#include <bits/stdc++.h>
#define task "lyson"
//#pragma GCC optimize("O3,unroll-loops")
#define pb push_back
#define pii pair <int, int>
#define pli pair <ll, int>
#define fi first
#define se second
using namespace std;
typedef long long ll;
const ll oo = 1e18;
const int nmax = 1e5 + 5;
const int LG = 19;
const ll mod = 1e9 + 7;
void start()
{
// freopen(task".inp","r",stdin);
// freopen(task".out","w",stdout);
ios::sync_with_stdio(0);
cin.tie(0);
cout.tie(0);
}
int n, m;
int s, t, u, v, x, y, w, dh[nmax];
vector<pii> adj[nmax];
vector<int> dark[nmax];
ll d[nmax][4], dp[nmax];
pli topo[nmax];
priority_queue<pli, vector<pli>, greater<pli>> pq;
bool isdag[nmax];
void dijkstra(int u, int t)
{
for(int i = 1; i <= n; i++)
d[i][t] = oo;
d[u][t] = 0;
pq.push({d[u][t], u});
while(!pq.empty())
{
pii temp = pq.top();
if(temp.fi > d[temp.se][t])
continue;
pq.pop();
for(auto &[to, w] : adj[temp.se])
{
if(d[to][t] > d[temp.se][t] + w)
{
d[to][t] = d[temp.se][t] + w;
pq.push({d[to][t], to});
}
}
}
}
int main()
{
start();
cin >> n >> m;
cin >> s >> t >> u >> v;
for(int i = 1; i <= m; i++)
{
cin >> x >> y >> w;
adj[x].pb({y, w});
adj[y].pb({x, w});
}
dijkstra(s, 0);
dijkstra(t, 1);
dijkstra(u, 2);
dijkstra(v, 3);
// cout << d[1][1];
for(int i = 1; i <= n; i++)
{
topo[i] = {d[i][0], i};
dp[i] = d[i][3]; // từ v -> i
}
sort(topo + 1, topo + n + 1);
isdag[t] = true;
ll ans = oo;
//dp[x] cost min để từ 1 nút con của x đi đến v
//truong hop u tren v duoi
for(int i = n; i >= 1; i--)
{
if(isdag[topo[i].se])
{
ans = min(ans, d[topo[i].se][2] + dp[topo[i].se]); // min(u->x) + dp[x]
for(auto &[past, w] : adj[topo[i].se])
{
if(d[past][0] + w == d[topo[i].se][0])
{
isdag[past] = true;
dp[past] = min(dp[past], dp[topo[i].se]);
}
}
}
}
// cout << ans;
//truong hop v tren u duoi
memset(isdag, 0, sizeof(isdag));
isdag[t] = true;
for(int i = 1; i <= n; i++)
dp[i] = d[i][2]; // tu u -> i
for(int i = n; i >= 1; i--)
{
if(isdag[topo[i].se])
{
ans = min(ans, d[topo[i].se][3] + dp[topo[i].se]); // min(v->x) + dp[x]
for(auto &[past, w] : adj[topo[i].se])
{
if(d[past][0] + w == d[topo[i].se][0])
{
isdag[past] = true;
dp[past] = min(dp[past], dp[topo[i].se]);
}
}
}
}
ans = min(ans, d[v][2]); // u -> v
cout << ans;
}
