//https://play.google.com/store/apps/details?id=prod.com.pingidentity.pingid
#pragma GCC optimize("O3,no-stack-protector,unroll-loops,fast-math")
#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
using namespace std;
using namespace __gnu_pbds;
#define lim 10000005
#define kk 1000000007
#define INF 1e16
#define ll long long
#define mp make_pair
#define pb push_back
#define x first
#define y second
#define sz(x) x.size()
#define vl vector<ll>
#define bug printf("Yes %d\n", tmp)
#define enter printf("\n")
#define space printf(" ")
#define error(args...) { string _s = #args; replace(_s.begin(), _s.end(), ',', ' '); stringstream _ss(_s); istream_iterator<string> _it(_ss); err(_it, args); }
void err(istream_iterator<string> it) {}
template<typename T, typename... Args>
void err(istream_iterator<string> it, T a, Args... args) {
cerr << *it << " = " << a << endl;
err(++it, args...);
}
struct yo
{
ll x, y, w;
bool operator <(const yo &t) const
{
return w < t.w;
}
}edge[200005];
template <typename D>
void put(vector<D> aa,int st, int ed)
{
for (int i = st; i < ed; i++)
{
cout << aa[i] << " ";
}
cout << aa[ed] << endl;
}
#define mod (int)(1e9 + 7)
ll bg(ll x, ll y)
{ // big mod
if (y == 1)
return x % mod;
else if (y % 2 == 0)
{
ll tmp = bg(x, y / 2);
return ((tmp % mod) * tmp) % mod;
}
else
return (bg(x, y - 1) * x) % mod;
}
typedef tree<int, null_type, less_equal<int>, rb_tree_tag, tree_order_statistics_node_update> Multi_Set;
// typedef tree<int, null_type, less<int>, rb_tree_tag, tree_order_statistics_node_update> Multi_Set; -> normal set // can change to multi_set by pair<int , occ[int]>
//*find_by_order(), order_of_key()
template <typename T = int>
class bit
{
private:
vector<T> a;
public:
bit(int n) { a.resize(n + 1); }
void add(int i, T x)
{
for (; i < a.size(); i += i & -i)
a[i] += x;
}
T sum(int i)
{
T ans = 0;
for (; i > 0; i -= i & -i)
ans += a[i];
return ans;
}
void clear() { a.assign(a.size(), 0); }
};
// bit<ll > b2(300);
vl fac, inv, numinv; // ncr and fac
inline ll ncr(int n, int r)
{
if (n < 0 || r < 0 || r > n)
return 0;
return fac[n] * inv[r] % mod * inv[n - r] % mod;
}
inline void calfacinv(int n)
{
fac.reserve(n + 1);
fac[0] = fac[1] = 1;
for (int i = 2; i <= n; i++)
{
fac[i] = fac[i - 1] * i % mod;
}
numinv.reserve(n + 1);
numinv[0] = numinv[1] = 1;
for (int i = 2; i <= n; i++)
{
numinv[i] = numinv[mod % i] * (mod - mod / i) % mod;
}
inv.reserve(n + 1);
inv[0] = inv[1] = 1;
for (int i = 2; i <= n; i++)
{
inv[i] = numinv[i] * inv[i - 1] % mod;
}
return;
}
/* SOS DP
for(int i = 0;i < N; ++i) for(int mask = 0; mask < (1<<N); ++mask){ //order is not important
if(mask & (1<<i))
F[mask] += F[mask^(1<<i)];
}
*/
// ll rectsum(int x,int y,int xx,int yy){
// if (y > yy || x > xx) return 0;
// return psum[xx][yy] - psum[xx][y-1] - psum[x-1][yy] + psum[x-1][y-1];
// }
ll bt(ll x){
return (1<<x);
}
ll t, n, m, k, ans, l, r, mi, tot, cnt, q, c, S, T, U, V;
string ss1, ss2, ss[505];
vector<ll> ee[300005];
vector<pair<ll, ll> > ee2[300005], ee3[300005];
int cycle = 0;
ll cost(pair<ll, ll> a, pair<ll, ll> b){
return (a.x - b.x) * (a.x - b.x) + (a.y - b.y) * (a.y - b.y);
//return (abs(a.x - b.x) + abs(a.y - b.y)) * (abs(a.x - b.x) + abs(a.y - b.y));
}
vector<ll> sp1(200005, INF), sp2(200005, INF), sp3(200005, INF), sp5(200005, INF);
void dijk(int st, vector<ll>& sp, vector<pair<ll, ll>> adj[]){
sp[st] = 0;
priority_queue<pair<ll, ll>> q;
vector<int> vis(n+5);
q.push({0,st});
while (!q.empty()){
ll len = -q.top().x;
ll x = q.top().y;
q.pop();
if (sp[x] != len || vis[x] == 1) continue;
vis[x] = 1;
for (auto u: adj[x]){
//if (u.x == n) continue;
if (sp[u.x] > len + u.y){
sp[u.x] = len + u.y;
q.push({-sp[u.x],u.x});
}
}
}
}
void dijk2(int st, vector<pair<ll, ll>> adj[], int ed, int ed2){
vector<ll> sp4(200005, INF);
priority_queue<pair<ll, ll>> q;
vector<ll> sp(n+5, INF);
vector<int> vis(n+5);
sp[st] = 0;
q.push({0,st});
if (ed == U) sp4[st] = sp1[st];
if (ed == V) sp4[st] = sp2[st];
while (!q.empty()){
ll len = -q.top().x;
ll x = q.top().y;
q.pop();
if (sp[x] != len || vis[x] == 1) continue;
vis[x] = 1;
if (sp3[x] + sp5[x] == sp5[S]){ // this is one of the station that can buy pass
ll tmp1, tmp2;
if (ed == U){
tmp1 = sp1[x];
tmp2 = sp2[x];
}else{
tmp2 = sp1[x];
tmp1 = sp2[x];
}
sp4[x] = min(sp4[x], tmp1);
ans = min(ans, sp4[x] + tmp2);
}
for (auto u: adj[x]){
//if (u.x == n) continue;
if (sp[u.x] > len + u.y){
sp[u.x] = len + u.y;
q.push({-sp[u.x],u.x});
}
if (sp3[u.x] == len + u.y){
sp4[u.x] = min(sp4[u.x], sp4[x]);
}
}
}
for (int i=1;i<=n;i++){
error(i, sp4[i])
}
}
void solve(){
ios::sync_with_stdio(false), cin.tie(0);
// freopen("dining.in","r",stdin);
// freopen("dining.out","w",stdout);
//set<ll> ss;
cin >> n >> m >> S >> T >> U >> V;
map<int, int> mm;
//pair<ll, ll> hh[100005];
//vector<int> cc(n+5), dd(n+5), lis;
//vector<vector<int>> cc(n+5, vector<int> (n+5)), dd(n+5, vector<int> (n+5));
//vector<vector<ll>> dp(bt(n), vector<ll> (n+5, 0));
//vector<vector<ll>> dp(n+5, vector<ll> (n+5, 0));
for (int i=0;i<m;i++){
ll x, y, w;
cin >> x >> y >> w;
edge[i] = {x,y,w};
ee2[x].pb({y,w});
ee2[y].pb({x,w});
}
dijk(U, sp1, ee2);
dijk(V, sp2, ee2);
dijk(S, sp3, ee2);
dijk(T, sp5, ee2);
ans = sp1[V];
error(ans)
dijk2(S, ee2, U, V);
dijk2(S, ee2, V, U);
//cout << sp1[n] << " " << sp2[n] << " " << sp4[n] << " " << sp3[n] << endl;
cout << ans << endl;
//vector<vector<ll>> cc(n+5, vector<ll> (n+5, 0));
//dp[0][0] = 0;
//ll tot = 0;
//ll ans = 0;
vector<ll> tmp;
//sort(hh+1, hh+n+1);
//vector<vector<vector<ll>>> dp(n + 5, vector<vector<ll>> (m + 5, vector<ll> (2, 1e16)));
//cout << dp[n][m][0] << endl;
// vector<vector<ll>> dp(n+5, vector<ll>(n+5, kk));
// dp[0][0] = 0;
//vector<ll> dp();
//cout << ans << endl;
return;
// for (int i=0;i<n;i++){
// if (i == n-1) cout << cc[i] << endl;
// else cout << cc[i] << " ";
// }
// if (ans) cout << "YES" << endl;
// else cout << "NO" << endl;
// for (int i=1;i<=n;i++) cc[i] = 0;
// for (int i=1;i<=n;i++) printf("%d ",dd[i]);
}
int main()
{
ios::sync_with_stdio(false), cin.tie(0);
t = 1;
//cin >> t;
while (t--){
solve();
}
}
/*
*/
