#pragma GCC optimize("Ofast")
#include<bits/stdc++.h>
using namespace std;
#define pb push_back
#define fi first
#define se second
#define sz(a) (int)(a.size())
#define all(a) a.begin(),a.end()
#define lb lower_bound
#define ub upper_bound
#define owo ios_base::sync_with_stdio(0);cin.tie(0);
#define MOD (ll)(1e9+7)
#define INF (ll)(1e18)
#define debug(...) fprintf(stderr, __VA_ARGS__),fflush(stderr)
#define time__(d) for(long blockTime = 0; (blockTime == 0 ? (blockTime=clock()) != 0 : false);\
debug("%s time : %.4fs\n", d, (double)(clock() - blockTime) / CLOCKS_PER_SEC))
typedef long long int ll;
typedef long double ld;
typedef pair<ll,ll> PII;
typedef pair<int,int> pii;
typedef vector<vector<int>> vii;
typedef vector<vector<ll>> VII;
ll gcd(ll a,ll b){if(!b)return a;else return gcd(b,a%b);}
const int MAXN = 1e5+2;
vector<vector<pii>> adj(MAXN);
vector<ll>udist(MAXN,INF),vdist(MAXN,INF),sdist(MAXN,INF),tdist(MAXN,INF);
vector<bool>vis(MAXN,0);
vii tadj(MAXN);
void djikstra(int s,vector<ll>&dist){
priority_queue<PII,vector<PII>,greater<PII>>pq;
pq.push({0,s});
dist[s] = 0;
while(!pq.empty()){
ll d = pq.top().fi;
int v = pq.top().se;
pq.pop();
if(d != dist[v])continue;
for(auto x:adj[v]){
int to = x.fi;
ll w = x.se;
if(dist[to] > d+w){
dist[to] = d+w;
pq.push({d+w,to});
}
}
}
}
vector<ll>topo;
void dfs(int v){
vis[v] = 1;
for(int x:tadj[v]){
if(!vis[x]){
dfs(x);
}
}
topo.pb(v);
}
int main()
{
owo
int n,m;
cin>>n>>m;
int s,t,u,v;
cin>>s>>t>>u>>v;
for(int i=0;i<m;i++){
ll a,b,c;
cin>>a>>b>>c;
adj[a].pb({b,c});
adj[b].pb({a,c});
}
djikstra(u,udist);
djikstra(v,vdist);
djikstra(s,sdist);
djikstra(t,tdist);
queue<int>q;
q.push(s);
vis[s] = 1;
while(!q.empty()){
int v = q.front();
q.pop();
for(auto x:adj[v]){
int to = x.fi;
ll w = x.se;
if(sdist[v]+w + tdist[to] == sdist[t]){
tadj[v].pb(to);
if(!vis[to])q.push(to);
vis[to] = 1;
}
}
}
for(int i=1;i<=n;i++)vis[i] = 0;
dfs(s);
ll ans = vdist[u];
vector<ll>dp(n+1,INF);
/*
for(int i=1;i<=n;i++){
cout<<i<<":";
for(int x:tadj[i])cout<<x<<" ";
cout<<'\n';
}*/
for(ll z:topo){
dp[z] = vdist[z];
for(int x:tadj[z]){
dp[z] = min(dp[x],dp[z]);
}
ans = min(ans,dp[z]+udist[z]);
}
for(int i=1;i<=n;i++)dp[i] = INF;
for(ll z:topo){
dp[z] = udist[z];
for(int x:tadj[z]){
dp[z] = min(dp[x],dp[z]);
}
ans = min(ans,dp[z]+vdist[z]);
}
cout<<ans<<'\n';
}
