#include <bits/stdc++.h>
#define all(v) begin(v), end(v)
#define ii pair<int, int>
#define fi first
#define se second
#define siz(v) (int)(v).size()
#define BIT(x, i) (((x) >> (i)) & 1)
#define MASK(i) (1LL << (i))
#define lli pair<long long, int>
using namespace std;
template<class X, class Y> bool minimize(X &x, const Y &y){return x > y ? x = y, 1: 0;}
template<class X, class Y> bool maximize(X &x, const Y &y){return x < y ? x = y, 1: 0;}
const int infINT = 1e9 + 243, MAXN = 1e5 + 5, mod = 20240131;
const long long inf = 1e18 + 234;
void add(int &a, const int &b){
a += b;
if (a >= mod) a -= mod;
}
int mul(const int &a, const int &b){
return 1LL * a * 1LL * b % mod;
}
struct E{
int u, v, w;
E (int _u = 0, int _v = 0, int _w = 0):
u(_u), v(_v), w(_w) {};
};
int numNode, numEdge, S, T, U, V, in[MAXN], preIn[MAXN];
long long distS[MAXN], distT[MAXN], distU[MAXN], distV[MAXN], res, dp[MAXN];
vector<ii> adj[MAXN];
vector<int> g[MAXN];
E edge[MAXN << 1];
void input(){
cin >> numNode >> numEdge;
cin >> S >> T >> U >> V;
for(int i = 1; i <= numEdge; i++){
int u, v, w; cin >> u >> v >> w;
adj[u].emplace_back(v, w);
adj[v].emplace_back(u, w);
edge[i] = E(u, v, w);
}
}
#define PUSH(u, d) if (minimize(dist[u], d)) q.push(lli(d, u))
void dijsktra(const int &sta, long long dist[MAXN]){
memset(dist, 0x3f, (numNode + 1) * sizeof(long long));
priority_queue<lli, vector<lli>, greater<lli> > q;
PUSH(sta, 0);
while(q.size()){
long long len = q.top().fi;
int u = q.top().se;
q.pop();
if (len > dist[u]) continue;
for(ii x: adj[u]){
int v = x.fi, w = x.se;
PUSH(v, dist[u] + w);
}
}
}
void addEdge(int u, int v){
g[u].push_back(v);
in[v]++;
}
void bfs(long long distU[MAXN], long long distV[MAXN]){
queue<int> q;
for(int i = 1; i <= numNode; i++) if (!in[i]) q.push(i);
while(q.size()){
int u = q.front();
minimize(dp[u], distU[u]);
q.pop();
minimize(res, dp[u] + distV[u]);
for(int v: g[u]){
minimize(dp[v], dp[u]);
if (--in[v] == 0) q.push(v);
}
}
}
void solve(){
dijsktra(S, distS);
dijsktra(T, distT);
dijsktra(U, distU);
dijsktra(V, distV);
res = distV[U];
for(int i = 1; i <= numEdge; i++){
int u = edge[i].u, v = edge[i].v, w = edge[i].w;
if (distS[u] + w + distT[v] == distT[S]) addEdge(u, v);
else if (distS[v] + w + distT[u] == distT[S]) addEdge(v, u);
}
for(int i = 1; i <= numNode; i++) preIn[i] = in[i];
memset(dp, 0x3f, sizeof dp);
bfs(distU, distV);
for(int i = 1; i <= numNode; i++) in[i] = preIn[i];
memset(dp, 0x3f, sizeof dp);
bfs(distV, distU);
cout << res << '\n';
}
signed main(){
ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0);
#define task "test"
if (fopen(task".inp", "r")){
freopen(task".inp", "r", stdin);
freopen(task".out", "w", stdout);
}
input();
solve();
}
