#include <bits/stdc++.h>
#define fi first
#define se second
#define all(r) (r).begin(), (r).end()
#define MASK(i) (1 << (i))
#define BIT(x, i) ((x) >> (i) & 1)
#define ll long long
#define pb push_back
#define TASK "task"
using namespace std;
template <typename T1, typename T2> bool minimize(T1 &a, T2 b){ if (a > b) {a = b; return true;} return false;}
template <typename T1, typename T2> bool maximize(T1 &a, T2 b){if (a < b) {a = b; return true;} return false;}
const int oo = 1e9 + 7;
const ll loo = (ll)1e18 + 7;
const int LOG = 18;
const int BASE = 323;
const int N = 1e5 + 7;
int n, m, s, t, u, v;
ll du[N], dv[N], ds[N], dp[2][N], ans;
vector<pair<int, int> > g[N];
void dijkstra1(int start, ll arr[]){
priority_queue<pair<ll, ll>, vector<pair<ll, ll>>, greater<pair<ll, ll>> > kew;
kew.push({0, start});
for (int i = 1; i <= n; i++) arr[i] = loo;
arr[start] = 0;
while (!kew.empty()){
auto k = kew.top();
kew.pop();
if (arr[k.se] < k.fi) continue;
for (auto u : g[k.se]){
if (u.se + k.fi < arr[u.fi]){
arr[u.fi] = u.se + k.fi;
kew.push({arr[u.fi], u.fi});
}
}
}
}
void dijkstra2(int start, int end){
fill(dp[0], dp[0] + N - 1, loo);
fill(dp[1], dp[1] + N - 1, loo);
fill(ds, ds + N - 1, loo);
priority_queue<pair<ll, ll>, vector<pair<ll, ll> >, greater<pair<ll, ll>> > kew;
kew.push({0, start});
dp[0][start] = du[start];
dp[1][start] = dv[start];
while (!kew.empty()){
auto k = kew.top();
kew.pop();
if (ds[k.se] < k.fi) continue;
for (auto u : g[k.se]){
if (u.se + k.fi < ds[u.fi]){
ds[u.fi] = u.se + k.fi;
dp[0][u.fi] = min(du[u.fi], dp[0][k.se]);
dp[1][u.fi] = min(dv[u.fi], dp[1][k.se]);
kew.push({ds[u.fi], u.fi});
}
else if (u.se + k.fi == ds[u.fi]){
if (min(du[u.fi], dp[0][k.se]) + min(dv[u.fi], dp[1][k.se]) <= dp[0][u.fi] + dp[1][u.fi]){
dp[0][u.fi] = min(du[u.fi], dp[0][k.se]);
dp[1][u.fi] = min(dv[u.fi], dp[1][k.se]);
}
}
}
}
minimize(ans, dp[0][end] + dp[1][end]);
}
int main(){
ios_base::sync_with_stdio(0); cin.tie(0);
// freopen(TASK".inp", "r", stdin);
// freopen(TASK".out", "w", stdout);
cin >> n >> m >> s >> t >> u >> v;
for (int i = 1; i <= m; i++){
int a, b, c; cin >> a >> b >> c;
g[a].pb({b, c});
g[b].pb({a, c});
}
dijkstra1(u, du);
dijkstra1(v, dv);
ans = du[v];
dijkstra2(s, t);
dijkstra2(t, s);
// for (int i = 1; i <= n; i++){
// cout << du[i] << " " << dv[i] << " " << ds[i] << "\n";
// }
cout << ans;
return 0;
}
