#include <bits/stdc++.h>
using namespace std;
using ll = long long;
vector<pair<int, int>> adj[100001];
void dijkstra(int X, auto& minCostX)
{
using E = pair<ll, int>;
priority_queue<E, vector<E>, greater<E>> q;
q.push({0, X});
while (!q.empty())
{
auto [cost, node] = q.top();
q.pop();
if (cost != minCostX[node])
continue;
for (auto [i, x] : adj[node])
{
if (cost + x < minCostX[i])
q.push({minCostX[i] = cost + x, i});
}
}
}
int main()
{
cin.tie(NULL) -> sync_with_stdio(false);
int N, M, S, T, U, V;
cin >> N >> M >> S >> T >> U >> V;
vector<ll> minCostS(N + 1, LLONG_MAX), minCostU(N + 1, LLONG_MAX), minCostV(N + 1, LLONG_MAX);
minCostS[S] = minCostU[U] = minCostV[V] = 0;
while (M--)
{
int a, b, x;
cin >> a >> b >> x;
adj[a].push_back({b, x});
adj[b].push_back({a, x});
}
dijkstra(S, minCostS);
dijkstra(U, minCostU);
dijkstra(V, minCostV);
vector<bool> visited(N + 1);
queue<int> q;
q.push(T);
vector<vector<int>> DAG(N + 1), rDAG(N + 1);
vector<int> indegree(N + 1), rIndegree(N + 1);
while (!q.empty())
{
int node = q.front();
q.pop();
for (auto [i, x] : adj[node])
if (minCostS[i] + x == minCostS[node])
{
if (!visited[i])
q.push(i), visited[i] = true;
DAG[i].push_back(node), rDAG[node].push_back(i);
++indegree[node], ++rIndegree[i];
}
}
vector<ll> RminU = minCostU;
vector<ll> RminV = minCostV;
q.push(T);
while (!q.empty())
{
int node = q.front();
q.pop();
for (auto i : rDAG[node])
{
if (--rIndegree[i] == 0)
q.push(i);
RminU[i] = min(RminU[i], RminU[node]);
RminV[i] = min(RminV[i], RminV[node]);
}
}
ll ans = LLONG_MAX;
q.push(S);
while (!q.empty())
{
int node = q.front();
q.pop();
ans = min(ans, minCostU[node] + RminV[node]);
ans = min(ans, minCostV[node] + RminU[node]);
for (auto i : DAG[node])
{
if (--indegree[i] == 0)
q.push(i);
minCostU[i] = min(minCostU[i], minCostU[node]);
minCostV[i] = min(minCostV[i], minCostV[node]);
}
}
cout << min(minCostU[V], ans) << endl;
return 0;
}
/* stuff you should look for
* int overflow, array bounds
* special cases (n=1?)
* do smth instead of nothing and stay organized
* WRITE STUFF DOWN
* DON'T GET STUCK ON ONE APPROACH
*/
