#include <bits/stdc++.h>
//#include <bits/extc++.h>
//#include <ext/pb_ds/assoc_container.hpp> // Common file
//#include <ext/pb_ds/tree_policy.hpp> // Including tree_order_statistics_node_update
using namespace std;
//using namespace __gnu_pbds;
//template<typename T> using ordered_set = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
using ll = long long;
using pii = pair<int, int>;
using pll = pair<ll, ll>;
using ull = unsigned ll;
#define pb push_back
#define mp make_pair
#define eb emplace_back
#define all(x) (x).begin(),(x).end()
#define x first
#define y second
//const int MOD = 1e9 + 7;
const int MOD = 998244353;
const int dx[] = {0, 0, 1, -1};
const int dy[] = {1, -1, 0, 0};
const char dir[] = {'R', 'L', 'D', 'U'};
/*
int add(int a, int b){ //(a + b) % 1e9 + 7
a += b;
if(a < 0){
a += MOD;
}
if(a >= MOD){
a -= MOD;
}
return a;
}
int sub(int a, int b){
a -= b;
if(a < 0) a += MOD;
return a;
}
int mult(int a, int b){
return ((ll) a * b) % MOD;
}*/
void setIO() {
ios_base::sync_with_stdio(0);
cin.tie(0);
// freopen((s+".in").c_str(),"r",stdin);
// freopen((s+".text").c_str(),"w",stdout);
}
const int mxN = 100'000;
int n, m, s, t, u, v;
vector<pii> adj[mxN];
ll du[mxN], dv[mxN], ds[mxN];
ll dp[2][mxN];
ll ans;
void dijkstra(int src, ll dist[]){
for (int i = 0; i < n; ++i) dist[i] = LLONG_MAX;
using T = pair<ll,int>; priority_queue<T,vector<T>,greater<T>> pq;
dist[src] = 0;
pq.push({0, src});
while (pq.size()) {
ll cdist; int node; tie(cdist, node) = pq.top(); pq.pop();
if (cdist != dist[node]) continue;
for (pair<int, int> i : adj[node]) {
if (cdist+i.second < dist[i.first]) {
pq.push({dist[i.first] = cdist+i.second, i.first});
}
}
}
}
ll solve(int start, int end){
bool visited[mxN];
fill(visited, visited + mxN, false);
priority_queue<pair<ll, pii>, vector<pair<ll, pii>>, greater<pair<ll, pii>>> pq;
pq.push(mp(0, mp(start, 0)));
while (!pq.empty()) {
auto cur = pq.top(); pq.pop();
ll c = cur.x;
int node = cur.y.x;
int par = cur.y.y;
if (!visited[node]) {
ds[node] = c;
visited[node] = true;
dp[0][node] = min(dp[0][par], du[node]);
dp[1][node] = min(dp[1][par], dv[node]);
for (auto& i : adj[node]) pq.push({c + i.y, mp(i.x, node)});
} else {
if(c == ds[node] && min(du[node], dp[0][par]) + min(dv[node], dp[1][par]) <= dp[0][node] + dp[1][node]){
dp[0][node] = min(du[node], dp[0][par]);
dp[1][node] = min(dv[node], dp[1][par]);
}
}
}
return dp[0][end] + dp[1][end];
}
signed main(){
setIO();
//CHECK FOR LONG LONG!!!
//LONG LONG OVERFLOW??
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].eb(mp(b, c));
adj[b].eb(mp(a, c));
}
memset(dp, 0x3f, sizeof dp);
dijkstra(u, du);
dijkstra(v, dv);
ans = min(du[v], solve(s, t));
cout << ans << "\n";
//CHECK FOR LONG LONG!!!
}
