//Dost SEFEROĞLU
#include <bits/stdc++.h>
using namespace std;
#define int long long
#define pii pair<int,int>
#define ff first
#define ss second
#define sp << " " <<
#define all(cont) cont.begin(),cont.end()
#define vi vector<int>
const int MOD = 1e9+7,inf = 2e18;
const int N = 1e5+50;
int n;
vector<pii> edges[N];
vi dijkstra(int root) {
priority_queue<pii,vector<pii>,greater<pii>> pq;
vi dists(n+1,inf);
pq.push({0,root});
dists[root] = 0;
while (!pq.empty()) {
pii f = pq.top();
pq.pop();
if (dists[f.ss] < f.ff) continue;
for (auto it : edges[f.ss]) {
if (dists[it.ff] > f.ff+it.ss) {
dists[it.ff] = f.ff+it.ss;
pq.push({f.ff+it.ss,it.ff});
}
}
}
return dists;
}
void solve() {
int m;
cin >> n >> m;
int a,b,s,t;
cin >> a >> b >> s >> t;
for (int i=1;i<=m;i++) {
int a,b,c;
cin >> a >> b >> c;
edges[a].push_back({b,c});
edges[b].push_back({a,c});
}
vi da = dijkstra(a);
vi db = dijkstra(b);
using state = pair<int,pair<int,pair<pii,int>>>;
int dp[n+1][2][2][2];
for (int i=0;i<=n;i++) {
for (int j=0;j<2;j++) {
for (int jj=0;jj<2;jj++) {
for (int jjj=0;jjj<2;jjj++) {
dp[i][j][jj][jjj] = inf;
}
}
}
}
dp[s][0][0][0] = 0;
priority_queue<state,vector<state>,greater<state>> pq;
pq.push({0,{s,{{0,0},0}}});
while (!pq.empty()) {
state f = pq.top();
int city = f.ss.ff;
int cost = f.ff;
int ever = f.ss.ss.ff.ff;
int cur = f.ss.ss.ff.ss;
int dir = f.ss.ss.ss;
pq.pop();
if (dp[city][ever][cur][dir] < cost) continue;
if (!(ever && !cur)) {
for (auto& [go,w] : edges[city]) {
if ((da[city]+w+db[go]!=da[b] && db[city]+w+da[go] != da[b])) continue;
if (ever && (dir != db[go]>db[city])) continue;
if (dp[go][1][cur|1][db[go]>db[city]] > cost){
dp[go][1][cur|1][db[go]>db[city]] = cost;
pq.push({cost,{go,{{1,cur|1},db[go]>db[city]}}});
}
}
}
for (auto& [go,w] : edges[city]) {
if (dp[go][ever][0][dir] > cost+w){
dp[go][ever][0][dir] = cost+w;
pq.push({cost+w,{go,{{ever,0},dir}}});
}
}
}
int ans = inf;
for (int i=0;i<2;i++) for (int j=0;j<2;j++) for (int jj=0;jj<2;jj++) ans = min(ans,dp[t][i][j][jj]);
cout << ans << '\n';
}
signed main() {
ios_base::sync_with_stdio(0);cin.tie(0);cout.tie(0);
#ifdef Dodi
freopen("in.txt","r",stdin);
freopen("out.txt","w",stdout);
#endif
int t = 1;
//cin >> t;
while (t --> 0) solve();
}
