#include <bits/stdc++.h>
#include <queue>
using namespace std;
typedef long long ll;
typedef long double ld;
typedef vector<int> vi;
typedef vector<ll> vll;
typedef vector<vi> vvi;
typedef vector<vll> vvll;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
typedef vector<pii> vpii;
typedef vector<pll> vpll;
typedef vector<vpii> vvpii;
typedef vector<vpll> vvpll;
#define pb push_back
#define mp make_pair
#define all(x) (x).begin(), (x).end()
#define rall(x) (x).rbegin(), (x).rend()
#define sz(x) (int)(x).size()
#define fi first
#define se second
template<class T> bool ckmin(T &a, const T &b) {return a > b ? a = b, 1 : 0;}
template<class T> bool ckmax(T &a, const T &b) {return a < b ? a = b, 1 : 0;}
namespace debug {
void __print(int x) {cerr << x;}
void __print(long long x) {cerr << x;}
void __print(double x) {cerr << x;}
void __print(long double x) {cerr << x;}
void __print(char x) {cerr << '\'' << x << '\'';}
void __print(const string &x) {cerr << '\"' << x << '\"';}
void __print(const char *x) {cerr << '\"' << x << '\"';}
void __print(bool x) {cerr << (x ? "true" : "false");}
template<typename T, typename V>
void __print(const pair<T, V> &x) {cerr << '{'; __print(x.first); cerr << ','; __print(x.second); cerr << '}';}
template<typename T>
void __print(const T &x) {int f = 0; cerr << '{'; for(auto z : x) cerr << (f++ ? "," : ""), __print(z); cerr << "}";}
void _print() {cerr << "]\n";}
template <typename T, typename... V>
void _print(T t, V... v) {__print(t); if(sizeof...(v)) cerr << ", "; _print(v...);}
#ifdef ljuba
#define dbg(x...) cerr << "\e[91m" << "LINE(" << __LINE__ << ") -> " << "[" << #x << "] = ["; _print(x)
#else
#define dbg(x...)
#endif
}
using namespace debug;
const char nl = '\n';
mt19937 rng(chrono::high_resolution_clock::now().time_since_epoch().count());
/*
“If you win, you live. If you lose, you die. If you don’t fight, you can’t win!”
― Eren Yaeger
*/
const ll INF = 1e18 + 12;
vector<array<int, 3>> nadjiSpecijalne(int n, int s, int t, const vector<array<int, 3>> &edges) {
vector<vpll> adj(n);
vll dist(n, INF);
vvpii sa(n);
for(auto &z : edges) {
adj[z[0]].pb({z[1], z[2]});
adj[z[1]].pb({z[0], z[2]});
}
priority_queue<pll, vpll, greater<>> pq;
pq.push({0, s});
dist[s] = 0;
while(!pq.empty()) {
auto tren = pq.top();
pq.pop();
if(dist[tren.se] != tren.fi) continue;
for(auto e : adj[tren.se]) {
if(ckmin(dist[e.fi], dist[tren.se] + e.se)) {
pq.push({dist[e.fi], e.fi});
sa[e.fi].pb({tren.se, e.se});
} else if(dist[e.fi] == dist[tren.se] + e.se) {
sa[e.fi].pb({tren.se, e.se});
}
}
}
vector<array<int, 3>> ans;
set<int> trenutne;
trenutne.insert(t);
vector<bool> posetio(n, false);
while(sz(trenutne)) {
int tren = *trenutne.begin();
trenutne.erase(tren);
posetio[tren] = true;
for(auto e : sa[tren]) {
ans.pb({e.fi, tren, e.se});
if(!posetio[e.fi]) {
trenutne.insert(e.fi);
}
}
}
return ans;
}
ll dijkstra(int n, int s, int t, const vector<array<int, 3>> &edges) {
vvpii adj(n);
vll dist(n, INF);
for(auto &z : edges) {
adj[z[0]].pb({z[1], z[2]});
}
priority_queue<pll, vpll, greater<>> pq;
pq.push({0, s});
dist[s] = 0;
while(!pq.empty()) {
auto tren = pq.top();
pq.pop();
if(dist[tren.se] != tren.fi) continue;
for(auto e : adj[tren.se]) {
if(ckmin(dist[e.fi], dist[tren.se] + e.se)) {
pq.push({dist[e.fi], e.fi});
}
}
}
return dist[t];
}
void solve() {
int n, m;
cin >> n >> m;
int s, t, u, v;
cin >> s >> t >> u >> v;
--s, --t, --u, --v;
vector<array<int, 3>> edges;
for(int i = 0; i < m; ++i) {
int a, b, c;
cin >> a >> b >> c;
--a, --b;
edges.pb({a, b, c});
}
auto spec = nadjiSpecijalne(n, s, t, edges);
dbg(spec);
auto ostale = spec;
ostale.clear();
{
set<array<int, 3>> gas;
for(auto z : spec) {
gas.insert(z);
gas.insert({z[1], z[0], z[2]});
}
for(auto z : edges) {
if(gas.count(z)) continue;
ostale.pb(z);
}
}
vector<array<int, 3>> qwer;
for(auto z : ostale) {
qwer.pb(z);
qwer.pb({z[1], z[0], z[2]});
}
for(auto z : spec) {
qwer.pb({z[0], z[1], 0});
qwer.pb({z[1], z[0], z[2]});
}
dbg(qwer);
ll ans = dijkstra(n, u, v, qwer);
qwer.clear();
for(auto z : ostale) {
qwer.pb(z);
qwer.pb({z[1], z[0], z[2]});
}
for(auto z : spec) {
qwer.pb({z[0], z[1], z[2]});
qwer.pb({z[1], z[0], 0});
}
ckmin(ans, dijkstra(n, u, v, qwer));
cout << ans << nl;
}
int main() {
ios::sync_with_stdio(0);
cin.tie(0);
cout.tie(0);
int testCases = 1;
//cin >> testCases;
while(testCases--)
solve();
}
