#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef long double ld;
typedef pair<int, int> pi;
typedef pair<ll, ll> pl;
typedef vector<int> vi;
typedef vector<ld> vd;
typedef vector<ll> vl;
#define pb push_back
#define f first
#define s second
namespace debug {
const int DEBUG = true;
template<class T1, class T2>
void pr(const pair<T1, T2> &x);
template<class T, size_t SZ>
void pr(const array<T, SZ> &x);
template<class T>
void pr(const vector<T> &x);
template<class T>
void pr(const set<T> &x);
template<class T1, class T2>
void pr(const map<T1, T2> &x);
template<class T>
void pr(const T &x) { if (DEBUG) cout << x; }
template<class T, class... Ts>
void pr(const T &first, const Ts &... rest) { pr(first), pr(rest...); }
template<class T1, class T2>
void pr(const pair<T1, T2> &x) { pr("{", x.f, ", ", x.s, "}"); }
template<class T>
void prIn(const T &x) {
pr("{");
bool fst = 1;
for (auto &a : x) {
pr(fst ? "" : ", ", a), fst = 0;
}
pr("}");
}
template<class T, size_t SZ>
void pr(const array<T, SZ> &x) { prIn(x); }
template<class T>
void pr(const vector<T> &x) { prIn(x); }
template<class T>
void pr(const set<T> &x) { prIn(x); }
template<class T1, class T2>
void pr(const map<T1, T2> &x) { prIn(x); }
void ps() { pr("\n"), cout << flush; }
template<class Arg, class... Args>
void ps(const Arg &first, const Args &... rest) {
pr(first, " ");
ps(rest...);
}
}
using namespace debug;
const int MAXN = 1e5 + 10;
const ll INF = 1e15;
vector<pi> aL[MAXN];
vector<pi> sL[MAXN];
vector<pi> pre[MAXN];
int N, M;
int S, T, U, V;
// finds DAG for routes from S to T, adds directed edges to sL
void fOPath() {
ll cost[MAXN];
fill(cost, cost + MAXN, INF);
cost[S] = 0;
priority_queue<pl, vector<pl>, greater<pl>> q;
q.push({0, S});
while (q.size()) {
pi cS = q.top();
q.pop();
int cV = cS.s;
ll cC = cS.f;
if (cost[cV] < cC) {
continue;
}
for (pi aE : aL[cV]) {
int aV = aE.f;
ll eC = aE.s;
if (cC + eC < cost[aV]) {
cost[aV] = cC + eC;
pre[aV].clear();
pre[aV].pb({cV, eC});
q.push({cC + eC, aV});
} else if (cC + eC == cost[aV]) {
pre[aV].pb({cV, eC});
}
}
}
queue<int> q2;
bool inQ2[MAXN];
fill(inQ2, inQ2 + MAXN, false);
inQ2[T] = true;
q2.push(T);
while (q2.size()) {
int cV = q2.front();
q2.pop();
for (pi preE : pre[cV]) {
if (!inQ2[preE.f]) {
q2.push(preE.f);
inQ2[preE.f] = true;
}
sL[preE.f].pb({cV, 0});
// ps(preE.f, "->", cV);
}
}
}
// state depends on cV and whether we've used, are using, or haven't used the special edges
ll dp[MAXN][3];
// given aL and sL, finds best route
ll fBest() {
priority_queue<pair<ll, pi>, vector<pair<ll, pi>>, greater<pair<ll, pi>>> q;
for (int i = 0; i < MAXN; i++) {
for (int j = 0; j < 3; j++) {
dp[i][j] = INF;
}
}
q.push({0, {U, 0}});
dp[U][0] = 0;
while (q.size()) {
auto cS = q.top();
q.pop();
ll cC = cS.f;
int cV = cS.s.f;
int cCond = cS.s.s;
if (dp[cV][cCond] < cC) {
continue;
}
// normal transitions
for (pi aE : aL[cV]) {
int aV = aE.f;
ll eC = aE.s;
int nCond = cCond == 0 ? 0 : 2;
if (dp[aV][nCond] > cC + eC) {
dp[aV][nCond] = cC + eC;
q.push({cC + eC, {aV, nCond}});
}
}
// special transitions
if (cCond != 2) {
for (pi aE : sL[cV]) {
int aV = aE.f;
ll eC = aE.s;
int nCond = 1;
if (dp[aV][nCond] > cC + eC) {
dp[aV][nCond] = cC + eC;
q.push({cC + eC, {aV, nCond}});
}
}
}
}
return min(min(dp[V][0], dp[V][1]), dp[V][2]);
}
int main() {
cin >> N >> M;
cin >> S >> T >> U >> V;
for (int i = 0; i < M; i++) {
int A, B, C;
cin >> A >> B >> C;
aL[A].pb({B, C});
aL[B].pb({A, C});
}
fOPath();
ll a1 = fBest();
swap(U, V);
ll a2 = fBest();
ll ans = min(a1, a2);
cout << ans << endl;
}
