#include <bits/stdc++.h>
using namespace std;
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
int rnd(int l,int r)
{
return l+rng()%(r-l+1);
}
#define fasty ios_base::sync_with_stdio(0),cin.tie(0),cout.tie(0);
#define forinc(x,a,b) for(int x=a;x<=b;x++)
#define fordec(x,a,b) for(int x=a;x>=b;x--)
#define iii pair<ii,int>
#define fi first
#define se second
#define pb push_back
#define ll long long
#define ii pair<int,int>
#define mt make_tuple
#define getbit(x,i) ((x>>(i))&1)
#define batbit(x,i) (x|(1ll<<(i)))
#define tatbit(x,i) (x&~(1<<(i)))
#define endl '\n'
#define all(v) v.begin(), v.end()
#define gg exit(0);
#define int long long
const int N = 1e5 + 100;
int n,m;
vector<ii> ke[N];
int s, t, u, v;
vector<int> ditcha(int st)
{
vector<int> d(n+1,1e15);
priority_queue<ii, vector<ii>, greater<ii> > q;
q.push({0, st});
d[st] =0;
while(!q.empty())
{
ii u = q.top();
q.pop();
if(u.fi != d[u.se]) continue;
for(auto v : ke[u.se])
{
int cost = v.se;
if(d[v.fi] > d[u.se] + v.se)
{
d[v.fi] = d[u.se] + v.se;
q.push({d[v.fi], v.fi});
}
}
}
return d;
}
int f[N], dp[N];
main()
{
// freopen("task.inp" , "r" , stdin);
fasty;
cin >> n >> m;
cin >> s >> t;
cin >> u >> v;
forinc(i,1,m)
{
int u, v, c;
cin >> u >> v >>c;
ke[u].pb({v,c});
ke[v].pb({u,c});
}
vector<int> ds = ditcha(s);
vector<int> dt = ditcha(t);
vector<int> du = ditcha(u);
vector<int> dv = ditcha(v);
//cout << du[v] << "\n";
// cout << du[s] << "\n";
int res = 1e18;
for(int _ = 0 ; _ < 2 ; _++)
{
priority_queue<ii, vector<ii>, greater<ii> > q;
forinc(i,0,n+1) dp[i] = 1e15;
forinc(i,0,n+1) f[i] = 1e15;
f[s]=0;
dp[s] = du[s];
//cout << dp[s] << " ";
q.push({0,s});
while(!q.empty())
{
ii u = q.top();
q.pop();
if(f[u.se] != u.fi) continue;
//u - i
//cout << dp[u.se] + dv[u.se] << "\n";
//cout << u.se << " " << dp[u.se] << " " << dv[u.se] << "\n";
//gg;
res = min(res, dp[u.se] + dv[u.se]);
//cout << res << " ";
// s ----- u ------ v ----- t
for(auto v : ke[u.se])
{
if(ds[v.fi] + dt[v.fi] == ds[t] )
{
dp[v.fi] = min({dp[v.fi] , dp[u.se] , du[u.se]} );
}
if(f[v.fi] > v.se + f[u.se])
{
f[v.fi] = v.se + f[u.se];
q.push({f[v.fi], v.fi});
}
}
}
swap(du,dv);
}
// cout << res << "\n";
res = min(res , du[v]);
cout << res;
}
