#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
ll N, M, S, T, U, V;
struct edge {
ll v, w;
edge() {
v = w = 0;
}
edge(ll v_, ll w_) {
v = v_;
w = w_;
}
};
vector<edge> GR[200007];
ll dist[200007], visited[200007], dist2[200007];
set<pair<ll, ll>> config;
ll dijsktra() {
for(int i = 0; i <= N; ++i) {
dist2[i] = 1e18;
visited[i] = 0;
}
struct cmp {
bool operator () (ll x1, ll x2) {
return dist2[x1] > dist2[x2];
}
};
priority_queue<ll, vector<ll>, cmp> heap;
dist2[U] = 0;
heap.push(U);
while(!heap.empty()) {
ll u = heap.top();
heap.pop();
if (visited[u]) continue;
visited[u] = 1;
for(auto tmp : GR[u]) {
ll v = tmp.v;
ll w = tmp.w;
if (config.count({u, v}) || config.count({v, u})) w = 0;
if (dist2[v] > dist2[u] + w) {
dist2[v] = dist2[u] + w;
heap.push(v);
}
}
}
return dist2[V];
}
int main() {
ios_base :: sync_with_stdio(0);
cin.tie(0); cout.tie(0); cerr.tie(0);
if (fopen("test.inp", "r")) {
freopen("test.inp", "r", stdin);
freopen("test.ans", "w", stdout);
}
cin >> N >> M >> S >> T >> U >> V;
for(int i = 1; i <= M; ++i) {
ll u, v, c;
cin >> u >> v >> c;
GR[u].push_back(edge(v, c));
GR[v].push_back(edge(u, c));
}
for(int i = 0; i <= N; ++i) dist[i] = 1e18;
dist[S] = 0;
struct cmp {
bool operator () (ll x1, ll x2) {
return dist[x1] > dist[x2];
}
};
priority_queue<ll, vector<ll>, cmp> heap;
heap.push(S);
while(!heap.empty()) {
ll u = heap.top();
heap.pop();
if (visited[u]) continue;
visited[u] = 1;
for(auto tmp : GR[u]) {
ll v = tmp.v;
ll w = tmp.w;
if (dist[v] > dist[u] + w) {
dist[v] = dist[u] + w;
heap.push(v);
}
}
}
//for(int i = 1; i <= N; ++i) cerr << dist[i] << " "; cerr << '\n';
ll ans = 1e18;
auto dfs = [&](auto&& self, ll u) {
//cerr << u << " " << dist[u] << '\n';
if (u == S) {
ans = min(ans, dijsktra());
return;
}
for(auto tmp : GR[u]) {
ll v = tmp.v;
ll w = tmp.w;
if (dist[v] == dist[u] - w) {
config.insert({u, v});
self(self, v);
config.erase({u, v});
}
}
};
dfs(dfs, T);
cout << ans;
}
