#include<bits/stdc++.h>
using namespace std;
#define ll long long
#define pii pair<ll, int>
#define fi first
#define se second
const int ar = 1e5 + 5;
int n, m, u, v, s, t;
ll dp[ar][2], dis[ar][2], d[ar];
vector<pii> adj[ar];
ll ans = 1e18;
void dijktra(int u, int c) {
priority_queue<pii, vector<pii>, greater<pii>> q;
q.push({0, u});
dp[u][c] = 0;
while(q.size()) {
int vt = q.top().se; ll kc = q.top().fi; q.pop();
if(kc > dp[vt][c]) continue;
for(auto x : adj[vt]) {
if(dp[x.se][c] > dp[vt][c] + x.fi) {
dp[x.se][c] = dp[vt][c] + x.fi;
q.push({dp[x.se][c], x.se});
}
}
}
}
void dijktra2(int u) {
memset(dis, 0x3f, sizeof(dis));
memset(d, 0x3f, sizeof(d));
priority_queue<pii, vector<pii>, greater<pii>> q;
q.push({0, u});
dis[u][0] = dp[u][0];
dis[u][1] = dp[u][1];
d[u] = 0;
while(q.size()) {
int vt = q.top().se, pa = q.top().se; ll kc = q.top().fi; q.pop();
if(kc > d[vt]) continue;
for(auto x : adj[vt]) {
if(d[x.se] > d[vt] + x.fi) {
d[x.se] = d[vt] + x.fi;
dis[x.se][0] = min(dp[x.se][0], dis[vt][0]);
dis[x.se][1] = min(dp[x.se][1], dis[vt][1]);
q.push({d[x.se], x.se});
}
else if(d[x.se] == d[vt] + x.fi) {
if(min(dp[x.se][0], dis[vt][0]) + min(dp[x.se][1], dis[vt][1]) <= dis[x.se][0] + dis[x.se][1]) {
dis[x.se][0] = min(dp[x.se][0], dis[vt][0]);
dis[x.se][1] = min(dp[x.se][1], dis[vt][1]);
}
}
}
}
}
int main() {
ios::sync_with_stdio(0);
cin.tie(0); cout.tie(0);
cin >> n >> m >> s >> t >> u >> v;
for(int i = 1; i <= m; ++i) {
int x, y, w; cin >> x >> y >> w;
adj[x].push_back({w, y});
adj[y].push_back({w, x});
}
memset(dp, 0x3f, sizeof(dp));
dijktra(u, 0);
dijktra(v, 1);
ans = dp[v][0];
dijktra2(s);
ans = min(ans, dis[t][0] + dis[t][1]);
dijktra2(t);
ans = min(ans, dis[s][0] + dis[s][1]);
cout << ans;
}
