#pragma GCC optimize(3, "unroll-loops", "no-stack-protector")
#pragma GCC optimize("Ofast")
#pragma GCC optimize("03")
#pragma GCC target("avx,avx2,fma")
#pragma GCC optimize("03,fast-math")
#include<bits/stdc++.h>
#define en "\n"
#define s second
#define f first
#define fast_io ios_base::sync_with_stdio(false);cin.tie(NULL);cout.tie(NULL)
#define vi vector<int>
#define vii vector<pair<int,int>>
#define int long long
#define rall(x) x.rbegin(), x.rend()
#define pb push_back
#define loop(a) for(int i = 0; i < a; i++)
#define loopv(i,a) for (int i = 0; i < a; i++)
#define all(x) (x).begin(), (x).end())
#define prDouble(x) printf("%.8f", x)
#define goog(tno) printf("Case #%d: ", tno)
using namespace std;
const int INF = 1e17;
int n, m, s, t, u1, v1;
void solve() {
cin >> n >> m;
cin >> s >> t;
cin >> u1 >> v1;
vector <vector<pair<int,int>>> g(n+1);
for(int i=0; i<m; i++){
int from, to, cost;
cin>>from>>to>>cost;
g[from].pb({to, cost});
g[to].pb({from, cost});
}
vector<int> d (n+1, INF);
vector<pair<int,int>> p(n+1);
d[s] = 0;
set < pair<int,int> > q;
q.insert (make_pair (d[s], s));
while (!q.empty()) {
int v = q.begin()->second;
q.erase (q.begin());
for (size_t j=0; j<g[v].size(); ++j) {
int to = g[v][j].first,
len = g[v][j].second;
if (d[v] + len < d[to]) {
q.erase (make_pair (d[to], to));
d[to] = d[v] + len;
p[to] = {v, len};
q.insert (make_pair (d[to], to));
}
}
}
int tt = t;
while(tt!=s){
int f = p[tt].f, cost=p[tt].s;
// cout<<f<<" ";
for(int i=0; i<g[f].size(); i++){
if(g[f][i].f==tt and g[f][i].s==cost){
g[f][i].s=0;
break;
}
}
for(int i=0; i<g[tt].size(); i++){
if(g[tt][i].f==f and g[tt][i].s==cost){
g[tt][i].s=0;
break;
}
}
tt = f;
}
s = u1;
d.clear();
d.resize(n+1, INF);
// vector<int> d (n+1, INF);
p.clear();
p.resize(n+1);
// vector<pair<int,int>> p(n+1);
d[s] = 0;
// set < pair<int,int> > q;
q.insert (make_pair (d[s], s));
while (!q.empty()) {
int v = q.begin()->second;
q.erase (q.begin());
for (size_t j=0; j<g[v].size(); ++j) {
int to = g[v][j].first,
len = g[v][j].second;
if (d[v] + len < d[to]) {
q.erase (make_pair (d[to], to));
d[to] = d[v] + len;
p[to] = {v, len};
q.insert (make_pair (d[to], to));
}
}
}
cout<<d[v1];
}
signed main() {
fast_io;
int tc = 1;
while (tc--)
solve();
}
