#include <bits/stdc++.h>
#define pb push_back
#define F first
#define S second
#define all(x) x.begin(), x.end()
#define debug(x) cerr << #x << " : " << x << '\n'
using namespace std;
typedef long long ll;
typedef long double ld;
typedef string str;
typedef pair<ll, ll> pll;
const ll Mod = 1000000007LL;
const int N = 2e5 + 10;
const ll Inf = 2242545357980376863LL;
const ll Log = 30;
ll dis[2][N];
vector<pll> G[N];
set<pll> st;
void Dij(int sc, int idx){
memset(dis[idx], 31, sizeof dis[idx]);
dis[idx][sc] = 0;
st.insert({0, sc});
int fr;
while(!st.empty()){
fr = st.begin() -> S;
st.erase(st.begin());
for(auto ed : G[fr]){
if(dis[idx][ed.F] > dis[idx][fr] + ed.S){
st.erase({dis[idx][ed.F], ed.F});
dis[idx][ed.F] = dis[idx][fr] + ed.S;
st.insert({dis[idx][ed.F], ed.F});
}
}
}
}
ll dp[N][4], d[N];
int main(){
ios::sync_with_stdio(0); cin.tie(0); cout.tie(0);
ll n, m;
cin >> n >> m;
ll s, t, l1, l2;
cin >> s >> t >> l1 >> l2;
ll u, v, w;
for(int i = 0; i < m; i++){
cin >> u >> v >> w;
G[u].pb({v, w});
G[v].pb({u, w});
}
Dij(l1, 0);
Dij(l2, 1);
memset(dp, 31, sizeof dp);
memset(d, 31, sizeof d);
for(int i = 0; i < 4; i++) dp[s][i] = (i & 1 ? dis[0][s] : 0) + (i & 2 ? dis[1][s] : 0);
d[s] = 0;
st.insert({d[s], s});
int fr, adj;
while(!st.empty()){
fr = st.begin() -> S;
st.erase(st.begin());
for(auto e : G[fr]){
adj = e.F;
if(d[adj] > d[fr] + e.S){
st.erase({d[adj], adj});
d[adj] = d[fr] + e.S;
st.insert({d[adj], adj});
memset(dp[adj], 31, sizeof dp[adj]);
}
if(d[adj] == d[fr] + e.S){
for(int mk1 = 0; mk1 < 4; mk1 ++){
for(int mk2 = 0; mk2 < 4; mk2 ++){
if(mk1 & mk2) continue;
dp[adj][mk1 | mk2] = min(dp[adj][mk1 | mk2], dp[fr][mk1] + (mk2 & 1 ? dis[0][adj] : 0) + (mk2 & 2 ? dis[1][adj] : 0));
}
}
}
}
}
cout << min(dis[0][l2], dp[t][3]) << '\n';
return 0;
}
