#include<bits/stdc++.h>
using namespace std;
#define int long long
vector<pair<int, int>> adj[200100];
int dist[3][200100], dp[2][200100];
bitset<200100> vis;
void djikstra(int start, int ind) {
memset(dist[ind], 15, sizeof dist[ind]);
priority_queue<pair<int, int>, vector<pair<int, int>>, greater<pair<int, int>>> pq;
pq.push({0,start});
dist[ind][start] = 0;
while(pq.size()) {
int x = pq.top().second, y = dist[ind][x];
pq.pop();
if(vis[x]) continue;
vis[x] = 1;
for(auto [to,weight]: adj[x])
if(y+weight < dist[ind][to])
pq.push({dist[ind][to]=y+weight,to});
}
vis.reset();
}
int ans;
void dfs(int n) {
vis[n] = 1;
dp[0][n] = dist[0][n];
dp[1][n] = dist[1][n];
for (auto [to, weight]: adj[n]) {
if (dist[2][n] - weight != dist[2][to]) continue;
if (!vis[to]) dfs(to);
dp[0][n] = min(dp[0][n], dp[0][to]);
dp[1][n] = min(dp[1][n], dp[1][to]);
}
ans = min(ans, min(dp[0][n] + dist[1][n], dp[1][n] + dist[0][n]));
}
signed main() {
cin.sync_with_stdio(false);
cin.tie(nullptr);
int n, m, s, t, u, v;
cin >> n >> m >> s >> t >> u >> v;
while(m--) {
int a, b, c;
cin >> a >> b >> c;
adj[a].push_back({b,c});
adj[b].push_back({a,c});
}
djikstra(u,0);
djikstra(v,1);
djikstra(s,2);
ans = dist[0][v];
dfs(t);
cout << ans << '\n';
}
