#include <bits/stdc++.h>
#define fi first
#define se second
#define inf 0x3f3f3f3f3f3f3f3f
using namespace std;
using ll = long long;
const int nx=1e5+5;
int n, m, s, t, u, v;
ll dp[nx], d[nx][5], kq=inf;
pair<ll, ll> a[nx];
vector<int> topo;
struct dak
{
int v;
ll w;
bool operator <(const dak &o)
const
{
return w>o.w;
}
};
priority_queue<dak> f;
vector<dak> adj[nx];
void find(int u, int k)
{
d[u][k]=0;
f.push({u, d[u][k]});
while(f.size())
{
dak v=f.top();
f.pop();
if(d[v.v][k]<v.w)
continue;
for(auto it:adj[v.v])
{
if(d[it.v][k]>d[v.v][k]+it.w)
{
d[it.v][k]=d[v.v][k]+it.w;
f.push({it.v, d[it.v][k]});
}
}
}
}
bool cmp(pair<ll, ll> a, pair<ll, ll> b)
{
return a.fi>b.fi;
}
signed main()
{
ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0);
cin>>n>>m>>s>>t>>u>>v;
while(m--)
{
int a, b;
ll c;
cin>>a>>b>>c;
adj[a].push_back({b, c});
adj[b].push_back({a, c});
}
memset(d, 0x3f, sizeof(d));
memset(dp, 0x3f, sizeof(dp));
find(s, 0);
find(t, 1);
find(u, 2);
find(v, 3);
for(int i = 1; i <= n; i++)
a[i]=make_pair(d[i][0], i);
sort(a+1, a+n+1, cmp);
for(int i = 1; i <= n; i++)
topo.emplace_back(a[i].se);
for(int l:topo)
{
if(d[l][0]+d[l][1]==d[t][0])
{
for(auto r:adj[l])
{
if(d[l][0]+r.w==d[r.v][0])
dp[l]=min({dp[l], dp[r.v], d[l][3]});
}
}
}
kq=d[u][3];
for(int i = 1; i <= n; i++)
kq=min(kq, d[i][2]+dp[i]);
memset(dp, 0x3f, sizeof(dp));
for(int l:topo)
{
if(d[l][0]+d[l][1]==d[t][0])
{
for(auto r:adj[l])
{
if(d[l][0]+r.w==d[r.v][0])
dp[l]=min({dp[l], dp[r.v], d[l][2]});
}
}
}
for(int i = 1; i <= n; i++)
kq=min(kq, d[i][3]+dp[i]);
cout<<kq;
}
