#include <bits/stdc++.h>
#define FOR(i,x,n) for(int i=x; i<n; i++)
#define F0R(i,n) FOR(i,0,n)
#define ROF(i,x,n) for(int i=n-1; i>=x; i--)
#define R0F(i,n) ROF(i,0,n)
#define WTF cout << "WTF" << endl
#define IOS ios::sync_with_stdio(false); cin.tie(0)
#define F first
#define S second
#define pb push_back
#define ALL(x) x.begin(), x.end()
#define RALL(x) x.rbegin(), x.rend()
using namespace std;
typedef long long LL;
typedef pair<int, int> PII;
typedef pair<LL, LL> PLL;
typedef vector<int> VI;
typedef vector<LL> VLL;
typedef vector<PII> VPII;
typedef vector<PLL> VPLL;
const int N = 2e5 + 7;
const int ALPHA = 27;
const LL INF = 1e18;
const int MOD = 1e9 + 7;
const int LOG = 22;
int n, m, s, t, u, v;
int deg[N], rm[N];
bool colored[N];
LL dist[N], sdist[N], udist[N], vdist[N];
LL mnu[N], mnv[N];
VPLL adj[N];
VI dag[N], par[N], order, rdag[N];
void sdijk() {
fill(sdist, sdist + n, INF);
sdist[s] = 0;
priority_queue<PLL> keep;
keep.push({0, s});
while(!keep.empty()) {
int now = keep.top().S;
if (dist[now] != -keep.top().F) {
keep.pop();
continue;
}
keep.pop();
for(auto [on, w] : adj[now]) {
if (sdist[on] > sdist[now] + w) {
sdist[on] = sdist[now] + w;
par[on].clear();
par[on].pb(now);
keep.push({-dist[on], on});
}
if (sdist[on] == sdist[now] + w)
par[on].pb(now);
}
}
F0R(i, n) {
sort(ALL(par[i]));
par[i].resize(unique(ALL(par[i])) - par[i].begin());
}
return;
}
void odijk(int sc) {
fill(dist, dist + n, INF);
dist[sc] = 0;
priority_queue<PLL> keep;
keep.push({0, sc});
while(!keep.empty()) {
int now = keep.top().S;
if (dist[now] != -(keep.top().F)) {
keep.pop();
continue;
}
keep.pop();
for(auto [on, w] : adj[now]) if (dist[on] > dist[now] + w) {
dist[on] = dist[now] + w;
keep.push({-dist[on], on});
}
}
return;
}
void clarify() {
F0R(i, n) for(int on : par[i])
deg[on]++;
queue<int> dl;
F0R(i, n) if (!deg[i] && i != t)
dl.push(i);
while(!dl.empty()) {
int now = dl.front();
dl.pop();
for(int on : par[now]) {
deg[on]--;
if (!deg[on]) dl.push(on);
}
rm[now] = 1;
}
F0R(i, n) if (!rm[i]) for(int on : par[i])
if (!rm[on]) {
dag[on].pb(i);
rdag[i].pb(on);
}
return;
}
void dfs(int now) {
colored[now] = 1;
for(int on : dag[now]) if (!colored[on])
dfs(on);
order.pb(now);
return;
}
int main() {
IOS;
cin >> n >> m >> s >> t >> u >> v;
s--; t--; v--; u--;
F0R(i, m) {
LL a, b, w; cin >> a >> b >> w;
adj[--a].pb({--b, w});
adj[b].pb({a, w});
}
/*F0R(i, n) {
cout << i << " : ";
for(auto [on, w] : adj[i]) cout << on << ' ';
cout << endl;
}*/
sdijk();
assert(0);
odijk(u);
F0R(i, n) udist[i] = dist[i];
odijk(v);
F0R(i, n) vdist[i] = dist[i];
clarify();
dfs(s);
reverse(ALL(order));
fill(mnu, mnu + n, INF);
fill(mnv, mnv + n, INF);
LL ans = INF;
for(int now : order) {
for(int on : rdag[now]) {
mnu[now] = min(mnu[now], mnu[on]);
mnv[now] = min(mnv[now], mnv[on]);
}
mnu[now] = min(mnu[now], udist[now]);
mnv[now] = min(mnv[now], vdist[now]);
ans = min({ans, udist[now] + mnv[now], vdist[now] + mnu[now]});
}
ans = min(ans, udist[v]);
/*F0R(i, n) {
cout << i << " : ";
for(int on : par[i]) cout << on << ' ';
cout << endl;
}*/
cout << ans;
}
