#include<iostream>
#include<vector>
#include<algorithm>
#include<set>
#include<map>
#include<queue>
#include<utility>
#define int long long
#define INF 1000000000000000000
#define pii pair<long long, long long>
using namespace std;
struct DS{
int a, b, c;
};
signed main() {
int n, m, s, t, u, v;
cin >> n >> m >> s >> t >> u >> v;
vector<vector<pii> >G(n+1);
vector<DS>routes;
int a, b, c;
while (m--) {
cin >> a >> b >> c;
G[a].push_back({b, c});
G[b].push_back({a, c});
routes.push_back({a, b, c});
}
vector<int>sdis(n+5, INF), tdis(n+5, INF), vdis(n+5, INF);
sdis[s] = 0;
set<pii>q; q.insert({0, s});
while (!q.empty()) {
auto tmp = *q.begin(); q.erase(q.begin());
int len = tmp.first, i = tmp.second;
//cout << i << " " << len << "\n";
if (len > sdis[i]) continue;
for (auto &j : G[i]) {
if (sdis[j.first] < len + j.second) continue;
if (sdis[j.first] != INF) {
q.erase({sdis[j.first], j.first});
}
sdis[j.first] = len + j.second;
q.insert({sdis[j.first], j.first});
}
}
tdis[t] = 0;
q.insert({0, t});
while (!q.empty()) {
auto tmp = *q.begin(); q.erase(q.begin());
int len = tmp.first, i = tmp.second;
//cout << i << " " << len << "\n";
if (len > tdis[i]) continue;
for (auto &j : G[i]) {
if (tdis[j.first] < len + j.second) continue;
if (tdis[j.first] != INF) {
q.erase({tdis[j.first], j.first});
}
tdis[j.first] = len + j.second;
q.insert({tdis[j.first], j.first});
}
}
int minroute = INF;
vector<int>onroute(n+1, 0);
for (int i = 1 ; i <= n ; i++) {
minroute = min(minroute, sdis[i] + tdis[i]);
}
for (int i = 1 ; i <= n ; i++) {
if (sdis[i] + tdis[i] == minroute) {
onroute[i] = 1;
}
}
if (s == u) {
vdis[v] = 0;
q.insert({0, v});
while (!q.empty()) {
auto tmp = *q.begin(); q.erase(q.begin());
int len = tmp.first, i = tmp.second;
//cout << i << " " << len << "\n";
if (len > vdis[i]) continue;
for (auto &j : G[i]) {
if (vdis[j.first] < len + j.second) continue;
if (vdis[j.first] != INF) {
q.erase({vdis[j.first], j.first});
}
vdis[j.first] = len + j.second;
q.insert({vdis[j.first], j.first});
}
}
int ans = INF;
for (int i = 1 ; i <= n ; i++) {
if (sdis[i] + tdis[i] == minroute) {
ans = min(ans, vdis[i]);
}
}
cout << ans << "\n";
} else {
for (auto &i : routes) {
if (onroute[i.a] && onroute[i.b]) {
i.c = 0;
}
}
for (int i = 1 ; i <= n ; i++) G[i].clear();
for (auto &i : routes) {
G[i.a].push_back({i.b, i.c});
G[i.b].push_back({i.a, i.c});
}
vdis[v] = 0;
q.insert({0, v});
while (!q.empty()) {
auto tmp = *q.begin(); q.erase(q.begin());
int len = tmp.first, i = tmp.second;
//cout << i << " " << len << "\n";
if (len > vdis[i]) continue;
for (auto &j : G[i]) {
if (vdis[j.first] <= len + j.second) continue;
if (vdis[j.first] != INF) {
q.erase({vdis[j.first], j.first});
}
vdis[j.first] = len + j.second;
q.insert({vdis[j.first], j.first});
}
}
cout << vdis[u] << "\n";
}
}
