#include <bits/stdc++.h>
using namespace std;
#define endl '\n'
#define db double
#define ll __int128
#define int long long
#define pb push_back
#define fs first
#define sd second
#define Mod long(1e9 + 7)
#define all(x) x.begin(), x.end()
#define unvisited long(-1)
#define Eps double(1e-9)
#define _for(i, n) for(int i = 0; i < (n); i++)
#define dbg(x) cout << #x ": " << x << endl;
const int Max = 1e6 + 7, Inf = 1e16 + 7;
void print(bool x) { cout << (x ? "YES" : "NO") << endl; }
string tostring (__int128 x)
{
string ans = "";
while(x > 0)
{
ans += (x % 10 + '0');
x /= 10;
}
reverse(all(ans));
return ans;
}
vector <vector<pair<int, int>>> v;
vector <int> Dijkstra(int n, int x)
{
vector <int> dist(n+1, Inf), pass(n+1, 0);
priority_queue <pair<int, int>> pq;
dist[x] = 0; pq.push({ 0, x });
while (!pq.empty())
{
int x = pq.top().sd; pq.pop();
if(pass[x]) continue;
pass[x] = 1;
for(auto& u : v[x])
{
int node = u.fs, w = u.sd;
if(dist[x] + w < dist[node])
{
dist[node] = dist[x] + w;
pq.push({ -dist[node], node });
}
}
}
return dist;
}
void solve()
{
int N, M, S, T, U, V; cin >> N >> M >> S >> T >> U >> V;
v.assign(N + 1, vector <pair<int, int>> ());
for(int i = 0; i < M; i++)
{
int a, b, c; cin >> a >> b >> c;
v[a].push_back({ b, c });
v[b].push_back({ a, c });
}
vector <vector<int>> dist(3, vector <int> ()),
dp(N + 1, vector <int> (2, 0));
dist[0] = Dijkstra(N, S);
dist[1] = Dijkstra(N, U);
dist[2] = Dijkstra(N, V);
priority_queue <pair<int, int>> pq;
int ans = dist[1][V]; pq.push({ 0, T });
for(int i = 1; i <= N; i++)
{
dp[i][0] = dist[1][i];
dp[i][1] = dist[2][i];
}
vector <int> pass(N + 1, 0);
while(!pq.empty())
{
int x = pq.top().sd; pq.pop();
if(pass[x]) continue;
pass[x] = 1;
ans = min(ans, min(dp[x][0] + dist[2][x], dp[x][1] + dist[1][x]));
for(auto& u : v[x])
{
if(dist[0][u.fs] + u.sd == dist[0][x])
{
dp[u.fs][0] = min(dp[u.fs][0], dp[x][0]);
dp[u.fs][1] = min(dp[u.fs][1], dp[x][1]);
pq.push({ dist[0][u.fs], u.fs });
}
}
}
cout << ans << endl;
}
int32_t main()
{
ios_base::sync_with_stdio(0);
cin.tie(0);
int Q = 1; //cin >> Q;
while (Q--)
{
solve();
}
return 0;
}
