxn = 2e5 + 5;
const int N = 1e9 + 7;
const ll INF = 1e18;
vector<pll> adj[maxn];
int n, m, s, t, u, v;
ll dist[maxn][6];
void dijkstra(int st, int id){
for(int i = 0; i < n; i++) dist[i][id] = INF;
dist[st][id] = 0;
priority_queue<pll, vector<pll>, greater<pll>> q;
q.push({0, st});
while(!q.empty()){
auto [d, pos] = q.top(); q.pop();
if(dist[pos][id] != d) continue;
for(auto [x, w] : adj[pos]){
if(dist[x][id] > dist[pos][id] + w){
dist[x][id] = dist[pos][id] + w;
q.push({dist[x][id], x});
}
}
}
}
void dijkstra2(int dir, int id){
priority_queue<pll, vector<pll>, greater<pll>> q;
for(int i = 0; i < n; i++) dist[i][id] = dist[i][2], q.push({dist[i][id], i});
while(!q.empty()){
auto [d, pos] = q.top(); q.pop();
if(dist[pos][id] != d) continue;
for(auto [x, w] : adj[pos]){
if(dist[pos][dir] + dist[x][dir ^ 1] + w == dist[t][0]){
if(dist[x][id] > dist[pos][id]){
dist[x][id] = dist[pos][id];
q.push({dist[x][id], x});
}
}
}
}
}
int main(void){
fastio;
cin>>n>>m>>s>>t>>u>>v;
s--, t--, u--, v--;
for(int i = 0; i < m; i++){
int a, b, c;
cin>>a>>b>>c;
a--, b--;
adj[a].eb(b, c);
adj[b].eb(a, c);
}
dijkstra(s, 0);
dijkstra(t, 1);
dijkstra(v, 2);
dijkstra2(0, 3);
dijkstra2(1, 4);
dijkstra(u, 5);
ll ans = INF;
for(int i = 0; i < n; i++) ans = min(ans, dist[i][5] + min(dist[i][3], dist[i][4]));
cout<<ans<<"\n";
}
