#include <bits/stdc++.h>
using namespace std;
#define fi first
#define se second
#define gcd __gcd
#define siz(v) v.size()
#define pb push_back
#define pi pair<int,int>
#define all(v) (v).begin(), (v).end()
#define FOR(i, a, b) for(int i = (a); i <= (b); i++)
///#define int long long
using ll = long long;
using ld = long double;
using ull = unsigned long long;
template<typename T> bool ckmx(T &a, T b){if(a < b) return a = b, true; return false;}
template<typename T> bool ckmn(T &a, T b){if(a > b) return a = b, true; return false;}
const int N = 2e5+5;
const ll MOD = 1e9+7;
const ll INF = 1e18;
struct Edge{
int u,v; ll w;
};
int n, m, S, T, X, Y;
ll d[4][N], dp[2][N];
vector<pair<int,ll>> g[N];
vector<int> adj[N], topo;
Edge E[N]; bool vis[N];
void Dijkstra(int id, int source)
{
priority_queue<pair<ll, int>> pq;
for(int i = 1; i <= n; i++){
d[id][i] = (i == source ? 0 : INF);
}
pq.push(make_pair(0, source));
while(!pq.empty()){
pair<ll,int> e = pq.top(); pq.pop();
if(e.fi > d[id][e.se]) continue;
int x = e.se;
for(pair<int,ll> eq : g[x]){
int v = eq.fi; ll w = eq.se;
if(d[id][v] > d[id][x] + w){
d[id][v] = d[id][x] + w;
pq.push(make_pair(-d[id][v], v));
}
}
}
return;
}
void get_topoOrder(int x){
vis[x] = true;
for(int v : adj[x]){
if(!vis[v]) get_topoOrder(v);
}
dp[0][x] = dp[1][x] = INF;
topo.push_back(x);
return;
}
void solve()
{
cin >> n >> m;
cin >> S >> T >> X >> Y;
for(int i = 1; i <= m; i++){
int u,v,w; cin >> u >> v >> w;
g[u].push_back(make_pair(v, w));
g[v].push_back(make_pair(u, w));
E[i] = {u, v, w};
}
Dijkstra(0, S);
Dijkstra(1, T);
Dijkstra(2, X);
Dijkstra(3, Y);
for(int i = 1; i <= m; i++){
int u = E[i].u, v = E[i].v;
if(d[0][u] + E[i].w + d[1][v] == d[0][T] || d[0][T] == d[1][u] + E[i].w + d[0][v]){
adj[u].push_back(v);
adj[v].push_back(u);
}
}
for(int i = 1; i <= n; i++){
sort(adj[i].begin(), adj[i].end());
adj[i].erase(unique(adj[i].begin(), adj[i].end()), adj[i].end());
}
get_topoOrder(S);
reverse(topo.begin(), topo.end());
ll answer = d[2][Y];
for(int v : topo){
dp[0][v] = min(dp[0][v], d[2][v]);
dp[1][v] = min(dp[1][v], d[3][v]);
answer = min(answer, dp[0][v] + dp[1][v]);
for(int x : adj[v]){
dp[0][x] = min(dp[0][x], dp[0][v]);
dp[1][x] = min(dp[1][x], dp[1][v]);
}
}
cout << answer <<"\n";
}
signed main()
{
ios_base::sync_with_stdio(0);
cin.tie(0);
cout.tie(0);
#define name "InvMOD"
if(fopen(name".INP", "r")){
freopen(name".INP","r",stdin);
freopen(name".OUT","w",stdout);
}
int t = 1; //cin >> t;
while(t--) solve();
return 0;
}
