#ifndef CPL_TEMPLATE
#define CPL_TEMPLATE
/*
Normie's Template v2.5
Changes:
Added warning against using pragmas on USACO.
*/
// Standard library in one include.
#include <bits/stdc++.h>
using namespace std;
// ordered_set library.
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
using namespace __gnu_pbds;
#define ordered_set(el) tree<el,null_type,less<el>,rb_tree_tag,tree_order_statistics_node_update>
// AtCoder library. (Comment out these two lines if you're not submitting in AtCoder.) (Or if you want to use it in other judges, run expander.py first.)
//#include <atcoder/all>
//using namespace atcoder;
//Pragmas (Comment out these three lines if you're submitting in szkopul or USACO.)
#pragma comment(linker, "/stack:200000000")
#pragma GCC optimize("Ofast,unroll-loops,tree-vectorize")
#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,avx2,tune=native")
//File I/O.
#define FILE_IN "cseq.inp"
#define FILE_OUT "cseq.out"
#define ofile freopen(FILE_IN,"r",stdin);freopen(FILE_OUT,"w",stdout)
//Fast I/O.
#define fio ios::sync_with_stdio(0);cin.tie(0)
#define nfio cin.tie(0)
#define endl "\n"
//Order checking.
#define ord(a,b,c) ((a>=b)and(b>=c))
//min/max redefines, so i dont have to resolve annoying compile errors.
#define min(a,b) (((a)<(b))?(a):(b))
#define max(a,b) (((a)>(b))?(a):(b))
// Fast min/max assigns to use with AVX.
// Requires g++ 9.2.0.
template<typename T>
__attribute__((always_inline)) void chkmin(T& a, const T& b) {
a=(a<b)?a:b;
}
template<typename T>
__attribute__((always_inline)) void chkmax(T& a, const T& b) {
a=(a>b)?a:b;
}
//Constants.
#define MOD (ll(998244353))
#define MAX 300001
#define mag 320
const long double PI=3.14159265358979;
//Pairs and 3-pairs.
#define p1 first
#define p2 second.first
#define p3 second.second
#define fi first
#define se second
#define pii(element_type) pair<element_type,element_type>
#define piii(element_type) pair<element_type,pii(element_type)>
//Quick power of 2.
#define pow2(x) (ll(1)<<x)
//Short for-loops.
#define ff(i,__,___) for(int i=__;i<=___;i++)
#define rr(i,__,___) for(int i=__;i>=___;i--)
//Typedefs.
#define bi BigInt
typedef long long ll;
typedef long double ld;
typedef short sh;
// Binpow and stuff
ll BOW(ll a, ll x, ll p)
{
if (!x) return 1;
ll res=BOW(a,x/2,p);
res*=res;
res%=p;
if (x%2) res*=a;
return res%p;
}
ll INV(ll a, ll p)
{
return BOW(a,p-2,p);
}
//---------END-------//
#endif
vector<pii(int)> gt[100001];
vector<pii(int)> gtn[400001];
int n,m,i,j,k,t,t1,u,v,a,b;
int ns,nt,nu,nv;
int eu[200001],ev[200001],ec[200001],ex[200001];
ll ds[100001],dt[100001];
ll dn[400001];
priority_queue<pii(ll),vector<pii(ll)>,greater<pii(ll)>> pq;
int main()
{
fio;
cin>>n>>m;
cin>>ns>>nt>>nu>>nv;
ns--;
nt--;
nu--;
nv--;
for (i=0;i<m;i++)
{
cin>>eu[i]>>ev[i]>>ec[i];
eu[i]--;
ev[i]--;
gt[eu[i]].push_back({ev[i],i});
gt[ev[i]].push_back({eu[i],i});
}
pq.push({0,ns});
for (i=0;i<n;i++) ds[i]=1e18;
ds[ns]=0;
while(pq.size())
{
auto pp=pq.top();
pq.pop();
if (ds[pp.se]<pp.fi) continue;
for (auto g : gt[pp.se])
{
if (ds[g.fi]>pp.fi+ec[g.se])
{
ds[g.fi]=pp.fi+ec[g.se];
pq.push({ds[g.fi],g.fi});
}
}
}
pq.push({0,nt});
for (i=0;i<n;i++) dt[i]=1e18;
dt[nt]=0;
while(pq.size())
{
auto pp=pq.top();
// cout<<pp.fi<<' '<<pp.se<<endl;
pq.pop();
if (dt[pp.se]<pp.fi) continue;
for (auto g : gt[pp.se])
{
// cout<<g.fi<<' '<<dt[g.fi]<<' '<<pp.fi<<' '<<ec[g.se]<<endl;
if (dt[g.fi]>pp.fi+ec[g.se])
{
dt[g.fi]=pp.fi+ec[g.se];
pq.push({dt[g.fi],g.fi});
}
}
}
// for (i=0;i<n;i++) cout<<ds[i]<<' '; cout<<endl;
// for (i=0;i<n;i++) cout<<dt[i]<<' '; cout<<endl;
for (i=0;i<m;i++)
{
if (ds[eu[i]]>ds[ev[i]]) swap(eu[i],ev[i]);
if (ds[eu[i]]+ec[i]+dt[ev[i]]>dt[ns])
{
gtn[4*eu[i]].push_back({4*ev[i],ec[i]});
gtn[4*ev[i]].push_back({4*eu[i],ec[i]});
gtn[4*eu[i]+1].push_back({4*ev[i]+3,ec[i]});
gtn[4*ev[i]+1].push_back({4*eu[i]+3,ec[i]});
gtn[4*eu[i]+2].push_back({4*ev[i]+3,ec[i]});
gtn[4*ev[i]+2].push_back({4*eu[i]+3,ec[i]});
}
else
{
gtn[4*eu[i]+1].push_back({4*ev[i]+1,0});
gtn[4*ev[i]+2].push_back({4*eu[i]+2,0});
gtn[4*eu[i]].push_back({4*ev[i]+1,0});
gtn[4*ev[i]].push_back({4*eu[i]+2,0});
gtn[4*eu[i]+2].push_back({4*ev[i]+3,ec[i]});
gtn[4*ev[i]+1].push_back({4*eu[i]+3,ec[i]});
}
gtn[4*eu[i]+3].push_back({4*ev[i]+3,ec[i]});
gtn[4*ev[i]+3].push_back({4*eu[i]+3,ec[i]});
}
// for (i=0;i<4*n;i++) for (auto g : gtn[i]) cout<<i<<' '<<g.fi<<' '<<g.se<<endl;
pq.push({0,4*nu});
for (i=0;i<4*n;i++) dn[i]=1e18;
dn[4*nu]=0;
while(pq.size())
{
auto pp=pq.top();
pq.pop();
if (dn[pp.se]<pp.fi) continue;
for (auto g : gtn[pp.se])
{
if (dn[g.fi]>pp.fi+g.se)
{
dn[g.fi]=pp.fi+g.se;
pq.push({dn[g.fi],g.fi});
}
}
}
ll res=1e18;
for (i=0;i<4;i++) res=min(res,dn[4*nv+i]);
cout<<res;
}
// Normie28
