#include <bits/stdc++.h>
using namespace std;
const int N = 1e6 + 5, MOD = 1e9 + 7;
const long long L = 1e18;
#define ll long long
#define fi first
#define se second
#define yes {cout << "YES";return;}
#define no {cout << "NO"; return;}
#define pb push_back
#define MASK(i) (1ll << (i))
#define BIT(i, s) ((1ll << (i)) & (s))
#define all(a) a.begin(), a.end()
int n, m, s, t, u, v;
ll dist[N][4];
bool visited[N];
vector <pair <int, int>> adj[N];
int a[4];
priority_queue <pair <ll, int>, vector <pair <ll, int>>, greater <pair <ll, int>>> p;
bool minimize(ll &x, const ll y){
if (x > y){
x = y;
return true;
}
return false;
}
void dijkstra(int id){
memset(visited, false, sizeof visited);
dist[a[id]][id] = 0;
p.push({0, a[id]});
while(p.size()){
ll i = p.top().fi;
int j = p.top().se;
p.pop();
if (visited[j]) continue;
visited[j] = true;
for (auto x: adj[j]){
if (minimize(dist[x.fi][id], i + x.se)){
p.push({dist[x.fi][id], x.fi});
}
}
}
}
ll res;
ll ans = 1e18;
ll f[N][2];
void solve()
{
cin >> n >> m >> s >> t >> u >> v;
for (int i = 1; i <= m; i++){
int x, y, w; cin >> x >> y >> w;
adj[x].pb({y, w});
adj[y].pb({x, w});
}
memset(dist, 0x3f, sizeof dist);
a[0] = s; a[1] = t; a[2] = u; a[3] = v;
dijkstra(0); dijkstra(1);
dijkstra(2); dijkstra(3);
res = dist[t][0];
memset(f, 0x3f, sizeof f);
memset(visited, false, sizeof visited);
p.push({0, s});
ans = dist[v][2];
while(p.size()){
ll i = p.top().fi;
int j = p.top().se;
p.pop();
if (visited[j]) continue;
visited[j] = true;
f[j][0] = min(f[j][0], dist[j][2]);
f[j][1] = min(f[j][1], dist[j][3]);
ans = min(ans, f[j][0] + dist[j][3]);
ans = min(ans, f[j][1] + dist[j][2]);
for (auto x: adj[j]){
if (i + x.se + dist[x.fi][1] == res){
f[x.fi][0] = min(f[x.fi][0], f[j][0]);
f[x.fi][1] = min(f[x.fi][1], f[j][1]);
p.push({dist[x.fi][0], x.fi});
}
}
}
cout << ans;
}
int main() {
ios_base::sync_with_stdio(false);
cin.tie(NULL);cout.tie(NULL);
if (fopen("VKhang.inp","r")){
freopen("VKhang.inp","r",stdin);
freopen("VKhang.out","w",stdout);
}
solve();
return 0;
}
