#include<bits/stdc++.h>
#define STIZE(x) fprintf(stderr, "STIZE%d\n", x);
#define PRINT(x) fprintf(stderr, "%s = %d\n", #x, x);
#define NL(x) printf("%c", " \n"[(x)]);
#define lld long long
#define pii pair<int,int>
#define pb push_back
#define fi first
#define se second
#define mid (l+r)/2
#define endl '\n'
#define all(a) begin(a),end(a)
#define sz(a) int((a).size())
#define LINF 1000000000000000LL
#define INF 1000000000
#define EPS 1e-9
using namespace std;
#define MAXN 100010
int N, M, S, T, U, V;
lld dist1[MAXN], dist2[MAXN], dp[MAXN], dpU[MAXN], dpV[MAXN];
bool pos[MAXN];
vector<pair<int, lld> > adj[MAXN];
vector<int> topo, dag[MAXN];
priority_queue<pair<lld, int>, vector<pair<lld, int> >, greater<pair<lld, int > > > pq;
void topoSort(int node) {
pos[node] = true;
for(auto x : dag[node]) if(!pos[node]) topoSort(x);
topo.pb(node);
}
void dijkstra(lld dist[], int src) {
for(int i = 1; i <= N; i++) dist[i] = pos[i] = 0;
pq.push({0, src});
while(!pq.empty()) {
pair<lld,int> vrh = pq.top(); pq.pop();
if(!pos[vrh.se]) {
pos[vrh.se] = 1;
dist[vrh.se] = vrh.fi;
for(auto x : adj[vrh.se]) {
if(!pos[x.fi]) pq.push({dist[vrh.se]+x.se, x.fi});
}
}
}
}
int main() {
ios::sync_with_stdio(false); cin.tie(0); cout.tie(0); cerr.tie(0);
cin >> N >> M >> S >> T >> U >> V;
for(int i = 0; i < M; i++) {
int A, B; lld C; cin >> A >> B >> C;
adj[A].pb({B, C});
adj[B].pb({A, C});
}
dijkstra(dist1, S);
dijkstra(dist2, T);
for(int i = 1; i <= N; i++) {
for(auto j : adj[i]) {
if(dist1[i]+j.se+dist2[j.fi] == dist1[T]) dag[i].pb(j.fi);
}
}
for(int i = 1; i <= N; i++) pos[i] = 0;
topoSort(S);
reverse(all(topo));
dijkstra(dist1, U);
dijkstra(dist2, V);
while(!topo.empty()) {
int node = topo.back(); topo.pop_back();
dp[node] = dist1[node]+dist2[node];
dpU[node] = dist1[node];
dpV[node] = dist2[node];
for(auto x : dag[node]) {
dpU[node] = min(dpU[node], dpU[x]);
dpV[node] = min(dpV[node], dpV[x]);
dp[node] = min(dp[node], dp[x]);
}
dp[node] = min(dp[node], dist1[node]+dpV[node]);
dp[node] = min(dp[node], dpU[node]+dist2[node]);
}
cout << min(dp[S], dist1[V]) << endl;
}
