#include <bits/stdc++.h>
using namespace std;
#define rep(i, a, b) for(int i = (a); i < (b); i++)
#define pb push_back
#define fi first
#define se second
using ll = long long;
using ld = long double;
using pii = pair<ll, ll>;
const int MAXN = 1e5 + 5;
const ll inf = 1e18 + 5;
int n, m, s, t, u, v, perm[MAXN];
vector<pii> adj[MAXN];
set<pii> marked;
bool vis1[MAXN], vis2[MAXN];
ll dis1[MAXN], dis2[MAXN], disu[MAXN], disv[MAXN], low1[MAXN], low2[MAXN];
ll dfs1(int i){
if(vis1[i]) return low1[i];
low1[i] = disv[i];
vis1[i] = 1;
for(auto [j, d]: adj[i]){
if(dis1[i] + d + dis2[j] == dis1[t])
low1[i] = min(low1[i], dfs1(j));
}
return low1[i];
}
ll dfs2(int i){
if(vis2[i]) return low2[i];
low2[i] = disv[i];
vis2[i] = 1;
for(auto [j, d]: adj[i]){
if(dis2[i] + d + dis1[j] == dis1[t])
low2[i] = min(low2[i], dfs2(j));
}
return low2[i];
}
int main(){
ios_base::sync_with_stdio(false);
cin.tie(0);
cin >> n >> m >> s >> t >> u >> v;
s--; t--; u--; v--;
rep(i, 0, m){
int a, b, c;
cin >> a >> b >> c;
a--; b--;
adj[a].pb({b, c});
adj[b].pb({a, c});
}
priority_queue<pii, vector<pii>, greater<pii>> pq;
fill(dis1, dis1 + n, inf);
dis1[s] = 0;
pq.push({0, s});
while(!pq.empty()){
auto [d, cur] = pq.top();
pq.pop();
if(d > dis1[cur]) continue;
for(auto [i, d2]: adj[cur]){
if(d + d2 < dis1[i]){
pq.push({d + d2, i});
dis1[i] = d + d2;
}
}
}
fill(dis2, dis2 + n, inf);
dis2[t] = 0;
pq.push({0, t});
while(!pq.empty()){
auto [d, cur] = pq.top();
pq.pop();
if(d > dis2[cur]) continue;
for(auto [i, d2]: adj[cur]){
if(d + d2 < dis2[i]){
pq.push({d + d2, i});
dis2[i] = d + d2;
}
}
}
fill(disu, disu + n, inf);
disu[u] = 0;
pq.push({0, u});
while(!pq.empty()){
auto [d, cur] = pq.top();
pq.pop();
if(d > disu[cur]) continue;
for(auto [i, d2]: adj[cur]){
if(d + d2 < disu[i]){
pq.push({d + d2, i});
disu[i] = d + d2;
}
}
}
fill(disv, disv + n, inf);
disv[v] = 0;
pq.push({0, v});
while(!pq.empty()){
auto [d, cur] = pq.top();
pq.pop();
if(d > disv[cur]) continue;
for(auto [i, d2]: adj[cur]){
if(d + d2 < disv[i]){
pq.push({d + d2, i});
disv[i] = d + d2;
}
}
}
ll res = inf;
rep(i, 0, n){
res = min(res, dfs1(i) + disu[i]);
res = min(res, dfs2(i) + disu[i]);
}
cout << res << "\n";
return 0;
}
