#include<bits/stdc++.h>
using namespace std;
#define ll long long
#define fi first
#define se second
#define task "code"
const int ar=1e5+5;
const ll mod=1e9+7;
int n,m;
int s,t;
int u,v;
ll dp[2][ar];
vector<pair<int,int>> ad[ar];
vector<int> it;
priority_queue<pair<ll,int>, vector<pair<ll,int>>, greater<pair<ll,int>> > pq;
ll dist[5][ar];
void dijkstra(int x,int t)
{
for (int i=1;i<=n;i++) dist[t][i]=1e18;
dist[t][x]=0;
pq.push({0,x});
while(pq.size())
{
pair<ll,int> top=pq.top();
pq.pop();
ll d=top.fi;
int u=top.se;
if (d>dist[t][u]) continue;
for (auto [v,w]:ad[u])
{
ll val=dist[t][u]+w;
if (val<dist[t][v])
{
dist[t][v]=val;
pq.push({val,v});
}
}
}
}
bool cmp(int x,int y)
{
return dist[1][x]<dist[1][y];
}
ll ans=1e18;
int main()
{
ios_base::sync_with_stdio(0);
cin.tie(0);cout.tie(0);
if (fopen(task".inp","r"))
{
freopen(task".inp","r",stdin);
freopen(task".out","w",stdout);
}
cin>>n>>m>>s>>t>>u>>v;
for (int i=1;i<=m;i++)
{
int a,b,c;
cin>>a>>b>>c;
ad[a].push_back({b,c});
ad[b].push_back({a,c});
}
dijkstra(s,1);
dijkstra(t,2);
dijkstra(u,3);
dijkstra(v,4);
for (int i=1;i<=n;i++) it.push_back(i);
sort(it.begin(),it.end(),cmp);
ans=dist[3][v];
for (auto ver:it)
{
if (dist[1][ver]+dist[2][ver]!=dist[1][t]) continue;
dp[0][ver]=dist[3][ver];
dp[1][ver]=dist[4][ver];
for (auto [p,w]:ad[ver])
{
if (dist[1][p]!=dist[1][ver]-w) continue;
if (dist[1][p]+dist[2][p]!=dist[1][t]) continue;
ans=min(ans,dist[3][ver]+dp[1][p]);
ans=min(ans,dist[4][ver]+dp[0][p]);
dp[0][ver]=min(dp[0][ver],dp[0][p]);
dp[1][ver]=min(dp[1][ver],dp[1][p]);
}
}
cout<<ans;
}
