#include <bits/stdc++.h>
using namespace std;
#define fo(i,s,t) for(int i = s; i <= t; ++ i)
#define fd(i,s,t) for(int i = s; i >= t; -- i)
#define bf(i,s) for(int i = head[s]; i; i = e[i].next)
#define mp make_pair
#define fi first
#define se second
#define pii pair<int,int>
#define pb push_back
#define VI vector<int>
#define sf scanf
#define pf printf
#define fp freopen
#define SZ(x) ((int)(x).size())
#ifdef MPS
#define D(x...) printf(x)
#else
#define D(x...)
#endif
typedef long long ll;
typedef double db;
typedef unsigned long long ull;
const int inf = 1<<30;
const ll INF = 1ll<<60;
const db Inf = 1e20;
const db eps = 1e-9;
void gmax(int &a,int b){a = (a > b ? a : b);}
void gmin(int &a,int b){a = (a < b ? a : b);}
const int maxn = 100050;
ll dist[4][maxn]; //0-> starts from u, 1->v, 2-> s, 3-> t,
ll f[2][maxn];
bool inq[maxn];
int S, T, U, V, n, m;
vector<pii> adj[maxn];
priority_queue<pair<ll,int> ,vector<pair<ll,int> >,greater<pair<ll,int> > > pq;
void dijkstra(int s, int k)
{
fo(i,1,n) dist[k][i] = INF;
pq.push(mp(0ll, s));
dist[k][s] = 0;
while(!pq.empty())
{
int h = pq.top().se; ll w = pq.top().fi; pq.pop();
if(w < dist[k][h]) continue;
for(auto p : adj[h]) if(dist[k][p.fi] > dist[k][h] + p.se)
{
dist[k][p.fi] = dist[k][h] + p.se;
pq.push(mp(dist[k][p.fi], p.fi));
}
}
}
void DP(int s, int k1, int k, int x)
{
fo(i,1,n) f[x][i] = INF;
f[x][s] = dist[k][s];
pq.push(mp(f[x][s], s));
while(!pq.empty())
{
int h = pq.top().se; pq.pop(); inq[h] = false;
for(auto p : adj[h]) if(dist[k1][h] + p.se == dist[k1][p.fi])
{
if(f[x][p.fi] > f[x][h])
{
f[x][p.fi] = min(f[x][h], dist[k][p.fi]);
if(!inq[p.fi])
{
inq[p.fi] = true;
pq.push(mp(f[x][p.fi], p.fi));
}
}
}
}
}
int main()
{
#ifdef MPS
fp("1.in","r",stdin);
fp("1.out","w",stdout);
#endif
sf("%d%d",&n,&m);
sf("%d%d%d%d",&S,&T,&U,&V);
fo(i,1,m)
{
int u, v, w;
sf("%d%d%d",&u,&v,&w);
adj[u].pb(mp(v, w));
adj[v].pb(mp(u, w));
}
dijkstra(U, 0);
dijkstra(V, 1);
dijkstra(S, 2);
dijkstra(T, 3);
DP(S, 2, 1, 0);
DP(T, 3, 1, 1);
ll ans = INF;
// D("%lld %lld %lld %lld\n",dist[2][S], dist[3][S], dist[2][T],f[1][3]);
fo(i,1,n) //iterate all y
if(dist[2][i] + dist[3][i] == dist[2][T]) // its on the shortest path from s to T
ans = min(ans, dist[0][i] + min(f[0][i], f[1][i]));
pf("%lld\n",min(ans,dist[0][V]));
return 0;
}
