#include <bits/stdc++.h>
using namespace std;
#define ll long long
int N, M, S, T, U, V;
ll distS[100005], distT[100005], distU[100005], distV[100005];
vector<pair<int,ll>> path[100005];
vector<int> adj1[100005], adj2[100005];
ll dp1[100005], dp2[100005];
vector<tuple<int,int,ll>> Edge;
priority_queue<pair<ll,int>, vector<pair<ll,int>>, greater<pair<ll,int>>> pq;
void dfs1(int u, int pa) {
dp1[u] = min({dp1[u], distU[u], dp1[pa]});
dp2[u] = min({dp2[u], dp1[u] + distV[u], dp2[pa]});
for (auto v : adj1[u]) {
dfs1(v, u);
}
}
void dfs2(int u, int pa) {
dp1[u] = min({dp1[u], distU[u], dp1[pa]});
dp2[u] = min({dp2[u], dp1[u] + distV[u], dp2[pa]});
for (auto v : adj2[u]) {
dfs2(v, u);
}
}
int main() {
ios_base::sync_with_stdio(0), cin.tie(0);
cin >> N >> M >> S >> T >> U >> V;
for (int i = 0; i < 100005; i++) {
distS[i] = 1e18;
distT[i] = 1e18;
distU[i] = 1e18;
distV[i] = 1e18;
}
for (int i = 0; i < M; i++) {
int u, v, w;
cin >> u >> v >> w;
path[u].emplace_back(v, w);
path[v].emplace_back(u, w);
Edge.emplace_back(u, v, w);
}
// calc distS
distS[S] = 0;
pq.emplace(0, S);
while (!pq.empty()) {
auto [w, u] = pq.top();
pq.pop();
if (distS[u] < w) continue;
distS[u] = w;
for (auto [v, ww] : path[u]) {
if (distS[v] <= w + ww) continue;
distS[v] = w + ww;
pq.emplace(w + ww, v);
}
}
// calc distT
distT[T] = 0;
pq.emplace(0, T);
while (!pq.empty()) {
auto [w, u] = pq.top();
pq.pop();
if (distT[u] < w) continue;
distT[u] = w;
for (auto [v, ww] : path[u]) {
if (distT[v] <= w + ww) continue;
distT[v] = w + ww;
pq.emplace(w + ww, v);
}
}
// calc distU
distU[U] = 0;
pq.emplace(0, U);
while (!pq.empty()) {
auto [w, u] = pq.top();
pq.pop();
if (distU[u] < w) continue;
distU[u] = w;
for (auto [v, ww] : path[u]) {
if (distU[v] <= w + ww) continue;
distU[v] = w + ww;
pq.emplace(w + ww, v);
}
}
// calc distV
distV[V] = 0;
pq.emplace(0, V);
while (!pq.empty()) {
auto [w, u] = pq.top();
pq.pop();
if (distV[u] < w) continue;
distV[u] = w;
for (auto [v, ww] : path[u]) {
if (distV[v] <= w + ww) continue;
distV[v] = w + ww;
pq.emplace(w + ww, v);
}
}
ll min_dist = distS[T];
for (auto [u, v, w] : Edge) {
if (distS[v] + w + distT[u] == min_dist) {
adj1[v].emplace_back(u);
adj2[u].emplace_back(v);
}
if (distS[u] + w + distT[v] == min_dist) {
adj2[v].emplace_back(u);
adj1[u].emplace_back(v);
}
}
ll ans = distU[V];
// process adj1
fill(dp1, dp1 + 100005, 1e18);
fill(dp2, dp2 + 100005, 1e18);
dfs1(S, 0);
ans = min(dp2[T], ans);
// process adj2
fill(dp1, dp1 + 100005, 1e18);
fill(dp2, dp2 + 100005, 1e18);
dfs2(T, 0);
ans = min(dp2[S], ans);
cout << ans;
}
