#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef pair<ll, ll> pll;
vector<pll> adj[100001];
ll du[100001], dv[100001], ds[100001], dp[2][100001], ans;
bool visited[100001];
void dijkstra1(ll start, ll arr[]) {
fill(visited, visited + 100001, false);
priority_queue<pll> pq;
pq.push({0, start});
while (!pq.empty()) {
ll c, node;
tie(c, node) = pq.top();
pq.pop();
if (visited[node]) continue;
arr[node] = -c;
visited[node] = true;
for (auto &i : adj[node]) {
pq.push({c - i.second, i.first});
}
}
}
void dijkstra2(ll start, ll end) {
fill(dp[0], dp[0] + 100001, LLONG_MAX / 2);
fill(dp[1], dp[1] + 100001, LLONG_MAX / 2);
fill(visited, visited + 100001, false);
priority_queue<pair<ll, pll>> pq;
pq.push({0, {start, 0}});
dp[0][0] = dp[1][0] = LLONG_MAX / 2;
while (!pq.empty()) {
pair<ll, pll> curr = pq.top();
pq.pop();
ll c = curr.first;
pll p = curr.second;
ll node = p.first, par = p.second;
if (!visited[node]) {
visited[node] = true;
ds[node] = -c;
dp[0][node] = min(du[node], dp[0][par]);
dp[1][node] = min(dv[node], dp[1][par]);
for (auto i : adj[node]) {
pq.push({c - i.second, {i.first, node}});
}
} else if (-c == ds[node]) {
if (min(du[node], dp[0][par]) + min(dv[node], dp[1][par]) <=
dp[0][node] + dp[1][node]) {
dp[0][node] = min(du[node], dp[0][par]);
dp[1][node] = min(dv[node], dp[1][par]);
}
}
}
ans = min(ans, dp[0][end] + dp[1][end]);
}
int main() {
iostream::sync_with_stdio(false);
cin.tie(0);
ll n, m, s, t, u, v;
cin >> n >> m >> s >> t >> u >> v;
for (int i = 0; i < m; i++) {
ll a, b, c;
cin >> a >> b >> c;
adj[a].push_back({b, c}), adj[b].push_back({a, c});
}
dijkstra1(u, du), dijkstra1(v, dv);
ans = du[v];
dijkstra2(s, t), dijkstra2(t, s);
cout << ans << "\n";
return 0;
}
