/**
* author: AgentPengin ( Độc cô cầu bại )
* created: 23.12.2022 10:08:02
* too lazy to update time
**/
#include<bits/stdc++.h>
#define EL '\n'
#define fi first
#define se second
#define NAME "TASK"
#define ll long long
#define lcm(a,b) (a/gcd(a,b))*b
#define db(val) "["#val" = " << (val) << "] "
#define bend(v) (v).begin(),(v).end()
#define sz(v) (int)(v).size()
#define ex exit(0)
#define int ll
using namespace std;
const ll mod = 1e9 + 7;
const int inf = 1e18;
const int MAXN = 1e5 + 5;
int n, m, S, T, U, V, dp[MAXN], ans;
bool visited[MAXN], r[MAXN];
vector<pair<int,int>> adj[MAXN];
vector<int> dag[MAXN];
int dist[3][MAXN];
void dijkstra(int startNode, int index) {
priority_queue<pair<int,int>, vector<pair<int,int>>, greater<pair<int,int>>> pq;
memset(dist[index], 0x3f, sizeof dist[index]);
dist[index][startNode] = 0;
pq.push(make_pair(dist[index][startNode], startNode));
while(!pq.empty()) {
int u = pq.top().se;
int du = pq.top().fi;
pq.pop();
if (du != dist[index][u]) continue;
for (auto it : adj[u]) {
int v = it.fi;
int uv = it.se;
if (dist[index][v] > du + uv) {
dist[index][v] = du + uv;
pq.push(make_pair(dist[index][v], v));
}
}
}
}
void dfs(int u) {
visited[u] = true;
for (auto v : dag[u]) {
if (!visited[v]) {
dfs(v);
}
dp[u] = min(dp[u], dp[v]);
r[u] |= r[v];
}
if (r[u]) dp[u] = min(dp[u], dist[1][u]);
}
signed main() {
ios_base::sync_with_stdio(0);cin.tie(0);cout.tie(0);
if (ifstream(NAME".inp")) {
freopen(NAME".inp","r",stdin);
freopen(NAME".out","w",stdout);
}
cin >> n >> m >> S >> T >> U >> V;
for (int i = 1, u, v, w;i <= m;i++) {
cin >> u >> v >> w;
adj[u].push_back(make_pair(v, w));
adj[v].push_back(make_pair(u, w));
}
dijkstra(U, 0); dijkstra(V, 1); dijkstra(S, 2);
ans = dist[0][V];
for (int i = 1;i <= n;i++) {
for (auto it : adj[i]) {
int v = it.fi;
int w = it.se;
if (dist[2][v] == dist[2][i] + w) {
dag[i].push_back(v);
}
}
}
memset(dp, 0x3f, sizeof dp);
r[T] = 1;
dfs(S);
for (int i = 1;i <= n;i++) {
ans = min(ans, dist[0][i] + dp[i]);
}
dijkstra(T, 2);
for (int i = 1;i <= n;i++) {
dag[i].clear();
for (auto it : adj[i]) {
int v = it.fi;
int w = it.se;
if (dist[2][v] == dist[2][i] + w) {
dag[i].push_back(v);
}
}
}
// for (auto x : dag[2]) cout << x << '\n';
memset(dp, 0x3f, sizeof dp);
memset(visited, 0, sizeof visited);
memset(r, 0, sizeof r);
r[S] = 1;
dfs(T);
for (int i = 1;i <= n;i++) {
ans = min(ans, dist[0][i] + dp[i]);
}
cout << ans;
cerr << "\nTime elapsed: " << 1000 * clock() / CLOCKS_PER_SEC << "ms\n";
return 0;
}
// agent pengin wants to take apio (with anya-san)
