#include<bits/stdc++.h>
using namespace std;
#define int long long
const int INF = LLONG_MAX / 2;
int n, m, s, t, u, v;
const int maxN = 1e5 + 5;
vector<pair<int, int>> G[maxN];
int du[maxN], dv[maxN], ds[maxN], ans;
int dp[2][maxN];
void dijkstra1(int s, int ds[]) {
fill(ds, ds+maxN, INF);
ds[s] = 0;
using T = pair<int, int>;
priority_queue<T, vector<T>, greater<T>> pq;
pq.push({0, s});
while(!pq.empty()) {
const auto [cdist, a] = pq.top(); pq.pop();
if(cdist != ds[a]) continue;
for(const auto &[b, w]: G[a]) {
if(ds[a] + w < ds[b]) {
pq.push({ds[b] = ds[a] + w, b});
}
}
}
}
void dijkstra2(int s, int e) {
fill(ds, ds+maxN, INF);
fill(dp[0], dp[0]+maxN, INF);
fill(dp[1], dp[1]+maxN, INF);
ds[s] = 0;
dp[0][s] = du[s], dp[1][s] = dv[s];
using T = pair<int, int>;
priority_queue<T, vector<T>, greater<T>> pq;
pq.push({0, s});
while(!pq.empty()) {
const auto [cdist, a] = pq.top(); pq.pop();
if(cdist != ds[a]) continue;
for(const auto &[b, w]: G[a]) {
int alt = ds[a] + w;
if(alt == ds[b]) {
if( min(dp[0][a], du[b]) + min(dp[1][a], dv[b]) <= dp[0][b] + dp[1][b] ) {
dp[0][b] = min(dp[0][a], du[b]);
dp[1][b] = min(dp[1][a], dv[b]);
}
} else if(alt < ds[b]) {
dp[0][b] = min(du[b], dp[0][a]);
dp[1][b] = min(dv[b], dp[1][a]);
pq.push({ds[b] = alt, b});
}
}
}
ans = min(ans, dp[0][e] + dp[1][e]);
}
void solve() {
cin >> n >> m >> s >> t >> u >> v;
for(int i=0; i<m; i++) {
int a, b, w;
cin >> a >> b >> w;
G[a].push_back({b, w});
G[b].push_back({a, w});
}
dijkstra1(u, du);
dijkstra1(v, dv);
ans = du[v];
dijkstra2(s, t);
dijkstra2(t, s);
cout << ans << "\n";
}
int32_t main() {
ios::sync_with_stdio(false);
cin.tie(nullptr);
cout.tie(nullptr);
cout << fixed << setprecision(10);
solve();
return 0;
}
