#include <bits/stdc++.h>
using namespace std;
#define EmiliaMyWife ios::sync_with_stdio(0); cin.tie(0);
using ll = int64_t;
using uint = uint32_t;
using ull = uint64_t;
using ld = long double;
const int INF = 0x3f3f3f3f;
const int MOD = 1e9 + 7;
const double EPS = 1e-8;
const ll LINF = ll(4e18) + ll(2e15);
static int LamyIsCute = []() {
EmiliaMyWife
return 48763;
}();
signed main() {
int n, m, s, t, a, b;
cin >> n >> m >> s >> t >> a >> b;
vector<vector<pair<int, int>>> edge(n + 1);
while(m--) {
int u, v, c;
cin >> u >> v >> c;
edge[u].push_back({v, c});
edge[v].push_back({u, c});
}
auto dijk = [&](vector<ll> &dis, int st) {
dis.resize(n + 1, LINF);
dis[st] = 0;
priority_queue<pair<ll, int>, vector<pair<ll, int>>, greater<pair<ll, int>>> pq;
pq.push({0, st});
while(!pq.empty()) {
auto [d, u] = pq.top();
pq.pop();
if(d > dis[u])
continue;
for(const auto &[v, c] : edge[u])
if(dis[v] > dis[u] + c)
dis[v] = dis[u] + c, pq.push({dis[v], v});
}
};
vector<ll> diss, dist;
dijk(diss, s);
dijk(dist, t);
const ll mn = diss[t];
vector<array<ll, 4>> ans(n + 1, {LINF, LINF, LINF, LINF});
ans[a][0] = 0;
priority_queue<tuple<ll, int, int>, vector<tuple<ll, int, int>>, greater<tuple<ll, int, int>>> pq;
pq.push({0, a, 0});
while(!pq.empty()) {
auto [d, u, w] = pq.top();
pq.pop();
if(d > ans[u][w])
continue;
//cerr << "xdd " << u << ' ' << w << ' ' << d << '\n';
//cerr << "owo " << u << ' ' << diss[u] << ' ' << dist[u] << '\n';
for(const auto &[v, c] : edge[u]) {
if((w == 0 || w == 3) && ans[v][w] > ans[u][w] + c) {
ans[v][w] = ans[u][w] + c;
pq.push({ans[v][w], v, w});
}
if((w == 1 || w == 2) && ans[v][3] > ans[u][w] + c) {
ans[v][3] = ans[u][w] + c;
pq.push({ans[v][3], v, 3});
}
if((w == 0 || w == 1) && diss[u] + dist[u] == mn && diss[v] + dist[v] == mn && diss[v] - diss[u] == c) {
if(ans[v][1] > ans[u][w]) {
ans[v][1] = ans[u][w];
pq.push({ans[v][1], v, 1});
}
}
if((w == 0 || w == 2) && diss[u] + dist[u] == mn && diss[v] + dist[v] == mn && diss[u] - diss[v] == c) {
if(ans[v][2] > ans[u][w]) {
ans[v][2] = ans[u][w];
pq.push({ans[v][2], v, 2});
}
}
}
}
cout << min({ans[b][0], ans[b][1], ans[b][2], ans[b][3]}) << '\n';
}
