#include <bits/stdc++.h>
using namespace std;
#define int long long
#define sp << ' ' <<
#define nl << '\n'
const int MAXN = 1e5, INF = 1e18;
vector<vector<pair<int, int>>> g(MAXN);
vector<int> distS(MAXN, INF), distT(MAXN, INF), distA(MAXN, INF), distB(MAXN, INF);
int n, m, s, t, a, b, x, y, z;
void dijkstra(int r, vector<int> &dist){
priority_queue<pair<int, int>> q;
dist[r] = 0;
q.emplace(0, r);
while(!q.empty()){
int u = q.top().second, d = -q.top().first; q.pop();
if(d != dist[u]) continue;
for(auto &e : g[u]){
int v = e.first, w = e.second;
if(dist[v] > d + w){
dist[v] = d + w;
q.emplace(-(d + w), v);
}
}
}
}
signed main(){
cin.tie(0)->sync_with_stdio(0);
cin >> n >> m >> s >> t >> a >> b;
--s, --t, --a, --b;
while(m--){
cin >> x >> y >> z; --x, --y;
g[x].emplace_back(y, z);
g[y].emplace_back(x, z);
}
dijkstra(s, distS);
dijkstra(t, distT);
dijkstra(a, distA);
dijkstra(b, distB);
int shortest = distS[t];
vector<array<int, 2>> dp(n, {INF, INF});
vector<pair<int, int>> onPath;
for(int i=0; i<n; ++i){
if(distS[i] + distT[i] == shortest) onPath.emplace_back(distS[i], i);
}
int ans = distA[b];
sort(onPath.begin(), onPath.end());
for(auto &i : onPath){
int u = i.second;
dp[u][0] = min(dp[u][0], distA[u]);
dp[u][1] = min(dp[u][1], distB[u]);
ans = min(ans, dp[u][0] + distB[u]);
ans = min(ans, dp[u][1] + distA[u]);
for(auto &e : g[u]){
int v = e.first, w = e.second;
dp[v][0] = min(dp[v][0], dp[u][0]);
dp[v][1] = min(dp[v][1], dp[u][1]);
}
}
cout << ans;
}
