#include <iostream>
#include <cmath>
#include <algorithm>
#include <stdio.h>
#include <cstdint>
#include <cstring>
#include <string>
#include <cstdlib>
#include <vector>
#include <bitset>
#include <map>
#include <queue>
#include <ctime>
#include <stack>
#include <set>
#include <list>
#include <random>
#include <deque>
#include <functional>
#include <iomanip>
#include <sstream>
#include <fstream>
#include <complex>
#include <numeric>
#include <cassert>
#include <array>
#include <tuple>
#include <unordered_map>
#include <unordered_set>
#include <thread>
typedef long long ll;
typedef long double ld;
using namespace std;
#define el '\n'
#define ff first
#define ss second
#define pb push_back
#define popb pop_back
#define point pair <ll, ll>
#define all(x) x.begin(), x.end()
#define rall(x) x.rbegin(), x.rend()
const ll N = 1e5 + 10;
const ll INF = 2e18 + 10;
const ll inf = 2e9 + 10;
vector <point> gr[N], ngr[3 * N];
ll dist[4][3 * N], tin[N], timer = 0;
void solve() {
ll n, m;
cin >> n >> m;
ll s, t, u, v;
cin >> s >> t >> u >> v;
ll a[m], b[m], c[m];
for (ll i = 0; i < m; i++) {
cin >> a[i] >> b[i] >> c[i];
gr[a[i]].pb(make_pair(b[i], c[i]));
gr[b[i]].pb(make_pair(a[i], c[i]));
}
set <point> st;
for (ll i = 1; i <= 3 * n; i++)
dist[0][i] = dist[1][i] = dist[2][i] = dist[3][i] = INF;
st.insert({0, s});
dist[0][s] = 0;
while (!st.empty()) {
ll ver = st.begin()->ss;
st.erase(st.begin());
tin[ver] = ++timer;
for (point to : gr[ver]) {
if (dist[0][to.ff] > dist[0][ver] + to.ss) {
st.erase(make_pair(dist[0][to.ff], to.ff));
dist[0][to.ff] = dist[0][ver] + to.ss;
st.insert(make_pair(dist[0][to.ff], to.ff));
}
}
}
st.insert({0, t});
dist[1][t] = 0;
while (!st.empty()) {
ll ver = st.begin()->ss;
st.erase(st.begin());
for (point to : gr[ver]) {
if (dist[1][to.ff] > dist[1][ver] + to.ss) {
st.erase(make_pair(dist[1][to.ff], to.ff));
dist[1][to.ff] = dist[1][ver] + to.ss;
st.insert(make_pair(dist[1][to.ff], to.ff));
}
}
}
ll way = dist[0][t];
for (ll i = 0; i < m; i++) {
if (tin[a[i]] > tin[b[i]])
swap(a[i], b[i]);
ngr[a[i]].pb(make_pair(b[i], c[i]));
ngr[b[i]].pb(make_pair(a[i], c[i]));
ngr[a[i] + 2 * n].pb(make_pair(b[i] + 2 * n, c[i]));
ngr[b[i] + 2 * n].pb(make_pair(a[i] + 2 * n, c[i]));
if (dist[0][a[i]] + c[i] + dist[1][b[i]] == way)
ngr[a[i] + n].pb(make_pair(b[i] + n, 0));
}
for (ll i = 1; i <= n; i++) {
ngr[i].pb(make_pair(i + n, 0));
ngr[i + n].pb(make_pair(i + 2 * n, 0));
}
st.insert({0, u});
dist[2][u] = 0;
while (!st.empty()) {
ll ver = st.begin()->ss;
st.erase(st.begin());
for (point to : ngr[ver]) {
if (dist[2][to.ff] > dist[2][ver] + to.ss) {
st.erase(make_pair(dist[2][to.ff], to.ff));
dist[2][to.ff] = dist[2][ver] + to.ss;
st.insert(make_pair(dist[2][to.ff], to.ff));
}
}
}
st.insert({0, v});
dist[3][v] = 0;
while (!st.empty()) {
ll ver = st.begin()->ss;
st.erase(st.begin());
for (point to : ngr[ver]) {
if (dist[3][to.ff] > dist[3][ver] + to.ss) {
st.erase(make_pair(dist[3][to.ff], to.ff));
dist[3][to.ff] = dist[3][ver] + to.ss;
st.insert(make_pair(dist[3][to.ff], to.ff));
}
}
}
cout << min(dist[2][v + 2 * n], dist[3][u + 2 * n]) << el;
return;
}
signed main() {
ios_base::sync_with_stdio(0);
cin.tie(0); cout.tie(0);
int tests = 1;
//cin >> tests;
while (tests--)
solve();
return 0;
}
