#include <bits/stdc++.h>
#pragma GCC oprimize("O3, unroll-loops")
#pragma GCC target("avx2,bmi,bmi2,popcnt,lzcnt")
#define edge pair<ll, int>
#define c first
#define vi second
using namespace std;
typedef long long ll;
const int N = 1e5+5;
const ll M = 1e18;
int n, m, s, t, u, v;
vector<edge> graf[N];
class vertex
{
private:
int v;
vector<ll> dist;
bool dw;
void dijkstra()
{
if(dw)
return;
dist.assign(n+5, M);
priority_queue<edge, vector<edge>, greater<edge>> pq;
bool vis[n] = {};
pq.push({0, v});
dist[v] = 0;
while(!pq.empty())
{
edge t = pq.top(); pq.pop();
if(vis[t.vi])
continue;
vis[t.vi] = 1;
for(auto x: graf[t.vi])
{
if(t.c + x.c < dist[x.vi])
{
pq.push({t.c + x.c, x.vi});
dist[x.vi] = t.c + x.c;
}
}
}
}
public:
vertex(int a)
{
v = a;
dw = 0;
}
ll distto_a(int a)
{
if(!dw)
{
dijkstra();
dw = 1;
}
return dist[a];
}
};
int main()
{
ios_base::sync_with_stdio(false); cin.tie(NULL); cout.tie(NULL);
cin >> n >> m >> s >> t >> u >> v;
vector<vertex> ver;
s--; t--; u--; v--;
for(int i=0; i<n; i++)
{
vertex a(i);
ver.push_back(a);
}
while(m--)
{
int a, b, c; cin >> a >> b >> c;
a--; b--;
graf[a].push_back({c, b});
graf[b].push_back({c, a});
}
ll gc = ver[s].distto_a(t);
ll ans=ver[u].distto_a(v);
ll mv[n], mu[n];
vector<edge> hm;
for(int i=0; i<n; i++)
{
if(ver[s].distto_a(i)+ver[t].distto_a(i) == gc)
hm.push_back({ver[s].distto_a(i), i});
mv[i] = M;
mu[i] = M;
}
sort(hm.begin(), hm.end(), greater<edge>());
for(auto x: hm)
{
mv[x.vi] = ver[v].distto_a(x.vi);
mu[x.vi] = ver[u].distto_a(x.vi);
ans = min(ans, mv[x.vi]+mu[x.vi]);
for(auto y: graf[x.vi])
{
if(ver[s].distto_a(y.vi) + ver[t].distto_a(y.vi) != gc)
continue;
if(ver[s].distto_a(y.vi) - y.c != x.c)
continue;
ans = min(ans, min(ver[v].distto_a(x.vi)+mu[y.vi],
ver[u].distto_a(x.vi)+mv[y.vi]));
mv[x.vi] = min(mv[x.vi], mv[y.vi]);
mu[x.vi] = min(mu[x.vi], mu[y.vi]);
}
}
cout << ans;
return 0;
}
