/*
Muqalzhar taui
*/
#include <bits/stdc++.h>
#include <iomanip>
#define ll long long
#define pb push_back
#define F first
#define S second
#define nl '\n'
#define all(x) x.begin(), x.end()
const int N = 2e5 + 7;
const int modd = 1e9 + 7;
const int INF = 1e9 + 7;
const double pi = 3.141592653589793238462643383279502884197;
const double EPS = 0.0000000000001;
using namespace std;
int gcd(int a, int b){
if (b == 0)
return a;
else
return gcd(b, a % b);
}
ll binpow(ll a, ll x){
if(x == 0) return 1;
if(x % 2 == 0){
ll y = binpow(a, x / 2);
return (y * y);
}
else{
return (binpow(a, x - 1) * a);
}
}
ll n, m, s, t, u, v;
vector <pair <ll, ll>> e[N];
ll dpu[N];
ll dpv[N];
ll du[N];
ll dv[N];
void Muqaltin(){
cin >> n >> m >> s >> t >> u >> v;
for(int i = 1; i <= m; i++){
ll a,b,c;
cin >> a >> b >> c;
e[a].pb({b, c});
e[b].pb({a, c});
}
for(int i = 1; i <= n; i++){
du[i] = INF;
dv[i] = INF;
dpu[i] = INF;
dpv[i] = INF;
}
set <pair <ll, ll>> q;
dv[t] = 0;
q.insert({dv[t], t});
while(!q.empty()){
ll x = q.begin()->second;
q.erase(q.begin());
for(auto to : e[x]){
if(dv[to.F] > dv[x] + to.S){
q.erase({dv[to.F], to.F});
dv[to.F] = dv[x] + to.S;
q.insert({dv[to.F], to.F});
}
}
}
du[s] = 0;
q.insert({du[s], s});
while(!q.empty()){
ll x = q.begin()->second;
q.erase(q.begin());
for(auto to : e[x]){
if(du[to.F] > du[x] + to.S){
q.erase({du[to.F], to.F});
du[to.F] = du[x] + to.S;
q.insert({du[to.F], to.F});
}
}
}
set <pair <ll, ll>> st;
dpu[u] = 0;
st.insert({dpu[u], u});
while(!st.empty()){
ll x = st.begin()->second;
st.erase(st.begin());
for(auto to : e[x]){
if(du[x] + to.S + dv[to.F] != du[t]){
if(dpu[to.F] > dpu[x] + to.S){
st.erase({dpu[to.F], to.F});
dpu[to.F] = dpu[x] + to.S;
st.insert({dpu[to.F], to.F});
}
}
else{
if(dpu[to.F] > dpu[x]){
st.erase({dpu[to.F], to.F});
dpu[to.F] = min(dpu[x], du[to.F]);
st.insert({dpu[to.F], to.F});
}
}
}
}
dpv[v] = 0;
st.insert({dpv[v], v});
while(!st.empty()){
ll x = st.begin()->second;
st.erase(st.begin());
for(auto to : e[x]){
if(du[x] + to.S + dv[to.F] != du[t]){
if(dpv[to.F] > dpv[x] + to.S){
st.erase({dpv[to.F], to.F});
dpv[to.F] = dpv[x] + to.S;
st.insert({dpv[to.F], to.F});
}
}
else{
if(dpv[to.F] > dpv[x]){
st.erase({dpv[to.F], to.F});
dpv[to.F] = min(dpv[x], du[to.F]);
st.insert({dpv[to.F], to.F});
}
}
}
}
cout << dpu[t] + dpv[t];
return;
}
int main(){
// freopen("pails.in", "r", stdin);
// freopen("pails.out", "w", stdout);
ios_base :: sync_with_stdio(0);
cin.tie(0), cout.tie(0);
int t = 1;
// cin >> t;
while(t--){
Muqaltin();
}
return 0;
}
