#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
#include <bits/stdc++.h>
#define fi first
#define se second
#define pb push_back
#define sz(a) (int)a.size()
#define all(a) a.begin(), a.end()
#define rall(a) a.rbegin(), a.rend()
#define ff(i,a,b) for(int i=a;i<=b;i++)
#define fb(i,b,a) for(int i=b;i>=a;i--)
using namespace std;
using namespace __gnu_pbds;
typedef long long ll;
typedef pair<ll,ll> pii;
const int maxn = 100005;
const ll inf = 1e18 + 5;
template<typename T>
using ordered_set = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
// os.order_of_key(k) the number of elements in the os less than k
// *os.find_by_order(k) print the k-th smallest number in os(0-based)
int n, m;
int S, T;
int A, B;
vector<pii> g[maxn];
// shortest path DAG graph za S do T
ll distS[maxn];
ll distT[maxn];
ll distA[maxn];
ll distB[maxn];
void dij(int s, ll dist[maxn]) {
ff(i,1,n)dist[i] = inf;
priority_queue<pii, vector<pii>, greater<pii>> pq;
pq.push({dist[s] = 0, s});
while(!pq.empty()) {
pii v = pq.top(); pq.pop();
if(dist[v.se] < v.fi)return;
for(auto c : g[v.se]) {
int u = c.fi;
ll w = c.se;
if(dist[u] > w + v.fi) {
pq.push({dist[u] = w + v.fi, u});
}
}
}
}
ll rez = inf;
ll dp[maxn];
bool visited[maxn];
void dfs(int v, bool dir){
visited[v] = 1;
dp[v] = distA[v];
for(auto c : g[v]){
int u = c.fi;
ll w = c.se;
if(dir == 0){
if(distS[v] + w + distT[u] == distS[T]){
if(!visited[u])dfs(u, dir);
dp[v] = min(dp[v], dp[u]);
}
}
else{
if(distT[v] + w + distS[u] == distT[S]){
if(!visited[u])dfs(u, dir);
dp[v] = min(dp[v], dp[u]);
}
}
}
rez = min(rez, dp[v] + distB[v]);
}
int main()
{
ios::sync_with_stdio(false);
cout.tie(nullptr);
cin.tie(nullptr);
cin >> n >> m >> S >> T >> A >> B;
ff(i,1,m) {
int u, v;
ll w;
cin >> u >> v >> w;
g[u].pb({v, w});
g[v].pb({u, w});
}
dij(S, distS);
dij(T, distT);
dij(A, distA);
dij(B, distB);
rez = distB[A];
dfs(S, 0);
ff(i,1,n)visited[i] = 0;
dfs(T, 1);
cout << rez << endl;
return 0;
}
/**
// probati bojenje sahovski ili slicno
**/
