#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <chrono>
#include <climits>
#include <cmath>
#include <complex>
#include <cstring>
#include <functional>
#include <iomanip>
#include <iostream>
#include <map>
#include <numeric>
#include <queue>
#include <random>
#include <set>
#include <unordered_set>
#include <vector>
using namespace std;
#define int long long
using ll = long long;
using ld = long double;
using str = string;
using pi = pair<int, int>;
using pl = pair<ll, ll>;
using pd = pair<ld, ld>;
#define mp make_pair
#define ff first
#define ss second
template<class T> using V = vector<T>;
#define arr array
using vi = V<int>;
using vb = V<bool>;
using vl = V<ll>;
using vd = V<ld>;
using vs = V<str>;
using vpi = V<pi>;
using vpl = V<pl>;
using vpd = V<pd>;
#define sz(x) (int)((x).size())
#define bg(x) begin(x)
#define all(x) bg(x), end(x)
#define rall(x) (x).rbegin(), (x).rend()
#define sor(x) sort(all(x))
#define rsz resize
#define ins insert
#define pb push_back
#define eb emplace_back
#define ft front()
#define bk back()
#define lb lower_bound
#define ub upper_bound
#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 rep(a) F0R(_, a)
#define trav(a, x) for(auto& a : x)
template<class T> bool ckmin(T& a, const T& b) { return (b < a ? a = b, 1 : 0); }
template<class T> bool ckmax(T& a, const T& b) { return (b > a ? a = b, 1 : 0); }
const ll INF = 0x3f3f3f3f3f3f3f3f;
const int maxn = 100000;
vpi adj[maxn];
vi par[maxn];
int N, M;
int S, T;
int U, Vv;
ll ans;
vl fromU, fromV;
void dijkstra(int st, vl& dis) {
dis = vl(N, INF);
priority_queue<pl> pq;
pq.push({dis[st] = 0, st});
while(sz(pq)) {
ll D; int cur;
tie(D, cur) = pq.top(); pq.pop();
D *= -1LL;
if(dis[cur] < D) {
continue;
}
trav(u, adj[cur]) {
if(dis[u.ff] > D + u.ss) {
pq.push({-(dis[u.ff] = D + u.ss), u.ff});
}
}
}
}
V<arr<ll, 2>> pp(int st, int en) {
vl dis(N, INF);
priority_queue<pl> pq;
pq.push({dis[st] = 0, st});
par[st].clear();
while(sz(pq)) {
ll D; int cur;
tie(D, cur) = pq.top(); pq.pop();
D *= -1LL;
if(dis[cur] < D) {
continue;
}
trav(u, adj[cur]) {
if(dis[u.ff] > D + u.ss) {
pq.push({-(dis[u.ff] = D + u.ss), u.ff});
par[u.ff].clear();
}
if(dis[u.ff] == D + u.ss) par[u.ff].eb(cur);
}
}
V<arr<ll, 2>> dp(N, arr<ll, 2>{INF, INF}); // 0 -> U; 1 -> V;
vi order;
queue<int> q;
q.push(en);
vb vis(N);
vis[en] = 1;
while(!q.empty()) {
order.eb(q.ft);
trav(u, par[q.ft]) {
if(!vis[u]) {
q.push(u);
vis[u] = 1;
}
}
q.pop();
}
reverse(all(order));
trav(u, order) {
dp[u][0] = fromU[u];
dp[u][1] = fromV[u];
trav(v, par[u]) {
ckmin(dp[u][0], dp[v][0]);
ckmin(dp[u][1], dp[v][1]);
}
}
return dp;
}
int32_t main() {
ios::sync_with_stdio(false);
cin.tie(nullptr);
cin >> N >> M;
cin >> S >> T;
cin >> U >> Vv;
--S; --T; --U; --Vv;
rep(M) {
int A, B, C; cin >> A >> B >> C;
--A; --B;
adj[A].eb(B, C);
adj[B].eb(A, C);
}
dijkstra(U, fromU);
dijkstra(Vv, fromV);
ans = fromU[Vv];
V<arr<ll, 2>> fS = pp(S, T);
V<arr<ll, 2>> fT = pp(T, S);
F0R(i, N) {
ckmin(ans, fS[i][0] + fT[i][1]);
ckmin(ans, fS[i][1] + fT[i][0]);
}
cout << ans << '\n';
return 0;
}
