#include <bits/stdc++.h>
using namespace std;
#define ll long long
#define int long long
#define sz(a) ((int)a.size())
#define all(a) a.begin(), a.end()
#define arr2 array<int,2>
#define arr3 array<int,3>
#define arr4 array<int,4>
#define arr5 array<int,5>
#define el '\n'
#define pii pair<int,int>
#define __ <<' '<<
#define i128 __int128
#define IMPOSSIBLE return cout << "-1" << endl,void();
#define FILE "cowmbat"
const int N = 1e5 + 7;
const int MOD = 1e9 + 7;
vector<pii> e[N];
bool visited[N];
int res[4][N];
void dijstra(int start,int type){
priority_queue<pii, vector<pii>, greater<>> q;
q.push({0,start});
res[type][start] = 0;
while(sz(q)){
auto [w,u] = q.top();q.pop();
if(w > res[type][u])continue;
for(auto [v,wv] : e[u]){
if(res[type][v] <= w + wv)continue;
res[type][v] = w + wv;
q.push({w + wv, v});
}
}
}
int tmp[3][N];
void dijstraress(int start){
priority_queue<arr2, vector<arr2>, greater<>> q;
q.push({0,start});
memset(res[0], 60, sizeof res[0]);
memset(tmp[1],60,sizeof tmp[1]);
memset(tmp[2],60,sizeof tmp[2]);
memset(res[3], 60, sizeof res[3]);
tmp[1][start] = res[1][start];
tmp[2][start] = res[2][start];
res[3][start] = tmp[1][start] + tmp[2][start];
res[0][start] = 0;
while(sz(q)){
auto [w,u] = q.top();q.pop();
if(w > res[0][u])continue;
for(auto [v,wv] : e[u]){
if(wv + w < res[0][v]){
res[0][v] = wv + w;
tmp[1][v] = min(tmp[1][u], res[1][v]);
tmp[2][v] = min(tmp[2][u], res[2][v]);
res[3][v] = min({res[3][u], res[2][v] + tmp[1][u], res[1][v] + tmp[2][u], res[2][v] + res[1][v]});
q.push({wv + w,v});
}
else if(wv + w == res[0][v]){
tmp[1][v] = min(tmp[1][v], res[1][v]);
tmp[2][v] = min(tmp[2][v], res[2][v]);
res[3][v] = min({res[3][v], res[3][u], res[2][v] + tmp[1][u], res[1][v] + tmp[2][u], res[2][v] + res[1][v]});
}
}
}
}
void solve(){
int n,m;
cin >> n >> m;
memset(res[1], 60, sizeof res[1]);
memset(res[2], 60, sizeof res[2]);
int S,T,U,V;
cin >> S >> T >> U >> V;
for(int i = 0;i < m; i++){
int u,v,w;
cin >> u >> v >> w;
e[u].push_back({v,w});
e[v].push_back({u,w});
}
dijstra(U,1);
dijstra(V,2);
int ans = res[1][V];
dijstraress(S);
ans = min(ans,res[3][T]);
dijstraress(T);
ans = min(ans,res[3][S]);
cout << ans << endl;
}
signed main()
{
ios_base::sync_with_stdio(0);
cin.tie(0);
#ifdef LOCAL
freopen("io\\ban.in","r",stdin);
freopen("io\\ban.txt","w",stdout);
// #elif !(ONLINE_JUDGE)
// freopen(FILE ".in","r",stdin);
// freopen(FILE ".out","w",stdout);
#endif
int q(1);
// cin >> q;
while(q--) solve();
return 0;
}
