#include <bits/stdc++.h>
using namespace std;
template<class A, class B> bool maximize(A& x, B y) {if (x < y) return x = y, true; else return false;}
template<class A, class B> bool minimize(A& x, B y) {if (x > y) return x = y, true; else return false;}
#define all(a) a.begin(), a.end()
#define pb push_back
#define pf push_front
#define fi first
#define se second
#define int long long
typedef long long ll;
typedef unsigned long long ull;
typedef double db;
typedef long double ld;
typedef pair<db, db> pdb;
typedef pair<ld, ld> pld;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
typedef pair<ll, int> plli;
typedef pair<int, ll> pill;
const int MAX_N = 1e5 + 5;
const ll inf = 1e18;
int n, m, S, T, U, V;
vector<pii> adj[MAX_N];
int distU[MAX_N], distV[MAX_N], distS[MAX_N], back[MAX_N];
int dp[MAX_N][2];
priority_queue<pii, vector<pii>, greater<pii>> pq;
int ans = inf;
void dijkstra1(int start, int *dist) {
for (int i = 1; i <= n; i++) {
dist[i] = inf;
}
dist[start] = 0;
pq.push({0, start});
while (!pq.empty()) {
int u = pq.top().se;
int currW = pq.top().fi;
pq.pop();
for (auto it : adj[u]) {
int v = it.fi;
int w = it.se;
if (currW + w < dist[v]) {
dist[v] = currW + w;
pq.push({dist[v], v});
}
}
}
}
void sol(int start, int end) {
for (int i = 1; i <= n; i++) {
dp[i][0] = dp[i][1] = distS[i] = inf;
}
distS[start] = 0;
dp[start][0] = distU[start];
dp[start][1] = distV[start];
pq.push({0, start});
while (!pq.empty()) {
int u = pq.top().se;
int currW = pq.top().fi;
pq.pop();
if (currW > distS[u]) {
continue;
}
for (auto it : adj[u]) {
int v = it.fi;
int w = it.se;
if (currW + w > distS[v]) {
continue;
}
if (currW + w == distS[v]) {
if (dp[v][0] + dp[v][1] > dp[u][0] + dp[u][1]) {
dp[v][0] = min(distU[v], dp[u][0]);
dp[v][1] = min(distV[v], dp[u][1]);
}
}
else {
distS[v] = currW + w;
pq.push({distS[v], v});
dp[v][0] = min(dp[u][0], distU[v]);
dp[v][1] = min(dp[u][1], distV[v]);
}
}
}
minimize(ans, dp[end][0] + dp[end][1]);
}
signed main() {
ios_base::sync_with_stdio(false);
cin.tie(nullptr);
cin >> n >> m >> S >> T >> U >> V;
for (int i = 1; i <= m; i++) {
int u, v, c;
cin >> u >> v >> c;
adj[u].pb({v, c});
adj[v].pb({u, c});
}
dijkstra1(U, distU);
dijkstra1(V, distV);
ans = distU[V];
sol(S, T);
sol(T, S);
cout << ans;
return 0;
}
/*
Tuesday, 24 October 2023
15:16:46
*/
