#include <bits/stdc++.h>
using namespace std;
#pragma GCC optimize ("trapv")
typedef long long ll;
const ll inf = 1e18;
const int MAXN = 1e5 + 25;
vector <pair <ll, ll>> adj[MAXN];
int n, m, s, t, u, v;
vector <int> adj2[MAXN];
ll dist[MAXN], dist2[MAXN];
ll dp[MAXN][2];
ll ans (int pos, int c) {
ll &ret = dp[pos][c];
if (ret != -1) return ret;
if (c == 0) {
ret = dist[pos] + ans(pos, 1);
ll mn = inf;
for (auto j : adj2[pos]) mn = min(mn, ans(j, 0));
ret = min(ret, mn);
} else {
ret = dist2[pos];
ll mn = inf;
for (auto j : adj2[pos]) mn = min(mn, ans(j, 1));
ret = min(ret, mn);
}
return ret;
}
ll ans2 (int pos, int c) {
ll &ret = dp[pos][c];
if (ret != -1) return ret;
if (c == 0) {
ret = dist2[pos] + ans2(pos, 1);
ll mn = inf;
for (auto j : adj2[pos]) mn = min(mn, ans2(j, 0));
ret = min(ret, mn);
} else {
ret = dist[pos];
ll mn = inf;
for (auto j : adj2[pos]) mn = min(mn, ans2(j, 1));
ret = min(ret, mn);
}
return ret;
}
int main () {
ios::sync_with_stdio(0); cin.tie(0);
cin >> n >> m >> s >> t >> u >> v;
for (int i = 1; i <= m; i++) {
int a, b, c;
cin >> a >> b >> c;
adj[a].push_back({b, c});
adj[b].push_back({a, c});
}
for (int i = 1; i <= n; i++) dist[i] = inf;
dist[s] = 0;
priority_queue <pair <ll, ll>, vector <pair <ll, ll>>, greater <>> pq;
pq.push({0, s});
while (!pq.empty()) {
auto k = pq.top();
pq.pop();
if (k.first > dist[k.second]) continue;
for (auto j : adj[k.second]) {
if (j.second + k.first < dist[j.first]) {
dist[j.first] = k.first + j.second;
pq.push({dist[j.first], j.first});
}
}
}
for (int i = 1; i <= n; i++) dist2[i] = inf;
dist2[t] = 0;
pq.push({0, t});
while (!pq.empty()) {
auto k = pq.top();
pq.pop();
if (k.first > dist2[k.second]) continue;
for (auto j : adj[k.second]) {
if (j.second + k.first < dist2[j.first]) {
dist2[j.first] = k.first + j.second;
pq.push({dist2[j.first], j.first});
}
}
}
for (int i = 1; i <= n; i++) {
for (auto j : adj[i]) {
if (dist[i] + j.second == dist[j.first] && dist2[i] == dist2[j.first] + j.second && dist[i] + dist2[j.first] + j.second == dist[t]) {
adj2[i].push_back(j.first);
}
}
}
for (int i = 1; i <= n; i++) dist[i] = dist2[i] = inf;
dist[u] = 0;
pq.push({0, u});
while (!pq.empty()) {
auto k = pq.top();
pq.pop();
if (k.first > dist[k.second]) continue;
for (auto j : adj[k.second]) {
if (j.second + k.first < dist[j.first]) {
dist[j.first] = k.first + j.second;
pq.push({dist[j.first], j.first});
}
}
}
dist2[v] = 0;
pq.push({0, v});
while (!pq.empty()) {
auto k = pq.top();
pq.pop();
if (k.first > dist2[k.second]) continue;
for (auto j : adj[k.second]) {
if (j.second + k.first < dist2[j.first]) {
dist2[j.first] = k.first + j.second;
pq.push({dist2[j.first], j.first});
}
}
}
memset(dp, -1, sizeof(dp));
ll mn = inf;
for (int i = 1; i <= n; i++) mn = min(mn, ans(i, 0));
ll mn2 = inf;
memset(dp, -1, sizeof(dp));
for (int i = 1; i <= n; i++) mn2 = min(mn2, ans2(i, 0));
cout << min({dist[v], mn2, mn}) << '\n';
}
