#include <bits/stdc++.h>
using namespace std;
using ll = long long;
struct A {
int v;
ll w;
int p;
bool operator < (const A& o) const {
return w > o.w;
}
};
vector<A> adj[100100];
priority_queue<A> pq;
ll disu[100100], disv[100100], dis[100100];
ll dp[2][100100];
bool vis[100100];
int main() {
cin.tie(nullptr)->sync_with_stdio(false);
memset(disu, 0x3f, sizeof disu);
memset(disv, 0x3f, sizeof disv);
int n, m;
cin >> n >> m;
int s, t, u, v;
cin >> s >> t >> u >> v;
while (m--) {
int u, v;
ll w;
cin >> u >> v >> w;
adj[u].push_back({ v,w });
adj[v].push_back({ u,w });
}
disu[u] = 0;
pq.push({ u,0 });
while (!pq.empty()) {
auto x = pq.top();
pq.pop();
int v = x.v;
ll w = x.w;
for (auto& x : adj[v]) {
if (disu[x.v] > w + x.w) {
disu[x.v] = w + x.w;
pq.push({ x.v,disu[x.v] });
}
}
}
disv[v] = 0;
pq.push({ v,0 });
while (!pq.empty()) {
auto x = pq.top();
pq.pop();
int v = x.v;
ll w = x.w;
for (auto& x : adj[v]) {
if (disv[x.v] > w + x.w) {
disv[x.v] = w + x.w;
pq.push({ x.v,disv[x.v] });
}
}
}
ll ans = disu[v];
memset(dis, 0x3f, sizeof dis);
memset(dp, 0x3f, sizeof dp);
pq.push({ s,0,0 });
while (!pq.empty()) {
auto x = pq.top();
pq.pop();
int v = x.v, p = x.p;
ll w = x.w;
if (!vis[v]) {
vis[v] = 1;
dis[v] = w;
dp[0][v] = min(disv[v], dp[0][p]);
dp[1][v] = min(disu[v], dp[1][p]);
for (auto& x : adj[v]) {
pq.push({ x.v, w + x.w, v });
}
}
else if (w == dis[v]) {
if (dp[0][v] + dp[1][v] > min(disv[v], dp[0][p]) + min(disu[v], dp[1][p])) {
dp[0][v] = min(disv[v], dp[0][p]);
dp[1][v] = min(disu[v], dp[1][p]);
}
}
}
ans = min(ans, dp[0][t] + dp[1][t]);
memset(dis, 0x3f, sizeof dis);
memset(dp, 0x3f, sizeof dp);
memset(vis, 0, sizeof vis);
pq.push({ t,0,0 });
while (!pq.empty()) {
auto x = pq.top();
pq.pop();
int v = x.v, p = x.p;
ll w = x.w;
if (!vis[v]) {
vis[v] = 1;
dis[v] = w;
dp[0][v] = min(disv[v], dp[0][p]);
dp[1][v] = min(disu[v], dp[1][p]);
for (auto& x : adj[v]) {
pq.push({ x.v, w + x.w, v });
}
}
else if (w == dis[v]) {
if (dp[0][v] + dp[1][v] > min(disv[v], dp[0][p]) + min(disu[v], dp[1][p])) {
dp[0][v] = min(disv[v], dp[0][p]);
dp[1][v] = min(disu[v], dp[1][p]);
}
}
}
ans = min(ans, dp[0][s] + dp[1][s]);
cout << ans;
return 0;
}
