#include <bits/stdc++.h>
#define ll long long
#define pii pair<int, int>
#define piii pair<int, pii>
#define endl '\n'
#define int ll
using namespace std;
const int INF = 1e9*2e6 + 100;
struct node {
int v, w, dw, x;
};
class Compare {
public:
bool operator()(node &a, node &b)
{
if(a.w == b.w) return a.dw > b.dw;
return a.w > b.w;
}
};
signed main() {
ios_base::sync_with_stdio(0);
cin.tie(0);
int N, M;
cin >> N >> M;
int S, T, U, V;
cin >> S >> T >> U >> V;
--S; --T; --U; --V;
vector<vector<pii>> graph(N);
for(int i = 0; i < M; i++) {
int a, b, c;
cin >> a >> b >> c;
--a; --b;
graph[a].push_back({b, c});
graph[b].push_back({a, c});
}
auto dijkstra = [graph](int S, vector<int> &dist) {
priority_queue<pii, vector<pii>, greater<pii>> pq;
pq.push({0, S});
dist[S] = 0;
while(!pq.empty()) {
int w, v;
tie(w, v) = pq.top(); pq.pop();
for(pii u : graph[v]) {
if(dist[u.first] > w + u.second) {
dist[u.first] = w + u.second;
pq.push({dist[u.first], u.first});
}
}
}
};
vector<int> distV(N, INF), distU(N, INF);
dijkstra(V, distV); dijkstra(U, distU);
vector<vector<pii>> dist(N, vector<pii>(1LL << 2, {INF, INF}));
dist[S][0] = {0, 0};
priority_queue<node, vector<node>, Compare> pq;
pq.push({S, 0, 0, 0});
while(!pq.empty()) {
int v = pq.top().v, w = pq.top().w, dw = pq.top().dw, x = pq.top().x;
pq.pop();
// go to state 1
if(!(x & 1) && (dist[v][x | 1].first > w || (dist[v][x | 1].first == w && dist[v][x | 1].second > dw + distU[v]))) {
dist[v][x | 1] = {w, dw + distU[v]};
pq.push({v, w, dw + distU[v], x|1});
}
// go to state 2
if(!(x & 2) && (dist[v][x | 2].first > w || (dist[v][x | 2].first == w && dist[v][x | 2].second > dw + distV[v]))) {
dist[v][x | 2] = {w, dw + distV[v]};
pq.push({v, w, dw + distV[v], x|2});
}
for(pii u : graph[v]) {
if((dist[u.first][x].first > w + u.second) || (dist[u.first][x].first == w + u.second && dist[u.first][x].second > dw)) {
dist[u.first][x] = {w + u.second, dw};
pq.push({u.first, w + u.second, dw, x});
}
}
}
cout << min(distV[U], dist[T][3].second) << endl;
}
