#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef pair<ll, int> edge;
const int MAXN = 100010;
const ll INF = 0x0101010101010101;
//#define debug(...) fprintf(stderr, __VA_ARGS__)
#define debug(...)
#define fi first
#define se second
#define all(v) (v).begin(), (v).end()
#define fillchar(a, s) memset((a), (s), sizeof(a))
void setmin (ll &a, ll b) {
if (a > b) {
a = b;
}
}
int N, M, S, T, U, V;
vector<edge> adj[MAXN];
ll sdist[MAXN], tdist[MAXN], udist[MAXN], vdist[MAXN];
bool vis[MAXN];
void dijkstra (ll *dist, int s) {
fill_n(dist + 1, N, INF);
fill_n(vis + 1, N, false);
dist[s] = 0;
priority_queue<edge, vector<edge>, greater<edge>> pq;
pq.emplace(0ll, s);
while (!pq.empty()) {
int u = pq.top().se;
ll w = pq.top().fi;
pq.pop();
if (vis[u]) {
continue;
}
vis[u] = true;
for (edge e : adj[u]) {
ll nw = w + e.fi;
int v = e.se;
if (nw < dist[v]) {
dist[v] = nw;
pq.emplace(nw, v);
}
}
}
}
ll dp[MAXN];
vector<int> dag[MAXN];
ll getdp (int x) {
ll &ref = dp[x];
if (ref != INF) {
return ref;
}
ref = vdist[x];
for (int y : dag[x]) {
setmin(ref, getdp(y));
}
return ref;
}
ll go() {
debug("---------PROPAGANDA--------\n");
#warning reset EVERYTHING!
dijkstra(sdist, S);
dijkstra(tdist, T);
dijkstra(udist, U);
dijkstra(vdist, V);
//now start the work - calc SP dag
//U -> vertex -> somewhere in sub of vertex -> V
fillchar(dp, 1);
for (int i = 1; i <= N; i++) {
dag[i].clear();
for (edge e : adj[i]) {
int j = e.se;
//S -> i -> j -> T
if (sdist[i] + e.fi + tdist[j] == sdist[T]) {
debug("%d -> %d\n", i, j);
dag[i].push_back(j);
}
}
}
ll ans = udist[V];
for (int i = 1; i <= N; i++) {
setmin(ans, udist[i] + getdp(i));
}
return ans;
}
int main() {
scanf("%d %d %d %d %d %d", &N, &M, &S, &T, &U, &V);
for (int i = 1; i <= M; i++) {
int a, b, c;
scanf("%d %d %d", &a, &b, &c);
adj[a].emplace_back(c, b);
adj[b].emplace_back(c, a);
}
ll ans = INF;
for (int qi = 0; qi < 2; qi++) {
swap(U, V);
setmin(ans, go());
}
printf("%lld\n", ans);
}
