#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef pair<int, int> pii;
#define sep ' '
#define fastIO ios_base::sync_with_stdio(0);cin.tie(0);cout.tie(0);
#define F first
#define S second
const int N = 1e5+100;
const ll LLINF = 2e18;
int n, m, s, t, X, Y;
struct edge {
int w, st, fn;
edge() {
w = st = fn = 1;
}
};
edge Edge(int u, int v, int w) {
edge e;
e.st = u, e.fn = v, e.w = w;
return e;
}
struct cmp {
bool operator()(const pair<long long, edge>& lhs, const pair<long long, edge>& rhs) const {
if (lhs.first != rhs.first) return lhs.first < rhs.first;
if (lhs.S.w != rhs.S.w) return lhs.S.w < rhs.S.w;
if (lhs.S.st != rhs.S.st) return lhs.S.st < rhs.S.st;
return lhs.S.fn < rhs.S.fn;
}
};
vector<edge> adj[N], adj2[N], adj3[N], g1[N], g2[N];
ll dis[N];
int cnt = 10;
void dfs1(int v) {
for(edge e: adj2[v]) {
dfs1(e.fn);
e.w = 0;
g1[e.st].push_back(e);
swap(e.st, e.fn);
g2[e.st].push_back(e);
}
}
signed main() {
fastIO;
cin >> n >> m;
cin >> s >> t;
cin >> X >> Y;
s--, t--, X--, Y--;
for(int i = 0 ; i < m ; i ++) {
int u, v, w;
cin >> u >> v >> w;
u--, v--;
adj[v].push_back(Edge(v, u, w));
adj[u].push_back(Edge(u, v, w));
}
set<pair<ll, edge>, cmp> q;
fill(dis, dis+n, LLINF);
dis[s] = 0;
for(edge e: adj[s])
q.insert({e.w, e});
while(q.size()) {
auto [x, k] = *q.begin();
q.erase(q.begin());
if (dis[k.fn] != LLINF) {
if (dis[k.fn] == x) adj2[k.fn].push_back(Edge(k.fn, k.st, k.w));
continue;
}
dis[k.fn] = x;
adj2[k.fn].push_back(Edge(k.fn, k.st, k.w));
for(edge e: adj[k.fn])
q.insert({0ll+x+e.w, e});
}
dfs1(t);
for(int i = 0 ; i < n ; i ++) {
adj3[i].clear();
for(edge e: adj[i]) adj3[i].push_back(e);
for(edge e: g1[i]) adj3[i].push_back(e);
}
fill(dis, dis+n, LLINF);
dis[X] = 0;
for(edge e: adj3[X])
q.insert({e.w, e});
while(q.size()) {
auto [x, k] = *q.begin();
q.erase(q.begin());
if (dis[k.fn] != LLINF) continue;
dis[k.fn] = x;
for(edge e: adj3[k.fn])
q.insert({0ll+x+e.w, e});
}
long long ans = dis[Y];
for(int i = 0 ; i < n ; i ++) {
adj3[i].clear();
for(edge e: adj[i]) adj3[i].push_back(e);
for(edge e: g2[i]) adj3[i].push_back(e);
}
fill(dis, dis+n, LLINF);
dis[X] = 0;
for(edge e: adj3[X])
q.insert({e.w, e});
while(q.size()) {
auto [x, k] = *q.begin();
q.erase(q.begin());
if (dis[k.fn] != LLINF) continue;
dis[k.fn] = x;
for(edge e: adj3[k.fn])
q.insert({0ll+x+e.w, e});
}
ans = min(ans, dis[Y]);
cout << ans << endl;
return 0;
}
