#include <bits/stdc++.h>
using namespace std;
#define ll long long
#define fi first
#define se second
#define pii pair<ll, ll>
const ll MAX = 4e5 + 10;
ll n, m;
ll s, t;
ll u, v;
ll x, y, w, w2;
vector <pii> veze[MAX];
ll dis[MAX][2];
ll sol[MAX][2];
ll arr[MAX][2];
ll trm[MAX][2];
priority_queue <pii> q;
void distance(ll root, ll o) {
priority_queue <pii> q;
q.push({0, root});
dis[root][o] = 0;
while (!q.empty()) {
w = -q.top().fi;
x = q.top().se;
q.pop();
if (dis[x][o] != w) continue;
for (auto e : veze[x]) {
y = e.fi;
w2 = w + e.se;
if (dis[y][o] != -1 && dis[y][o] <= w2) continue;
dis[y][o] = w2;
q.push({-w2, y});
}
}
}
void bfs(ll root, int o) {
priority_queue <pii> q;
q.push({0, root});
arr[root][o] = 0;
while (!q.empty()) {
w = -q.top().fi;
x = q.top().se;
q.pop();
if (arr[x][o] != w) continue;
for (auto e : veze[x]) {
y = e.fi;
w2 = w + e.se;
if (arr[y][o] != -1 && arr[y][o] <= w2) continue;
arr[y][o] = w2;
q.push({-w2, y});
}
}
}
void tramvaj(ll root, int o) {
queue <ll> q;
q.push(root);
trm[root][o] = 1;
while (!q.empty()) {
x = q.front();
q.pop();
for (auto e : veze[x]) {
if (arr[e.fi][o] + e.se != arr[x][o]) continue;
if (trm[e.fi][o]) continue;
trm[e.fi][o] = 1;
q.push(e.fi);
}
}
}
int main() {
ios_base::sync_with_stdio(0);
cin.tie(0);
cin >> n >> m;
cin >> s >> t >> u >> v;
memset(dis, -1, sizeof(dis));
memset(arr, -1, sizeof(arr));
for (ll i = 0; i < m; i++) {
cin >> x >> y >> w;
veze[x].push_back({y, w});
veze[y].push_back({x, w});
}
distance(u, 0);
distance(v, 1);
bfs(s, 0);
bfs(t, 1);
tramvaj(t, 0);
tramvaj(s, 1);
ll rez = 1e18;
for (int i = 0; i < 2; i++) {
for (ll j = 1; j <= n; j++) {
if (!trm[j][i]) continue;
sol[j][0] = dis[j][0];
sol[j][1] = dis[j][1];
}
for (int j = 1; j <= n; j++) q.push({-sol[j][0], j});
while (!q.empty()) {
w = -q.top().fi;
x = q.top().se;
q.pop();
if (w != sol[x][0]) continue;
for (auto e : veze[x]) {
if (arr[e.fi][i] != arr[x][i] + e.se) continue;
if (sol[x][0] >= sol[e.fi][0]) continue;
sol[e.fi][0] = sol[x][0];
q.push({sol[e.fi][0], e.fi});
}
}
for (int j = 1; j <= n; j++) q.push({-sol[j][1], j});
while (!q.empty()) {
w = -q.top().fi;
x = q.top().se;
q.pop();
if (w != sol[x][1]) continue;
for (auto e : veze[x]) {
if (arr[e.fi][1 - i] != arr[x][1 - i] + e.se) continue;
if (sol[x][1] >= sol[e.fi][1]) continue;
sol[e.fi][1] = sol[x][1];
q.push({sol[e.fi][1], e.fi});
}
}
// cout << rez << " || ";
rez = min(rez, dis[v][0]);
// cout << rez << " || ";
for (ll j = 1; j <= n; j++) {
if (!trm[j][i]) continue;
// cout << j << " j " << sol[j][0] + sol[j][1] << " | ";
//
rez = min(rez, sol[j][0] + sol[j][1]);
// cout << rez << " | ";
}
// cout << "\n";
// cout << "___________________________________________\n";
// cout << rez << "\n";
//
// cout << "U dis[" << u << "] = "; for (ll j = 1; j <= n; j++) cout << dis[j][0] << " "; cout << "\n";
// cout << "V dis[" << v << "] = "; for (ll j = 1; j <= n; j++) cout << dis[j][1] << " "; cout << "\n";
// cout << "\n";
//
// cout << "bfs -> "; for (ll j = 1; j <= n; j++) cout << arr[j][i] << " "; cout << "\n";
// cout << "trm -> "; for (ll j = 1; j <= n; j++) cout << trm[j][i] << " "; cout << "\n";
// cout << "\n";
//
// cout << "0 sol -> "; for (ll j = 1; j <= n; j++) cout << sol[j][0] << " "; cout << "\n";
// cout << "1 sol -> "; for (ll j = 1; j <= n; j++) cout << sol[j][1] << " "; cout << "\n";
// cout << "\n";
//
// cout << "___________________________________________\n";
}
cout << rez << "\n";
return 0;
}
