// BEGIN BOILERPLATE CODE
#include <bits/stdc++.h>
using namespace std;
#ifdef KAMIRULEZ
const bool kami_loc = true;
const long long kami_seed = 69420;
#else
const bool kami_loc = false;
const long long kami_seed = chrono::steady_clock::now().time_since_epoch().count();
#endif
const string kami_fi = "kamirulez.inp";
const string kami_fo = "kamirulez.out";
mt19937_64 kami_gen(kami_seed);
long long rand_range(long long rmin, long long rmax) {
uniform_int_distribution<long long> rdist(rmin, rmax);
return rdist(kami_gen);
}
long double rand_real(long double rmin, long double rmax) {
uniform_real_distribution<long double> rdist(rmin, rmax);
return rdist(kami_gen);
}
void file_io(string fi, string fo) {
if (fi != "" && (!kami_loc || fi == kami_fi)) {
freopen(fi.c_str(), "r", stdin);
}
if (fo != "" && (!kami_loc || fo == kami_fo)) {
freopen(fo.c_str(), "w", stdout);
}
}
void set_up() {
if (kami_loc) {
file_io(kami_fi, kami_fo);
}
ios_base::sync_with_stdio(0);
cin.tie(0);
}
void just_do_it();
void just_exec_it() {
if (kami_loc) {
auto pstart = chrono::steady_clock::now();
just_do_it();
auto pend = chrono::steady_clock::now();
long long ptime = chrono::duration_cast<chrono::milliseconds>(pend - pstart).count();
string bar(50, '=');
cout << '\n' << bar << '\n';
cout << "Time: " << ptime << " ms" << '\n';
}
else {
just_do_it();
}
}
int main() {
set_up();
just_exec_it();
return 0;
}
// END BOILERPLATE CODE
// BEGIN MAIN CODE
const long long inf = 1e18L + 20;
const int ms = 1e5 + 20;
vector<pair<int, int>> adj[ms];
long long d_sx[ms];
long long d_tx[ms];
long long d_ty[ms];
long long dp_tx[ms];
long long dp_ty[ms];
bool g1[ms];
bool g2[ms];
bool g3[ms];
bool f[ms];
int n, m, sx, sy, tx, ty;
void dijk(int cx, long long d[]) {
for (int i = 1; i <= n; i++) {
d[i] = inf;
}
d[cx] = 0;
priority_queue<pair<long long, int>, vector<pair<long long, int>>, greater<pair<long long, int>>> q;
q.push({0, cx});
while (!q.empty()) {
int u = q.top().second;
long long cd = q.top().first;
q.pop();
if (d[u] != cd) {
continue;
}
for (auto x: adj[u]) {
int v = x.first;
int w = x.second;
if (d[u] + w < d[v]) {
d[v] = d[u] + w;
q.push({d[v], v});
}
}
}
}
void dfs1(int u) {
if (u == sy) {
f[u] = true;
return;
}
for (auto x: adj[u]) {
int v = x.first;
int w = x.second;
if (d_sx[u] + w == d_sx[v]) {
if (!g3[v]) {
dfs1(v);
g3[v] = true;
}
f[u] |= f[v];
}
}
}
void dfs2(int u, long long dp[], long long d[], bool g[]) {
dp[u] = d[u];
if (u == sy) {
return;
}
for (auto x: adj[u]) {
int v = x.first;
int w = x.second;
if (d_sx[u] + w == d_sx[v]) {
if (f[v]) {
if (!g[v]) {
dfs2(v, dp, d, g);
g[v] = true;
}
dp[u] = min(dp[u], dp[v]);
}
}
}
}
void just_do_it() {
cin >> n >> m;
cin >> sx >> sy >> tx >> ty;
for (int i = 0; i < m; i++) {
int u, v, w;
cin >> u >> v >> w;
adj[u].push_back({v, w});
adj[v].push_back({u, w});
}
dijk(sx, d_sx);
dijk(tx, d_tx);
dijk(ty, d_ty);
dfs1(sx);
dfs2(sx, dp_tx, d_tx, g1);
dfs2(sx, dp_ty, d_ty, g2);
long long res = d_tx[ty];
for (int u = 1; u <= n; u++) {
if (f[u]) {
res = min(res, dp_tx[u] + d_ty[u]);
res = min(res, dp_ty[u] + d_tx[u]);
}
}
cout << res;
}
// END MAIN CODE
