#include<bits/stdc++.h>
using namespace std;
void DBG() { cerr << "]\n"; }
template<class H, class... T> void DBG(H h, T... t) {
cerr << h; if(sizeof...(t)) cerr << ", ";
DBG(t...);
}
#ifdef LOCAL
#define dbg(...) cerr << "[" << #__VA_ARGS__ << "]: [", DBG(__VA_ARGS__)
#else
#define dbg(...) 0
#endif // LOCAL
#define FOR(i,a,b) for(int i = (a) ; i<(b) ; i++)
#define F0R(i,a) FOR(i,0,a)
#define ROF(i,a,b) for(int i = (b)-1 ; i>=(a) ; i--)
#define R0F(i,a) ROF(i,0,a)
#define each(e,a) for(auto &e : (a))
#define sz(v) (int)(v).size()
#define all(v) (v).begin(),(v).end()
#define rall(v) (v).rbegin(),(v).rend()
#define pb push_back
#define tcT template<class T
#define nl "\n"
using ll = long long;
using vi = vector<int>;
using pi = pair<int,int>;
using str = string;
tcT> using V = vector<T>;
tcT> using pqg = priority_queue<T,vector<T>,greater<T>>;
void setIO(string NAME = "") {
cin.tie(0)->sync_with_stdio(0);
if(sz(NAME)) {
freopen((NAME + ".inp").c_str(),"r",stdin);
freopen((NAME + ".out").c_str(),"w",stdout);
}
}
tcT> bool ckmin(T&a, const T&b) {
return b < a ? a = b, 1 : 0;
}
const int MX = 1e5+5;
const ll INF = 1e18;
int N, M, s, t, u, v;
V<pi> adj[MX];
ll Dist[2][MX], dist[MX], dp[2][MX], ans = INF;
void gen(int src, int st) {
memset(Dist[st], 0x3f, sizeof Dist[st]);
pqg<pair<ll,int>> pq;
pq.push({Dist[st][src] = 0, src});
while(sz(pq)) {
int ver = pq.top().second; ll dver = pq.top().first;
pq.pop();
if(dver != Dist[st][ver]) continue;
each(ed, adj[ver]) {
int nver = ed.first;
ll ndver = dver + ed.second;
if(ckmin(Dist[st][nver], ndver)) pq.push({Dist[st][nver], nver});
}
}
}
void ijk(int src, int dst) {
memset(dist, 0x3f, sizeof dist);
memset(dp, 0x3f, sizeof dp);
pqg<pair<ll,int>> pq;
pq.push({dist[src] = 0, src});
dp[0][src] = Dist[0][src];
dp[1][src] = Dist[1][src];
while(sz(pq)) {
int ver = pq.top().second; ll dver = pq.top().first;
pq.pop();
if(dver != dist[ver]) continue;
each(ed, adj[ver]) {
int nver = ed.first; ll dnver = dver + ed.second;
if(ckmin(dist[nver], dnver)) {
pq.push({dist[nver], nver});
F0R(i,2) dp[i][nver] = min(dp[i][ver], Dist[i][nver]);
}
else if(dist[nver] == dnver && min(dp[0][ver], Dist[0][nver]) + min(dp[1][ver], Dist[1][nver]) <= dp[0][nver] + dp[1][nver]) {
dp[0][nver] = min(Dist[0][nver], dp[0][ver]);
dp[1][nver] = min(Dist[1][nver], dp[1][ver]);
}
}
}
ckmin(ans, dp[0][dst] + dp[1][dst]);
}
void solve() {
cin>>N>>M>>s>>t>>u>>v;
F0R(i,M) {
int a,b,c;
cin>>a>>b>>c;
adj[a].pb({b,c});
adj[b].pb({a,c});
}
gen(u, 0);
ans = Dist[0][v];
gen(v, 1);
F0R(i,2) FOR(j,1,N+1) dbg(Dist[i][j], i, j);
ijk(s, t); ijk(t, s);
cout << ans << nl;
}
int main() {
setIO();
int t=1;
//cin>>t;
while(t-->0) {
solve();
}
return 0;
}
