#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef vector<int> vi;
typedef vector<pair<int, int>> vii;
typedef pair<int, int> pi;
#define MOD 1000000007LL
int N, M, S, T, U, V;
vector<pair<int, ll>> adj[100001];
ll disu[100001], disv[100001], diss[100001];
bool vis[100001];
bool indag[100001]={false};
ll dpu[100001], dpv[100001]; // shortest path from u/v to node in dag (where edges are 0 in dag --> cascade)
void dij(int s, ll (&dis)[100001]) {
memset(vis, 0, sizeof(vis));
for (int i = 1; i <= N; i++) dis[i] = 1e18;
dis[s] = 0;
using T = pair<ll, ll>; priority_queue<T, vector<T>, greater<T>> q;
q.push({0, s});
while (!q.empty()) {
int v = q.top().second; q.pop();
if (vis[v]) continue;
vis[v] = true;
for (auto pp : adj[v]) {
ll u = pp.first, w = pp.second;
if (dis[v]+w < dis[u]) {
dis[u] = dis[v]+w;
q.push({dis[u], u});
}
}
}
}
void cdag(int v) {
if (indag[v]) return;
indag[v] = true;
for (auto pp : adj[v]) {
ll u = pp.first, w = pp.second;
if (diss[u]+w == diss[v]) cdag(u);
}
}
// starting from S to T
ll rdpu(int v) {
if (dpu[v] != -1) return dpu[v];
ll res = disu[v];
for (auto pp : adj[v]) {
ll u = pp.first, w = pp.second;
if (indag[u] && diss[u]+w == diss[v]) res = min(res, rdpu(u));
}
return dpu[v] = res;
}
// starting from T to S
ll rdpv(int v) {
if (dpv[v] != -1) return dpv[v];
ll res = disv[v];
for (auto pp : adj[v]) {
ll u = pp.first, w = pp.second;
if (indag[u] && diss[v]+w == diss[u]) res = min(res, rdpv(u));
}
return dpv[v] = res;
}
int main() {
//freopen("feast.in", "r", stdin);
//freopen("feast.out", "w", stdout);
//ios_base::sync_with_stdio(false);
//cin.tie(0);
cin >> N >> M >> S >> T >> U >> V;
for (int i = 0; i < M; i++) {
int a, b, c; cin >> a >> b >> c;
adj[a].push_back({b, c});
adj[b].push_back({a, c});
}
dij(U, disu); dij(V, disv); dij(S, diss);
//cout << "Debugging dijkstras" << endl;
//for (int i = 1; i <= N; i++) cout << disu[i] << " "; cout << endl;
//for (int i = 1; i <= N; i++) cout << disv[i] << " "; cout << endl;
//for (int i = 1; i <= N; i++) cout << diss[i] << " "; cout << endl;
cdag(T);
//cout << "Debugging nodes in dag" << endl;
//for (int i = 1; i <= N; i++) cout << indag[i] << " "; cout << endl;
for (int i = 1; i <= N; i++) {
if (indag[i]) {
dpu[i] = -1; //disu[i];
dpv[i] = -1; //disv[i];
} else {
dpu[i] = 1e18;
dpv[i] = 1e18;
}
}
// first case: U is closer to S
rdpu(T); rdpv(S);
//cout << "Debugging dps" << endl;
//for (int i = 1; i <= N; i++) cout << dpu[i] << " "; cout << endl;
//for (int i = 1; i <= N; i++) cout << dpv[i] << " "; cout << endl;
ll ans = disu[V];
for (int i = 1; i <= N; i++)
if (indag[i]) ans = min(ans, dpu[i]+dpv[i]);
// second case: U is closer to T
for (int i = 1; i <= N; i++) {
if (indag[i]) {
dpv[i] = -1;
dpu[i] = -1;
} else {
dpv[i] = 1e18;
dpu[i] = 1e18;
}
}
swap(disu, disv);
rdpu(T); rdpv(S);
for (int i = 1; i <= N; i++)
if (indag[i]) ans = min(ans, dpu[i]+dpv[i]);
//cout << "Debugging dps2" << endl;
//for (int i = 1; i <= N; i++) cout << dpu[i] << " "; cout << endl;
//for (int i = 1; i <= N; i++) cout << dpv[i] << " "; cout << endl;
cout << ans << endl;
}
