#include <bits/stdc++.h>
#define fastio ios_base::sync_with_stdio(false); cin.tie(NULL); cout.tie(NULL)
#define debug(x) cout << "Line " << __LINE__ << ", " << #x << " is " << x << endl
#define all(x) x.begin(), x.end()
#define fi first
#define se second
#define mp make_pair
#define pb push_back
#define ll long long
#define ull unsigned long long
#define pll pair<ll, ll>
#define pii pair<int, int>
#define ld long double
#define nl endl
#define tb '\t'
#define sp ' '
#define sqr(x) (x)*(x)
#define arr3 array<int, 3>
using namespace std;
const int MX=100005, MOD=1000000007, BLOCK=160, INF=2e9+7, LG=62;
const ll INFF=1000000000000000007;
const ld ERR=1e-6, pi=3.14159265358979323846;
int N, M, S, T, U, V, st[4];
ll dist[4][MX], ans=INFF, vis[2][MX];
vector<pll> adj[MX];
bool valid(int x, int y, ll v=0){
return (dist[0][x]+v+dist[1][y]==dist[0][T]);
}
ll DP(int x, int dir){
ll &ret=vis[dir][x];
if(ret==-1){
ret=dist[3][x];
for(pll i:adj[x]){
if(dir){
if(valid(x, i.fi, i.se))
ret=min(ret, DP(i.fi, dir));
}else{
if(valid(i.fi, x, i.se))
ret=min(ret, DP(i.fi, dir));
}
}
}
return ret;
}
int main(){
fastio;
memset(vis, -1, sizeof(vis));
cin >> N >> M >> S >> T >> U >> V;
st[0]=S;
st[1]=T;
st[2]=U;
st[3]=V;
for(int i=0, u, v, w; i<M; i++){
cin >> u >> v >> w;
adj[u].pb({v, w});
adj[v].pb({u, w});
}
for(int ii=0; ii<4; ii++){
priority_queue<pll, vector<pll>, greater<pll>> PQ;
PQ.push({0, st[ii]});
for(int i=0; i<=N; i++)
dist[ii][i]=INFF;
dist[ii][st[ii]]=0;
while(PQ.size()){
ll idx=PQ.top().se, cost=PQ.top().fi;
PQ.pop();
if(cost>dist[ii][idx])
continue;
for(pll i:adj[idx]){
if(cost+i.se<dist[ii][i.fi]){
dist[ii][i.fi]=cost+i.se;
PQ.push({dist[ii][i.fi], i.fi});
}
}
}
}
ans=dist[2][V];
vis[0][V]=vis[1][V]=0;
for(int i=1; i<=N; i++){
if(valid(i, i)){
ans=min(ans, dist[2][i]+min(DP(i, 1), DP(i, 0)));
}
}
cout << ans << nl;
}
