#include <bits/stdc++.h>
/* #include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp> */
using namespace std;
// using namespace __gnu_pbds;
using ll = long long;
using ull = unsigned ll;
template<typename T> using vt = vector<T>;
using vi = vt<int>;
using vvi = vt<vi>;
using ii = pair<int, int>;
using vii = vt<ii>;
/* template<typename T>
using indexed_set = tree<T,null_type,less<T>,rb_tree_tag,tree_order_statistics_node_update>; */
/* struct chash {
static ull hash_f(ull x) {x += 0x9e3779b97f4a7c15; x = (x ^ (x >> 30)) * 0xbf58476d1ce4e5b9; x = (x ^ (x >> 27)) * 0x94d049bb133111eb; return x ^ (x >> 31);}
size_t operator()(ull x) const {static const ull RANDOM = chrono::steady_clock::now().time_since_epoch().count();return hash_f(x + RANDOM);}
};
struct iihash {
template <class T1, class T2>
size_t operator () (const pair<T1,T2> &p) const {auto h1 = hash<T1>{}(p.first);auto h2 = hash<T2>{}(p.second);return h1 ^ h2;}
};
template<class T1, class T2, class T3> using ii_umap = gp_hash_table<pair<T1,T2>,T3,iihash>;
template<class T1, class T2> using f_umap = gp_hash_table<T1,T2,chash>;
template<class T1, class T2> using o_umap = gp_hash_table<T1,T2>; */
#define sqr(x) (x)*(x)
#define all(x) begin(x), end(x)
#define rall(x) (x).rbegin(), (x).rend()
#define sz(x) (int)(x).size()
#define debug(x) cerr << #x << " -> " << x << '\n'
#define F first
#define S second
#define mp make_pair
#define pb push_back
#define eb emplace_back
const int inf = 1e9 + 7;
const ll infll = 1e18 + 10;
template <typename T> inline T fgcd(T a, T b) {while(b) swap(b, a %= b); return a;}
ll fpow(ll a, ll b) {ll o = 1; for(;b;b >>= 1) {if(b & 1) o = o * a;a = a * a;} return o;}
ll fpow(ll a, ll b, ll m) {ll o = 1; a %= m; for(;b;b >>= 1) {if(b & 1) o = o * a % m;a = a * a % m;} return o;}
template<class T> void uniq(vt<T> &a) {sort(all(a));a.resize(unique(all(a)) - a.begin());}
const int N = 1e5;
using pli = pair<ll, int>;
int n,m,s,t,u,v,x,y,z;
vii a[N + 1];
vi ts,ed[N + 1];
void dfs(int uu) {
for(int e : ed[uu]) dfs(e);
ts.pb(uu);
}
void dijkstra(int st, vt<ll> &d) {
priority_queue<pli, vt<pli>, greater<pli>> pq;
pq.push({0,st});
d.assign(n + 1, infll);
d[st] = 0;
while(!pq.empty()) {
ll du = pq.top().F;
int uu = pq.top().S;
pq.pop();
if(d[uu] != du) continue;
for(ii e : a[uu]) {
if(d[e.S] > du + e.F) pq.push({d[e.S] = du + e.F, e.S});
}
}
}
int main() {
scanf("%d%d%d%d%d%d", &n, &m, &s, &t, &u, &v);
while(m--) {
scanf("%d%d%d", &x, &y, &z);
a[x].eb(z,y);
a[y].eb(z,x);
}
vt<ll> b,d,e,h;
dijkstra(s, b);
dijkstra(u, d);
dijkstra(v, e);
dijkstra(t, h);
queue<int> q;
q.push(s);
while(!q.empty()) {
int c = q.front();
q.pop();
for(ii g : a[c]) {
if(b[t] == b[c] + g.F + h[g.S]) {
ed[c].pb(g.S);
if(g.S != t) q.push(g.S);
}
}
}
dfs(s);
reverse(all(ts));
ll ans = d[v];
vt<ll> minu(n + 1, infll), minv(n + 1, infll);
for(int i : ts) {
minu[i] = min(minu[i], d[i]);
minv[i] = min(minv[i], e[i]);
for(int j : ed[i]) {
minu[j] = min(minu[j], minu[i]);
minv[j] = min(minv[j], minv[i]);
}
ans = min(ans, min(minu[i] + e[i], minv[i] + d[i]));
}
printf("%lld", ans);
return 0;
}
