#include<bits/stdc++.h>
using namespace std;
using i64 = long long;
#define debug false
void SETIO(string name)
{
if (name=="") return;
freopen((name + ".inp").c_str(),"r",stdin);
freopen((name + ".out").c_str(),"w",stdout);
return;
}
const int maxn = 2e5;
const i64 INF = 1e18;
vector<pair<int,int>> g[maxn+2];
int u[maxn+2],v[maxn+2],c[maxn+2];
#define fi first
#define se second
int n , m , source , sink , nsource , nsink;
struct _D
{
i64 val;
i64 rem;
int u;
int t;
bool operator <(const _D & other) const {
if (other.val != val) return other.val < val;
if (other.rem != rem) return other.rem < rem;
}
} ;
bool vis[maxn+2][2];
vector<i64> dist[2];
i64 dp[maxn+2][2];
i64 mn ;
vector<i64> djisktra(int source)
{
vector<i64> d; d.assign(n+2,INF);
d[source] = 0;
priority_queue<pair<i64,int>,vector<pair<i64,int>>,greater<pair<i64,int>>> q;
q.push({d[source] , source});
while (q.size())
{
int u = q.top().se;
i64 val = q.top().fi;
q.pop();
if (d[u] != val) continue;
for (auto& v : g[u])
{
if (d[v.first] > d[u] + v.second)
{
d[v.first] = d[u] + v.second;
q.push({d[v.first] , v.first});
}
}
}
return d;
}
int trans(int v , int t , int t1 , int t2){
if (t==1) return t;
if (t==0){
if (dist[t1][v] + dist[t2][v] == mn) return 1;
}
return 0;
}
i64 cost(int v , int w , i64 rem , int t , int t1 , int t2){
if (t==0){
if (dist[t1][v] + dist[t2][v] == mn) return 0;
return w;
}
if (t==1){
if (rem==INF) return w;
if (dist[t1][v] + dist[t2][v] == mn && rem + w == dist[t1][v]) return 0;
return w;
}
return INF;
}
i64 calc(int s , int snk , int t1 , int t2)
{
memset(vis,0,sizeof vis);
memset(dp,0x3f,sizeof dp);
priority_queue<_D> q; int zz = trans(s,0,t1,t2);
dp[s][zz] = 0;
if (zz==1) q.push({dp[s][zz] , dist[t1][s] , s , 1});
else q.push({dp[s][zz] , INF , s , 0});
if (debug){
cout << "START THE SEASON\n";
cout << t1 << ' ' << t2 << '\n';
}
while (q.size()){
int u = q.top().u , t = q.top().t;
i64 val = q.top().val , rem = q.top().rem;
q.pop();
if (vis[u][t]) continue;
vis[u][t]=true;
dp[u][t]=val;
if (debug){
cout << "DEBUG\n";
cout << dp[u][t] << ' ' << u << ' ' << t << '\n';
}
for (auto& v : g[u]){
int to = v.first , w = v.second;
int nxt = trans(to , t , t1 , t2);
if (vis[to][nxt]) continue;
i64 c = cost(to , w , rem , t , t1 , t2);
if (debug){
cout << "( SHOW OUT FOR THE CASE : " << u << ')' << '\n';
cout << u << " -> " << to << ' ' << w << ' ' << nxt << ' ' << c << '\n';
cout << dist[t1][to] << ' ' << dist[t2][to] << ' ' << mn << '\n';
cout << '\n';
}
if (t == 0){
if (nxt==0) q.push({val + w , INF , to , 0});
else q.push({val + w , dist[t1][to] , to , 1});
}
if (t == 1){
if (c > 0) q.push({val + w , INF , to , 1});
else q.push({val , dist[t1][to] , to , 1});
}
}
}
return min(dp[snk][0],dp[snk][1]);
}
int main()
{
ios::sync_with_stdio(false);
cin.tie(0); cout.tie(0);
SETIO("");
cin >> n >> m;
cin >> source >> sink;
cin >> nsource >> nsink;
for (int i = 1; i <= m; ++i){
cin >> u[i] >> v[i] >> c[i];
g[u[i]].push_back({v[i],c[i]});
g[v[i]].push_back({u[i],c[i]});
}
dist[0] = djisktra(source);
dist[1] = djisktra(sink);
mn = dist[0][sink];
if (debug){
cout << "MINIMUM DIST : " << mn << '\n';
}
cout << min({calc(nsource,nsink,0,1),calc(nsource , nsink,1,0),calc(nsink,nsource,0,1),calc(nsink,nsource,1,0)});
}
