#include<bits/stdc++.h>
#define ll long long
#define ld long double
#define fs first
#define sc second
using namespace std;
typedef pair<ll,ll> LL;
const ll N = 2e5 + 9;
const ll inf = 1e16 + 7;
struct Edge{
ll u,v,w;
};
Edge a[N];
ll S,T,U,V,n,m,u,v,w,d[N],D[2][N],dp[N][5];
vector<LL> g[N];
void Dij(ll scr,ll cond){
fill(d,d + n + 1,inf); d[scr] = 0;
priority_queue<LL,vector<LL>,greater<LL>> pq; pq.push({0,scr});
while(!pq.empty()){
LL t = pq.top(); pq.pop();
ll u = t.sc;
for (auto i : g[u]){
ll v = i.fs,L = i.sc;
if (d[v] > d[u] + L) d[v] = d[u] + L,pq.push({d[v],v});
}
}
for (ll i = 1;i <= n;i++) D[cond][i] = d[i];
}
bool Is_in(ll u,ll v,ll w){
ll lens = D[0][T];
if (D[0][u] + D[1][v] + w == lens||D[0][v] + D[1][u] + w == lens) return 1;
return 0;
}
bool direct(ll u,ll v){
return (D[0][u] < D[0][v]);
}
struct Node{
ll val,cur,cond;
};
bool operator < (Node a,Node b){
return a.val > b.val;
}
priority_queue<Node> pq;
void update(ll u,ll cond,ll val){
if (dp[u][cond] <= val) return;
dp[u][cond] = val; pq.push({val,u,cond});
}
/// 0 not in 1 in but small -> big 2 in but big -> small 3 out
void Find_opt(ll scr){
for (ll i = 1;i <= n;i++)
for (ll j = 0;j < 5;j++) dp[i][j] = inf;
dp[scr][0] = 0; pq.push({0,scr,0});
while(!pq.empty()){
Node t = pq.top(); pq.pop();
ll u = t.cur,now = t.cond;
for (auto i : g[u]){
ll v = i.fs,L = i.sc;
if (Is_in(u,v,L)){
if (!now){
if (direct(u,v)) update(v,1,dp[u][now]);
else update(v,2,dp[u][now]);
}
if (now == 1 && direct(u,v)) update(v,1,dp[u][now]);
if (now == 2 && !direct(u,v)) update(v,2,dp[u][now]);
}
ll nxt = now;
if (now == 1 || now == 2) nxt = 3;
if (dp[v][nxt] > dp[u][now] + L) dp[v][nxt] = dp[u][now] + L,pq.push({dp[v][nxt],v,nxt});
}
}
//cout<<direct(3,2); exit(0);
//cout<<dp[4][0]<<" "<<dp[1][1]<<" "<<dp[4][2]<<" "<<dp[4][3]; exit(0);
cout<<min(min(dp[V][0],min(dp[V][1],dp[V][2])),dp[V][3]);
}
int main(){
ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0);
#define task "tst"
if (fopen(task".inp","r")){
freopen(task".inp","r",stdin);
//freopen(task".out","w",stdout);
}
cin>>n>>m>>S>>T>>U>>V;
for (ll i = 1;i <= m;i++){
cin>>u>>v>>w; a[i] = {u,v,w};
g[u].push_back({v,w}); g[v].push_back({u,w});
}
Dij(S,0); Dij(T,1); Find_opt(U);
}
