#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef pair<ll,ll> pl;
typedef vector<int> vi;
typedef vector<vi> vvi;
typedef vector<pl> vpl;
typedef vector<vpl> al;
typedef vector<ll> vl;
typedef pair<pl,int> stt;
const ll INFL = 1e18;
al g[3];
void dja(int su, int sv) {
int so[2] = {su,sv};
vl dist[2];
for(int idx=0;idx<2;idx++) {
int bu = so[idx];
dist[idx].assign(g[0].size(),INFL);
priority_queue<pl,vpl, greater<pl>> pq;
dist[idx][bu] = 0;
pq.push({0,bu});
while(!pq.empty()) {
pl co = pq.top();pq.pop();
ll u = co.second;
if(co.first > dist[idx][u]) {continue;}
for(int i=0;i<g[0][u].size();i++) {
pl no = g[0][u][i];
ll v = no.first;
ll ko = no.second;
if(dist[idx][v] > dist[idx][u]+ko) {
dist[idx][v] = dist[idx][u]+ko;
pq.push({dist[idx][v],v});
}
}
}
}
ll mu = dist[1][su]+dist[0][su];
for(int idx=0;idx<2;idx++) {
for(int i=0;i<g[0].size();i++) {
if(dist[1][i]+dist[0][i] != mu) {continue;}
for(int j=0;j<g[0][i].size();j++) {
pl no = g[0][i][j];
ll v = no.first;
ll ko = no.second;
if(dist[idx][v]+ko == dist[idx][i]) {
g[idx+1][i].push_back({v,0});
}
}
}
}
}
vl dist[4];
int main() {
ll n,m;
cin >> n >> m;
ll so,to;
cin >> so >> to;
so--;to--;
ll ru,rv;
cin >> ru >> rv;
ru--;rv--;
g[0].assign(n,vpl());
g[1].assign(n,vpl());
g[2].assign(n,vpl());
for(int i=0;i<m;i++) {
ll a,b,c;
cin >> a >> b >> c;
a--;b--;
g[0][a].push_back({b,c});
g[0][b].push_back({a,c});
}
for(int i=0;i<4;i++) {
dist[i].assign(n,INFL);
}
priority_queue<stt,vector<stt>,greater<stt> > pq;
dja(so,to);
pq.push({{0,ru},0});
dist[0][ru] = 0;
while(!pq.empty()) {
stt cb = pq.top();pq.pop();
pl co = cb.first;
ll u = co.second;
ll gid = cb.second;
if(co.first > dist[gid][u]) {continue;}
vpl& bob = g[gid%3][u];
for(int i=0;i<bob.size();i++) {
pl co = bob[i];
ll v = co.first;
ll di = co.second;
if(dist[gid][v] > dist[gid][u]+di) {
dist[gid][v] = dist[gid][u]+di;
pq.push({{dist[gid][v],v},gid});
}
}
if(gid == 0) {
for(int i=1;i<=2;i++) {
if(dist[i][u] > dist[0][u]) {
dist[i][u] = dist[0][u];
pq.push({{dist[i][u],u},i});
}
}
} else if(gid < 3) {
if(dist[3][u] > dist[gid][u]) {
dist[3][u] = dist[gid][u];
pq.push({{dist[3][u],u},3});
}
}
}
ll res = INFL;
for(int i=0;i<4;i++) {
res = min(res,dist[i][rv]);
}
cout << res << '\n';
}
