#include <bits/stdc++.h>
using namespace std;
#define FOR(i, j, k) for(int i=(j); i<=(k); i++)
#define FFOR(i, j, k) for(int i=(j); i<(k); i++)
#define DFOR(i, j, k) for(int i=(j); i>=(k); i--)
#define bug(x) cerr<<#x<<" = "<<(x)<<'\n'
#define pb push_back
#define mp make_pair
#define bit(s, i) (((s)>>(i))&1LL)
#define mask(i) ((1LL<<(i)))
#define builtin_popcount __builtin_popcountll
#define __builtin_popcount __builtin_popcountll
using ll=long long; using ld=long double;
mt19937_64 rng(chrono::high_resolution_clock::now().time_since_epoch().count()); const ld pi=acos(0)*2;
template <typename T> inline void read(T &x){char c; bool nega=0; while((!isdigit(c=getchar()))&&(c!='-')); if(c=='-'){nega=1; c=getchar();} x=c-48; while(isdigit(c=getchar())) x=x*10+c-48; if(nega) x=-x;}
template <typename T> inline void writep(T x){if(x>9) writep(x/10); putchar(x%10+48);}
template <typename T> inline void write(T x){if(x<0){ putchar('-'); x=-x;} writep(x);}
template <typename T> inline void writeln(T x){write(x); putchar('\n');}
#define taskname "Commuter"
int n, m;
int s, t, u, v;
class edge{
public:
int a, b, c, x;
bool good;
void input(){
read(a);
read(b);
read(c);
x=a^b;
good=0;
}
} e[200001];
vector <int> g[100001];
ll f[100001];
ll d[100001][3];
class cmp{
public:
bool operator ()(pair <int, ll> A, pair <int, ll> B){
return A.second>B.second;
}
};
priority_queue <pair <int, ll>, vector <pair <int, ll>>, cmp> q;
void dij(int a){
FOR(i, 1, n) f[i]=1e18;
while(!q.empty()) q.pop();
q.push(mp(a, 0));
f[a]=0;
while(!q.empty()){
pair <int, ll> p=q.top();
q.pop();
if(f[p.first]<p.second) continue;
for(int i: g[p.first]){
int v=e[i].x^p.first;
int cost=e[i].c;
if(f[v]>p.second+cost){
f[v]=p.second+cost;
q.push(mp(v, f[v]));
}
}
}
}
class cmp2{
public:
bool operator ()(pair <pair <int, int>, ll> A, pair <pair <int, int>, ll> B){
return A.second>B.second;
}
};
priority_queue <pair <pair <int, int>, ll>, vector <pair <pair <int, int>, ll>>, cmp2> q2;
void dij2(int a){
FOR(i, 1, n) FOR(j, 0, 2) d[i][j]=1e18;
while(!q2.empty()) q2.pop();
q2.push(mp(mp(a, 0), 0));
d[a][0]=0;
while(!q2.empty()){
pair <pair <int, int>, ll> p=q2.top();
q2.pop();
if(d[p.first.first][p.first.second]<p.second) continue;
// cerr<<p.first.first<<' '<<p.first.second<<' '<<p.second<<'\n';
for(int i: g[p.first.first]){
int v=e[i].x^p.first.first;
int cost=e[i].c;
if((p.first.second<=1)&&e[i].good&&(p.first.first==e[i].a)) cost=0;
int nx=(cost==0);
if(nx!=1) if(p.first.second) nx=2;
if(d[v][nx]>p.second+cost){
d[v][nx]=p.second+cost;
q2.push(mp(mp(v, nx), d[v][nx]));
}
}
}
}
bool done[100001];
void mark(){
queue <int> q;
q.push(t);
done[t]=1;
while(!q.empty()){
int u=q.front();
q.pop();
for(int i: g[u]){
int v=e[i].x^u;
if(f[v]+e[i].c==f[u]){
e[i].good=1;
if(e[i].a!=v) swap(e[i].a, e[i].b);
if(!done[v]){
done[v]=1;
q.push(v);
}
}
}
}
}
int main(){
#ifdef Aria
if(fopen(taskname".in", "r"))
freopen(taskname".in", "r", stdin);
#endif // Aria
read(n);
read(m);
read(s);
read(t);
read(u);
read(v);
FOR(i, 1, m){
e[i].input();
g[e[i].a].pb(i);
g[e[i].b].pb(i);
}
dij(s);
mark();
dij2(u);
ll ans=min(d[v][0], min(d[v][1], d[v][2]));
dij2(v);
ans=min(ans, min(d[u][0], min(d[u][1], d[u][2])));
writeln(ans);
}
