/*
in the name of god
created by: mohammadsam
*/
#include <bits/stdc++.h>
using namespace std;
#define int long long
typedef pair<int,int> pii;
typedef pair<long long ,long long> pll;
typedef long long ll ;
#define min_heap(X) priority_queue<X,vector<X>,greater<X>>
#define max_heap(X) priority_queue<X>
#define File freopen("input.txt", "r", stdin); freopen("output.txt", "w", stdout);
#define loop(i,f,d) for(int i = f;i<d;i++)
#define loop2(j,f,d) for(int j = f;j>=d;j--)
#define len(V) V.size()
#define sep ' '
#define endl '\n'
#define pb(x) push_back(x)
#define debug(x) cerr << "bug " << x << endl;
#define migmig cin.tie(NULL);ios_base::sync_with_stdio(false);
#define fi first
#define sec second
#define popcount(x) __builtin_popcount(x)
#define md(x) (((x%MD)+MD)%MD)
#define all(V) V.begin(),V.end()
#define Mp(a,b) make_pair(a,b)
#define gaws(a,b) (((b-a+1LL)*(a+b))/2LL)
#define vvi vector<vector<int>>
#define setprec(x) fixed << setprecision(x)
const ll N = 2e5 + 100, MD = 1e9 + 7;
const ll inf = 1e17 , riz = -2e9;
int n , m , s, t , u ,v;
vector<pii> g[N];
int dis2[2][N],dp[2][N],dis[2][N];
min_heap(pii) pq;
int ans = inf;
void dij(int u,int p){
fill(dis2[p],dis2[p]+n+1,inf);
dis2[p][u] = 0;
pq.push(Mp(0,u));
while(!pq.empty()){
auto [d,u] = pq.top();pq.pop();
if(d!=dis2[p][u]) continue;
for(auto [h,w] : g[u]){
if(dis2[p][h] > dis2[p][u] + w){
dis2[p][h] = dis2[p][u] + w;
pq.push(Mp(dis2[p][h],h));
}
}
}
}
void dij2(int u,int ind,int p=1){
fill(dis[ind],dis[ind]+n+1,inf);
loop(i,1,n+1) dp[ind][i] = dis2[p][i];
dis[ind][u] = 0 ;
pq.push(Mp(0,u));
while(!pq.empty()){
auto [d,u] = pq.top();pq.pop();
if(dis[ind][u] != d) continue;
for(auto [h,w] : g[u]){
if(dis[ind][h] > dis[ind][u] + w){
dis[ind][h] = dis[ind][u] + w;
dp[ind][h] = min(dp[ind][h],dp[ind][u]);
pq.push(Mp(dis[ind][h],h));
}
}
}
}
int32_t main() {
migmig
cin >> n >> m >> s >> t >> u >> v;
loop(i,0,m){
int a,b,w;
cin >> a >> b >> w;
g[a].pb(Mp(b,w));
g[b].pb(Mp(a,w));
}
dij(u,0);
dij(v,1);
dij2(s,0);
dij2(t,1);
//cout<<"---" << endl;
//cout << dp[0][1] << endl;
loop(i,1,n+1){
if(dis[0][i] + dis[1][i] == dis[0][t]){
ans = min(ans,dis2[0][i]+min(dp[0][i],dp[1][i]));
//cout << i << sep << ans << sep << dis2[1][i] << sep << dp[0][i] << endl;
}
}
cout << min(ans,dis2[0][v]) << endl;
return 0;
}
