//Challenge: Accepted
#include <iostream>
#include <algorithm>
#include <utility>
#include <vector>
#include <set>
#include <map>
#include <queue>
#define maxn 100005
#define mod 1000000007
#define ll long long
#define pii pair<int, ll>
#define ff first
#define ss second
using namespace std;
const ll inf = 1LL<<60;
vector<pii> adj[maxn];
vector<int> dag[maxn];
bool poss[maxn];
int deg[maxn];
ll ms[maxn], mu[maxn], mv[maxn], dp[maxn], dp2[maxn];
inline bool cmp(const pii &a, const pii &b) {
return a.ss > b.ss;
}
priority_queue<pii, vector<pii>, bool (*) (const pii&, const pii&) > pq(cmp);
void dijkstra(int s, int n, ll mind[]) {
for (int i = 1;i <= n;i++) mind[i] = inf;
mind[s] = 0;
pq.push(make_pair(s, 0));
while (pq.size()) {
int cur = pq.top().ff;
ll dis = pq.top().ss;
pq.pop();
if (dis != mind[cur]) continue;
for (auto v:adj[cur]) {
ll nd = dis + v.ss;
if (nd < mind[v.ff]) {
mind[v.ff] = nd;
pq.push(make_pair(v.ff, nd));
}
}
}
}
int main() {
ios_base::sync_with_stdio(0);cin.tie(0);
int n, m, S, T, U, V;
cin >> n >> m >> S >> T >> U >> V;
for (int i = 0;i < m;i++) {
int a, b, c;
cin >> a >> b >> c;
adj[a].push_back(make_pair(b, c));
adj[b].push_back(make_pair(a, c));
}
dijkstra(S, n, ms);
dijkstra(U, n, mu);
dijkstra(V, n, mv);
poss[T] = true;
for (int i = 1;i <= n;i++) {
for (auto ed:adj[i]) {
if (ms[i] + ed.ss == ms[ed.ff]) {
dag[ed.ff].push_back(i);
deg[i]++;//reverse degree
}
}
}
queue<int> que;
for (int i = 1;i <= n;i++) {
dp[i] = dp2[i] = inf;
if (deg[i] == 0) que.push(i);
}
dp[T] = mv[T], dp2[T] = mu[T];
ll ans = mu[V];
while (que.size()) {
int cur = que.front();
if (poss[cur]) {
//cout << cur << " " << endl;
dp[cur] = min(dp[cur], mv[cur]);
dp2[cur] = min(dp2[cur], mu[cur]);
}
ans = min(ans, min(mu[cur] + dp[cur], mv[cur] + dp2[cur]));
que.pop();
for (int v:dag[cur]) {
poss[v] |= poss[cur];
if (poss[cur]) {
dp[v] = min(dp[v], dp[cur]);
dp2[v] = min(dp2[v], dp2[cur]);
}
if (--deg[v] == 0) {
que.push(v);
}
}
}
cout << ans << "\n";
}
/*
6 6
1 6
1 4
1 2 1
2 3 1
3 5 1
2 4 3
4 5 2
5 6 1
6 5
1 2
3 6
1 2 1000000000
2 3 1000000000
3 4 1000000000
4 5 1000000000
5 6 1000000000
10 15
6 8
7 9
2 7 12
8 10 17
1 3 1
3 8 14
5 7 15
2 3 7
1 10 14
3 6 12
1 5 10
8 9 1
2 9 7
1 4 1
1 8 1
2 4 7
5 6 16
*/
