#include <bits/stdc++.h>
#define int long long
#define debug cout << "ok\n";
#define SQR(x) (1LL * ((x) * (x)))
#define MASK(i) (1LL << (i))
#define BIT(x, i) (((x) >> (i)) & 1)
#define fi first
#define se second
#define pb push_back
#define mp make_pair
#define pii pair<int,int>
#define pli pair<ll,int>
#define vi vector<int>
#define FAST ios_base::sync_with_stdio(0);cin.tie(0);cout.tie(0);
typedef long long ll;
typedef unsigned long long ull;
typedef long double ld;
typedef unsigned int ui;
using namespace std;
const int M = 1e9 + 7;
const int INF = 1e9 + 7;
const ll INFLL = (ll)2e18 + 7LL;
const ld PI = acos(-1);
const int dx[] = {1, -1, 0, 0, -1, 1, 1, -1};
const int dy[] = {0, 0, 1, -1, -1, -1, 1, 1};
template<class _, class __>
bool minimize(_ &x, const __ y){
if(x > y){
x = y;
return true;
} else return false;
}
template<class _, class __>
bool maximize(_ &x, const __ y){
if(x < y){
x = y;
return true;
} else return false;
}
template<class _,class __>
void Add(_ &x, const __ y) {
x += y;
if (x >= M) {
x -= M;
}
return;
}
template<class _,class __>
void Diff(_ &x, const __ y) {
x -= y;
if (x < 0) {
x += M;
}
return;
}
//--------------------------------------------------------------
const int MaxN = 1e6+7;
int n,m,Dist[3][MaxN],s,t,x,y,f[MaxN][3];
vector<pii> a[MaxN];
bool ch[MaxN];
void dijkstra(int root,int r) {
memset(Dist[r],0x3f,sizeof(Dist[r]));
Dist[r][root] = 0;
priority_queue<pii,vector<pii>,greater<pii>> pq;
pq.push(mp(0,root));
while (!pq.empty()) {
int u = pq.top().se;
int du = pq.top().fi;
pq.pop();
if (du != Dist[r][u]) continue;
for (pii e : a[u]) {
int v = e.fi;
int w = e.se;
if (minimize(Dist[r][v],du + w)) {
pq.push(mp(Dist[r][v],v));
}
}
}
}
void sol() {
cin >> n >> m;
cin >> s >> t;
cin >> x >> y;
for (int i=1;i<=m;i++) {
int u,v,w;
cin >> u >> v >> w;
a[u].pb(mp(v,w));
a[v].pb(mp(u,w));
}
dijkstra(s,0);
dijkstra(x,1);
dijkstra(y,2);
priority_queue<pii> pq;
pq.push(mp(Dist[0][t],t));
ch[t] = true;
memset(f,0x3f,sizeof(f));
int res = Dist[1][y];
while (!pq.empty()) {
int u = pq.top().se;
pq.pop();
for (int i=1;i<=2;i++) minimize(f[u][i],Dist[i][u]);
minimize(res,Dist[1][u] + f[u][2]);
minimize(res,Dist[2][u] + f[u][1]);
for (pii e : a[u]) {
int v = e.fi;
int w = e.se;
if (Dist[0][v] + w == Dist[0][u]) {
for (int i=1;i<=2;i++) minimize(f[v][i],f[u][i]);
if (!ch[v]) pq.push(mp(Dist[0][v],v)),ch[v] = true;
}
}
}
cout << res;
}
signed main() {
// freopen("test.inp","r",stdin);
// freopen("test.out","w",stdout);
FAST
int t=1;
// cin >> t;
while (t--) sol();
}
