#include <bits/stdc++.h>
#define ff first
#define ss second
#define pb push_back
#define mp make_pair
using namespace std;
typedef long long ll;
typedef unsigned long long ull;
typedef long double ld;
typedef pair<ll, ll> pll;
typedef pair<ull, ull> pull;
typedef pair<int, int> pii;
typedef pair<ld, ld> pld;
const ll inf = 1e18 + 7;
ll n, m;
ll s, t;
ll u, v;
vector<pll> g[100009];
vector<ll> tree[100009];
ll diss[100009];
ll dist[100009];
ll disu[100009];
ll disv[100009];
ll ans;
void dijk(ll beg, ll dis[], ll calctree, ll umin[], ll vmin[], ll bothmin[]){
for(ll i = 1; i <= n; ++i){
dis[i] = inf;
if(calctree)
umin[i] = vmin[i] = bothmin[i] = inf;
}
dis[beg] = 0;
if(calctree){
umin[beg] = disu[beg];
vmin[beg] = disv[beg];
bothmin[beg] = disu[beg]+disv[beg];
}
priority_queue<pll, vector<pll>, greater<pll>> pq;
pq.push({dis[beg], beg});
while(pq.size()){
ll v = pq.top().ss;
ll d = pq.top().ff;
pq.pop();
if(dis[v] < d) continue;
for(auto u : g[v]){
if(calctree && d+u.ss <= dis[u.ff]){
umin[u.ff] = min(disu[u.ff], umin[v]);
vmin[u.ff] = min(disv[u.ff], vmin[v]);
bothmin[u.ff] = min({disu[u.ff]+vmin[u.ff],disv[u.ff]+umin[u.ff],bothmin[v]});
tree[u.ff].pb(v);
}
if(d+u.ss < dis[u.ff]){
dis[u.ff] = d+u.ss;
pq.push({dis[u.ff], u.ff});
}
}
}
}
ll um1[100009], vm1[100009], bm1[100009];
ll um2[100009], vm2[100009], bm2[100009];
ll clear[100009];
void dfs(ll v){
clear[v] = 1;
for(auto u : tree[v])
if(!clear[u])
dfs(u);
}
int main() {
ios_base::sync_with_stdio(false);
cin.tie(nullptr);
//freopen("in.txt", "r", stdin);
//freopen("out.txt", "w", stdout);
cin >> n >> m;
cin >> s >> t;
cin >> u >> v;
while(m--){
ll x, y, z;
cin >> x >> y >> z;
g[x].pb({y, z});
g[y].pb({x, z});
}
ll empty[1];
dijk(u, disu, 0, empty, empty, empty);
dijk(v, disv, 0, empty, empty, empty);
dijk(s, diss, 1, vm1, um1, bm1);
for(ll i = 1; i <= n; ++i) tree[i].clear();
dijk(t, dist, 1, vm2, um2, bm2);
dfs(s);
ans = disu[v];
for(ll i = 1; i <= n; ++i){
if(clear[i] == 0) continue;
ans = min({ans, bm1[i], bm2[i], vm1[i]+um2[i], um1[i]+vm2[i]});
}
cout << ans;
}
