#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[]){
for(ll i = 1; i <= n; ++i){
dis[i] = inf;
}
dis[beg] = 0;
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(d+u.ss < dis[u.ff]){
dis[u.ff] = d+u.ss;
pq.push({dis[u.ff], u.ff});
}
}
}
ll vis[100009];
void calctree(ll beg, ll dis[], ll um[], ll vm[], ll bm[], ll addtree){
for(ll i = 1; i <= n; ++i){
um[i] = vm[i] = bm[i] = inf;
vis[i] = 0;
}
vis[beg] = 1;
um[beg] = disu[beg];
vm[beg] = disv[beg];
bm[beg] = um[beg]+vm[beg];
priority_queue<pll, vector<pll>, greater<pll>> pq;
pq.push({dis[beg], beg});
while(pq.size()){
ll v = pq.top().ss;
pq.pop();
for(auto u : g[v]){
if(dis[v]+u.ss != dis[u.ff]) continue;
um[u.ff] = min({disu[u.ff], um[v], um[u.ff]});
vm[u.ff] = min({disv[u.ff], vm[v], vm[u.ff]});
bm[u.ff] = min({disu[u.ff]+vm[u.ff],disv[u.ff]+um[u.ff],bm[v], bm[u.ff]});
if(addtree)
tree[u.ff].pb(v);
if(vis[u.ff] == 0){
vis[u.ff] = 1;
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);
dijk(v, disv);
dijk(s, diss);
calctree(s, diss, um1, vm1, bm1, 0);
dijk(t, dist);
calctree(t, dist, um2, vm2, bm2, 1);
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;
}
