#include<bits/stdc++.h>
#define int long long
#define pii pair<int,int>
#define fi first
#define se second
/*#pragma GCC tarGet ("avx2")
#pragma GCC optimization ("O3")
#pragma GCC optimization ("unroll-loops")
#pragma GCC optimize("Ofast")
#pragma GCC tarGet("avx,avx2,fma")*/
using namespace std;
using ll = long long;
using ull = unsigned long long;
using ldb = long double;
const int N = 1e5;
const int maxN = 2e5 + 1;
const int mod = 1e9 + 7;
const int block_size = 700;
const ll infty = 1e18;
struct Tpq
{
int ver;
ll val;
};
struct functer
{
bool operator()(Tpq a,Tpq b)
{
return a.val > b.val;
}
};
int n,m;
int S,T;
int U,V;
vector<pii> adj[maxN];
ll du[maxN];
ll dv[maxN];
ll ds[maxN];
ll dt[maxN];
int x[maxN],y[maxN],w[maxN];
void Read()
{
cin >> n >> m >> S >> T >> U >> V;
for(int i = 1;i <= m;i++)
{
int a,b,c;
cin >> a >> b >> c;
x[i] = a;
y[i] = b;
w[i] = c;
adj[a].push_back({b,c});
adj[b].push_back({a,c});
}
}
void Dijkstra1()
{
fill(ds + 1,ds + n + 1,infty);
ds[S] = 0;
priority_queue<Tpq,vector<Tpq>,functer> q;
q.push({S,0});
do
{
Tpq pick = q.top();
q.pop();
if(ds[pick.ver] != pick.val) continue;
int u = pick.ver;
for(pii e : adj[u])
{
int v = e.fi;
ll wt = e.se;
if(ds[v] > ds[u] + wt)
{
ds[v] = ds[u] + wt;
q.push({v,ds[v]});
}
}
}
while(!q.empty());
}
void Dijkstra2()
{
fill(du + 1,du + n + 1,infty);
du[U] = 0;
priority_queue<Tpq,vector<Tpq>,functer> q;
q.push({U,0});
do
{
Tpq pick = q.top();
q.pop();
if(du[pick.ver] != pick.val) continue;
int u = pick.ver;
for(pii e : adj[u])
{
int v = e.fi;
ll wt = e.se;
if(du[v] > du[u] + wt)
{
du[v] = du[u] + wt;
q.push({v,du[v]});
}
}
}
while(!q.empty());
}
void Dijkstra3()
{
fill(dv + 1,dv + n + 1,infty);
dv[V] = 0;
priority_queue<Tpq,vector<Tpq>,functer> q;
q.push({V,0});
do
{
Tpq pick = q.top();
q.pop();
if(dv[pick.ver] != pick.val) continue;
int u = pick.ver;
for(pii e : adj[u])
{
int v = e.fi;
ll wt = e.se;
if(dv[v] > dv[u] + wt)
{
dv[v] = dv[u] + wt;
q.push({v,du[v]});
}
}
}
while(!q.empty());
}
void Dijkstra4()
{
fill(dt + 1,dt + n + 1,infty);
dt[T] = 0;
priority_queue<Tpq,vector<Tpq>,functer> q;
q.push({T,0});
do
{
Tpq pick = q.top();
q.pop();
if(dt[pick.ver] != pick.val) continue;
int u = pick.ver;
for(pii e : adj[u])
{
int v = e.fi;
ll wt = e.se;
if(dt[v] > dt[u] + wt)
{
dt[v] = dt[u] + wt;
q.push({v,dt[v]});
}
}
}
while(!q.empty());
}
vector<int> adj2[maxN];
int deg[maxN];
vector<int> Topo;
int min_u[maxN];
int min_v[maxN];
void Proceed_DAG()
{
for(int i = 1;i <= m;i++)
{
if(ds[x[i]] + w[i] + dt[y[i]] == ds[T])
{
adj2[x[i]].push_back(y[i]);
deg[y[i]]++;
}
else if(ds[y[i]] + w[i] + dt[x[i]] == ds[T])
{
adj2[y[i]].push_back(x[i]);
deg[x[i]]++;
}
}
queue<int> q;
q.push(S);
do
{
int u = q.front();
q.pop();
Topo.push_back(u);
for(int v : adj2[u])
{
if(--deg[v] == 0)
{
q.push(v);
}
}
}
while(!q.empty());
//cout << dt[5];return;
fill(min_u + 1,min_u + n + 1,infty);
fill(min_v + 1,min_v + n + 1,infty);
//min_u[1] = du[1];
//min_v[1] = dv[1];
ll res = du[V];
for(int i : Topo)
{
//cout << i <<' ';
min_u[i] = min(min_u[i],du[i]);
min_v[i] = min(min_v[i],dv[i]);
res = min(res,dv[i] + min_u[i]);
res = min(res,du[i] + min_v[i]);
for(int j : adj2[i])
{
min_u[j] = min(min_u[i],min_u[j]);
min_v[j] = min(min_v[i],min_v[j]);
}
}
cout << res;
}
void Solve()
{
Dijkstra1();
Dijkstra2();
Dijkstra3();
Dijkstra4();
Proceed_DAG();
//cout << dv[5];
}
int32_t main()
{
ios_base::sync_with_stdio(false);
cin.tie(nullptr);
//InputFile();
//int sub_type;
//cin >> sub_type;
//Sieve();
int test;
//cin >> test;
test = 1;
while(test--)
//for(int prc = 1; prc <= test; prc++)
{
Read();
Solve();
//Debug();
}
}
