#include <bits/stdc++.h>
/// #pragma GCC optimize ("Ofast")
/// #pragma GCC target ("avx2")
using namespace std;
using ll = long long;
using ii = pair<ll, ll>;
using vi = vector<int>;
using db = double;
#define ff first
#define ss second
#define pb push_back
#define all(x) x.begin(), x.end()
#define lb lower_bound
#define ub upper_bound
const ll INF = LONG_LONG_MAX / 2;
using pi = pair<ll, ii>;
ll n, m, s, t, u, v;
vector<array<ll, 2>> adj[100001];
ll disU[100001], disV[100001];
ll dp[2][100001], res;
void dijkstra(ll src, ll arr[]) {
for(ll l = 1; l <= n; l++) arr[l] = INF;
priority_queue<ii, vector<ii>, greater<ii>> pq;
arr[src] = 0; pq.push({0, src});
while(!pq.empty()) {
ll a = pq.top().ss; ll w = pq.top().ff; pq.pop();
if(arr[a] < w) continue;
for(auto e : adj[a]) {
ll len = e[1] + w; ll to = e[0];
if(arr[to] <= len) continue;
arr[to] = len; pq.push({len, to});
}
}
}
void dijkstra0() {
for(ll l = 0; l <= n; l++) dp[0][l] = dp[1][l] = INF;
priority_queue<pi, vector<pi>, greater<pi>> pq;
pq.push({0, {s, 0}}); vector<bool> vis(n + 1, 0);
vector<long long> dis(n + 1, INF);
while(!pq.empty()) {
ll a = pq.top().ss.ff, par = pq.top().ss.ss;
ll w = pq.top().ff; pq.pop();
if(!vis[a]) {
vis[a] = 1; dis[a] = w;
dp[0][a] = min(disU[a], dp[0][par]);
dp[1][a] = min(disV[a], dp[1][par]);
for(auto u : adj[a]) {
pq.push({u[1] + w, {u[0], a}});
}
}
else if(w == dis[a])
if(min(dp[0][par], disU[a]) + min(dp[1][par], disV[a]) <= dp[0][a] + dp[1][a]) {
dp[0][a] = min(disU[a], dp[0][par]);
dp[1][a] = min(disV[a], dp[1][par]);
}
}
res = min(res, dp[0][t] + dp[1][t]);
}
int32_t main() {
ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0);
cin >> n >> m >> s >> t >> u >> v;
for(ll l = 0; l < m; l++) {
ll x, y; ll w; cin >> x >> y >> w;
adj[x].pb({y, w}); adj[y].pb({x, w});
}
dijkstra(u, disU); dijkstra(v, disV);
res = disU[v]; dijkstra0();
swap(s, t); dijkstra0();
cout << res << "\n";
}
/**
8 8
5 7
6 8
1 2 2
2 3 3
3 4 4
1 4 1
1 5 5
2 6 6
3 7 7
4 8 8
**/
