#include <bits/stdc++.h>
#define N 1000000
#define fi first
#define se second
#define pb push_back
#define mp make_pair
#define int long long
#define rep(i, l, r) for(int i = l; i <= r; i++)
#define reprev(i, l, r) for(int i = l; i >= r; i--)
using namespace std;
typedef pair<int,int> i2;
typedef pair<i2,int> i3;
typedef pair<i2, i2> i4;
const int INF = 1e18;
const int MOD = 1e9 + 7;
int n, m, s, t, x, y;
int dp[N+5][2], dpu[N+5];
i3 edge[N+5];
vector<i2> g[N+5], g2[N+5];
void dijkstra(int start, int oper){
rep(i, 1, n) dp[i][oper] = INF;
priority_queue<i2, vector<i2>, greater<i2>> heap;
dp[start][oper] = 0;
heap.push(mp(0, start));
while (heap.size()){
i2 cur = heap.top(); heap.pop();
if (cur.fi > dp[cur.se][oper]) continue;
int u = cur.se;
for(auto p: g[u]){
int v = p.fi, w = p.se;
if (dp[v][oper] > cur.fi + w){
dp[v][oper] = cur.fi + w;
heap.push(mp(dp[v][oper], v));
}
}
}
}
void dijkstra_u(){
rep(i, 1, n) dpu[i] = INF;
priority_queue<i2, vector<i2>, greater<i2>> heap;
dpu[x] = 0;
heap.push(mp(0, x));
while (heap.size()){
i2 cur = heap.top(); heap.pop();
if (cur.fi > dpu[cur.se]) continue;
int u = cur.se;
for(auto p: g2[u]){
int v = p.fi, w = p.se;
if (dpu[v] > cur.fi + w){
dpu[v] = cur.fi + w;
heap.push(mp(dpu[v], v));
}
}
}
}
void solve(){
cin >> n >> m >> s >> t >> x >> y;
rep(i, 1, m) {
cin >> edge[i].fi.fi >> edge[i].fi.se >> edge[i].se;
g[edge[i].fi.fi].pb(mp(edge[i].fi.se, edge[i].se));
g[edge[i].fi.se].pb(mp(edge[i].fi.fi, edge[i].se));
}
dijkstra(s, 0);
dijkstra(t, 1);
rep(i, 1, m){
int u = edge[i].fi.fi, v = edge[i].fi.se, w = edge[i].se;
if (dp[u][0] + dp[v][1] + w == dp[t][0] || dp[u][1] + dp[v][0] + w == dp[t][0]){
g2[u].pb({v, 0});
g2[v].pb({u, 0});
} else {
g2[u].pb({v, w});
g2[v].pb({u, w});
}
}
dijkstra_u();
cout << dpu[y];
}
signed main(){
ios_base::sync_with_stdio(0);
cin.tie(0);
solve();
}
