#include<bits/stdc++.h>
#define IOS ios_base::sync_with_stdio(false);cin.tie();cout.tie();
#define all(x) x.begin(), x.end()
#define lnl long long
#define pii pair<int, int>
#define pq priority_queue
#define eb emplace_back
#define lb lower_bound
#define ub upper_bound
#define pb push_back
#define pp pop_back
#define F first
#define S second
using namespace std;
const lnl inf = INT_MAX;
int perm[100001];
int n, m, s, t, u, v;
lnl dis1[100001], dis2[100001];
lnl disu[100001], disv[100001];
lnl low1[100001], low2[100001];
bool vis1[100001], vis2[100001];
set<pii> marked;
vector<pii> adj[100001];
lnl 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];
}
lnl 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];
}
void solve () {
cin >> n >> m >> s >> t >> u >> v;
s--; t--; u--; v--;
for (int i = 0; i < m; i++) {
int a, b, c; cin >> a >> b >> c; a--; b--;
adj[a].pb({b, c}); adj[b].pb({a, c});
}
pq<pii, vector<pii>, greater<pii>> q;
fill(dis1, dis1 + n, inf);
dis1[s] = 0;
q.push({0, s});
while (!q.empty()) {
auto [d, cur] = q.top(); q.pop();
if (d > dis1[cur]) continue;
for (auto [i, d2]: adj[cur]) {
if (d + d2 < dis1[i]) {
q.push({d + d2, i});
dis1[i] = d + d2;
}
}
}
fill(dis2, dis2 + n, inf);
dis2[t] = 0;
q.push({0, t});
while(!q.empty()){
auto [d, cur] = q.top();
q.pop();
if (d > dis2[cur]) continue;
for (auto [i, d2]: adj[cur]) {
if (d + d2 < dis2[i]) {
q.push({d + d2, i});
dis2[i] = d + d2;
}
}
}
fill(disu, disu + n, inf);
disu[u] = 0;
q.push({0, u});
while(!q.empty()){
auto [d, cur] = q.top(); q.pop();
if (d > disu[cur]) continue;
for (auto [i, d2]: adj[cur]) {
if (d + d2 < disu[i]) {
q.push({d + d2, i});
disu[i] = d + d2;
}
}
}
fill(disv, disv + n, inf);
disv[v] = 0;
q.push({0, v});
while(!q.empty()){
auto [d, cur] = q.top(); q.pop();
if (d > disv[cur]) continue;
for (auto [i, d2]: adj[cur]) {
if (d + d2 < disv[i]) {
q.push({d + d2, i});
disv[i] = d + d2;
}
}
}
lnl res = inf;
for (int i = 0; i < n; i++) {
res = min(res, dfs1(i) + disu[i]);
res = min(res, dfs2(i) + disu[i]);
}
cout << res;
}
int main() {IOS solve(); return 0;}
