#include<bits/stdc++.h>
using namespace std;
#define pi pair<int,int>
#define ll long long
#define pb push_back
#define pf push_front
void fileIO(string filename) {
freopen((filename + ".in").c_str(), "r", stdin);
freopen((filename + ".out").c_str(), "w", stdout);
}
vector<pi> adj[100001];
ll du[100001], dv[100001], ds[100001], dp[2][100001], ans;
void dijkstra(int u, ll d[]) {
fill(d, d + 100001, LLONG_MAX / 2);
priority_queue<pair<ll, int>> pq;
pq.push({d[u] = 0, u});
while(!pq.empty()) {
auto [cdist, u] = pq.top();
pq.pop();
cdist *= -1;
if(cdist > d[u]) continue;
for(const auto [v, w] : adj[u]) {
ll new_len = cdist + w;
if(new_len < d[v]) {
d[v] = new_len;
pq.push({-d[v], v});
}
}
}
}
void dijkstra2(int start, int end) {
fill(dp[0], dp[0] + 100001, LLONG_MAX / 2);
fill(dp[1], dp[1] + 100001, LLONG_MAX / 2);
fill(ds, ds + 100001, LLONG_MAX / 2);
priority_queue<pair<ll, pair<int, int>>> pq;
pq.push({0, {start, 0}});
while(!pq.empty()) {
ll cdist = pq.top().first;
auto [u, par] = pq.top().second;
pq.pop();
cdist *= -1;
if(cdist > ds[u]) continue;
if(ds[u] == LLONG_MAX / 2) {
ds[u] = cdist;
dp[0][u] = min(du[u], dp[0][par]);
dp[1][u] = min(dv[u], dp[1][par]);
for(const auto [v, w] : adj[u]) {
if(ds[u] + w <= ds[v]) pq.push({-(cdist + w), {v, u}});
}
}
else if(cdist == ds[u]) {
if (min(du[u], dp[0][par]) + min(dv[u], dp[1][par]) <=
dp[0][u] + dp[1][u]) {
dp[0][u] = min(du[u], dp[0][par]);
dp[1][u] = min(dv[u], dp[1][par]);
}
}
}
ans = min(ans, dp[0][end] + dp[1][end]);
}
int main()
{
cin.tie(0)->sync_with_stdio(false);
//fileIO("");
int n, m, s, t, u, v;
cin >> n >> m >> s >> t >> u >> v;
for(int i = 0; i < m; i++) {
int a, b, w;
cin >> a >> b >> w;
adj[a].pb({b, w});
adj[b].pb({a, w});
}
dijkstra(u, du);
dijkstra(v, dv);
ans = du[v];
dijkstra2(s, t);
dijkstra2(t, s);
cout << ans << '\n';
}
