#include <bits/stdc++.h>
#define ll long long
#define pb push_back
#define task "asd"
#define pll pair<ll, ll>
#define pii pair<pll, ll>
#define fi first
#define se second
using namespace std;
const ll mod = 1e15+7;
const ll N = 2e5+5;
const int base = 313;
ll n, m, t, k, T, ans, tong, a[N], b[N], s, u, v, d[N][4], dp[N][4];
vector<pll> adj[N];
vector<ll> kq;
ll pw(ll k, ll n)
{
ll total = 1;
for(; n; n >>= 1)
{
if(n & 1)total = total * k % mod;
k = k * k % mod;
}
return total;
}
void dij(ll ui, ll id)
{
for(int i = 1; i <= n; i ++)d[i][id] = mod;
priority_queue< pll, vector<pll>, greater<pll> > pq;
pq.push({0, ui});
d[ui][id] = 0;
while(!pq.empty())
{
pll u = pq.top();
pq.pop();
if(u.fi != d[u.se][id])continue;
for(pll v : adj[u.se])
{
if(d[v.se][id] > u.fi + v.fi)
{
d[v.se][id] = u.fi + v.fi;
pq.push({d[v.se][id], v.se});
}
}
}
}
void sol()
{
cin >> n >> m >> s >> t >> u >> v;
for(int i = 1; i <= m; i ++)
{
ll x, y, w;
cin >> x >> y >> w;
adj[x].pb({w, y});
adj[y].pb({w, x});
}
dij(s, 0);
dij(u, 1);
dij(v, 2);
queue<ll> q;
for(int i = 1; i <= n; i ++)
{
dp[i][0] = dp[i][1] = dp[i][2] = mod;
for(pll vi : adj[i])
{
if(d[i][0] + vi.fi == d[vi.se][0])++a[vi.se];
}
}
q.push(s);
while(!q.empty())
{
ll ui = q.front();
q.pop();
dp[ui][0] = min(dp[ui][0], d[ui][1]);
dp[ui][1] = min(dp[ui][1], d[ui][2]);
dp[ui][2] = min(dp[ui][2], min(dp[ui][0] + d[ui][2], dp[ui][1] + d[ui][1]));
for(pll vi : adj[ui])
{
if(d[vi.se][0] == d[ui][0] + vi.fi)
{
--a[vi.se];
dp[vi.se][0] = min(dp[vi.se][0], dp[ui][0]);
dp[vi.se][1] = min(dp[vi.se][1], dp[ui][1]);
dp[vi.se][2] = min(dp[vi.se][2], dp[ui][2]);
if(!a[vi.se])q.push(vi.se);
}
}
}
cout << min(dp[t][2], d[u][2]);
}
int main()
{
if(fopen(task".INP", "r"))
{
freopen(task".INP", "r", stdin);
freopen(task".OUT", "w", stdout);
}
ios_base::sync_with_stdio(0);
cin.tie(0);
cout.tie(0);
int ntest = 1;
//cin >> ntest;
while(ntest -- > 0)
sol();
}
/*
5 1
1 2
2 3
3 4
4 5
*/
