#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using pii = pair<ll, ll>;
#define FOR(i, a, b) for (ll i = a; i < (b); i++)
#define F0R(i, a) for (ll i = 0; i < (a); i++)
#define F0R1(i, a) for (ll i = 1; i <= (a); i++)
#define FORd(i, a, b) for (ll i = (b)-1; i >= a; i--)
#define F0Rd(i, a) for (ll i = (a)-1; i >= 0; i--)
#define F0Rd1(i, a) for (ll i = a; i > 0; i--)
#define SORT(vec) sort(vec.begin(), vec.end())
#define S0RT(arr, n) sort(arr, arr + n)
#define pA first
#define pB second
#define MOD 1000000007
#define nl "\n"
#define pb push_back
ll n, m, s, t, u, v;
class cmp {
public:
bool operator()(vector<ll> a, vector<ll> b) { return a[1] > b[1]; }
};
ll dist[100000];
vector<pii> adj[100000];
bool inPass[100000];
unordered_set<ll> prevs[100000];
void dijkstra(ll root) { // traceback
for (ll i = 0; i < n; i++) {
dist[i] = 1e18;
}
dist[root] = 0;
priority_queue<vector<ll>, vector<vector<ll>>, cmp> nodes;
nodes.push({root, 0, -1});
while (!nodes.empty()) {
ll node = nodes.top()[0];
ll minDist = nodes.top()[1];
ll parent = nodes.top()[2];
nodes.pop();
if (node == t) {
return;
}
if (minDist != dist[node]) {
continue;
}
for (pii i : adj[node]) {
ll neighbor = i.pA;
ll length = i.pB;
if (dist[node] + length < dist[neighbor]) {
dist[neighbor] = dist[node] + length;
nodes.push({neighbor, dist[neighbor], node});
prevs[neighbor].insert(node);
} else if (dist[node] + length == dist[neighbor]) {
prevs[neighbor].insert(node);
}
}
}
}
bool vis[100000];
void dfs(ll node) {
inPass[node] = true;
vis[node] = true;
for (ll i : prevs[node]) {
if (!vis[i]) {
dfs(i);
}
}
}
ll distU[100000];
ll dijkstraU(ll root) { // traceback
for (ll i = 0; i < n; i++) {
distU[i] = 1e18;
}
distU[root] = 0;
priority_queue<vector<ll>, vector<vector<ll>>, cmp> nodes;
nodes.push({root, 0, -1});
ll dist1 = -1;
while (!nodes.empty()) {
ll node = nodes.top()[0];
ll minDist = nodes.top()[1];
ll parent = nodes.top()[2];
nodes.pop();
if (inPass[node] && dist1 == -1) {
minDist = dist1;
}
if (minDist != distU[node]) {
continue;
}
for (pii i : adj[node]) {
ll neighbor = i.pA;
ll length = i.pB;
if (distU[node] + length < distU[neighbor]) {
distU[neighbor] = distU[node] + length;
nodes.push({neighbor, distU[neighbor], node});
}
}
}
return (dist1 == -1) ? 1e18 : dist1;
}
ll distV[100000];
ll dijkstraV(ll root) { // traceback
for (ll i = 0; i < n; i++) {
distV[i] = 1e18;
}
distV[root] = 0;
priority_queue<vector<ll>, vector<vector<ll>>, cmp> nodes;
nodes.push({root, 0, -1});
ll dist1 = -1;
while (!nodes.empty()) {
ll node = nodes.top()[0];
ll minDist = nodes.top()[1];
ll parent = nodes.top()[2];
nodes.pop();
if (inPass[node] && dist1 == -1) {
minDist = dist1;
}
if (minDist != distV[node]) {
continue;
}
for (pii i : adj[node]) {
ll neighbor = i.pA;
ll length = i.pB;
if (distV[node] + length < distV[neighbor]) {
distV[neighbor] = distV[node] + length;
nodes.push({neighbor, distV[neighbor], node});
}
}
}
return (dist1 == -1) ? 1e18 : dist1;
}
int main() {
ios_base::sync_with_stdio(0);
cin.tie(0);
cin >> n >> m >> s >> t >> u >> v;
s--;
t--;
u--;
v--;
// go through and mark every node in shortest paths from S to T as part of the shortest path, since
// you'll never use more than 1 distinct shortest path going from U to V, as when you switch from one
// shortest path to another you're simply creating a new shortest path
for (ll i = 0; i < m; i++) {
ll a, b, c;
cin >> a >> b >> c;
a--;
b--;
adj[a].pb(pii(b, c));
adj[b].pb(pii(a, c));
}
dijkstra(s);
dfs(t);
cout << min(dijkstraU(u) + dijkstraV(v), distU[v]) << nl;
}
