#include <bits/stdc++.h>
#define ll long long
#define pb push_back
#define mp make_pair
#define pii pair<ll,ll>
using namespace std;
const int maxn = 100100;
vector<pii> g[maxn];
ll n, m, s, t, u, v;
ll x, y, z;
ll d[maxn][2];
ll dist[maxn][2];
ll dp[maxn][2];
void dijkstra() {
for(int i=0;i<=n;i++) {
d[i][0] = d[i][1] = LLONG_MAX;
}
d[u][0] = 0LL;
priority_queue<pii, vector<pii>, greater<pii> > pq;
pq.push(mp(0LL, u));
while(!pq.empty()) {
ll curr = pq.top().second;
ll currd = pq.top().first;
pq.pop();
for(auto i:g[curr]) {
ll nextd = currd + i.second;
if(nextd < d[i.first][0]) {
d[i.first][0] = nextd;
pq.push(mp(d[i.first][0], i.first));
}
}
}
d[v][1] = 0LL;
pq.push(mp(0LL, v));
while(!pq.empty()) {
ll curr = pq.top().second;
ll currd = pq.top().first;
pq.pop();
for(auto i:g[curr]) {
ll nextd = currd + i.second;
if(nextd < d[i.first][1]) {
d[i.first][1] = nextd;
pq.push(mp(d[i.first][1], i.first));
}
}
}
}
void solve() {
for(int i=0;i<=n;i++) {
dist[i][0] = dist[i][1] = LLONG_MAX;
dp[i][0] = dp[i][1] = LLONG_MAX;
}
dist[s][0] = 0LL;
priority_queue<pii, vector<pii>, greater<pii> > pq;
pq.push(mp(0LL, s));
dp[s][0] = d[s][1];
while(!pq.empty()) {
ll curr = pq.top().second;
ll currd = pq.top().first;
pq.pop();
for(auto i:g[curr]) {
ll nextd = currd + i.second;
if(nextd < dist[i.first][0]) {
dist[i.first][0] = nextd;
dp[i.first][0] = min(dp[curr][0], d[i.first][1]);
pq.push(mp(dist[i.first][0], i.first));;
}
else if(nextd == dist[i.first][0]) {
dp[i.first][0] = min(dp[i.first][0], min(dp[curr][0], d[i.first][1]));
}
}
}
dist[t][1] = 0LL;
dp[t][1] = d[t][1];
pq.push(mp(0LL, t));
while(!pq.empty()) {
ll curr = pq.top().second;
ll currd = pq.top().first;
pq.pop();
for(auto i:g[curr]) {
ll nextd = currd + i.second;
if(nextd < dist[i.first][1]) {
dist[i.first][1] = nextd;
dp[i.first][1] = min(dp[curr][1], d[i.first][1]);
pq.push(mp(dist[i.first][1], i.first));;
}
else if(nextd == dist[i.first][1]) {
dp[i.first][1] = min(dp[i.first][1], min(dp[curr][1], d[i.first][1]));
}
}
}
ll result = d[v][0];
for(int i=1;i<=n;i++) {
if(dist[i][0] + dist[i][1] == dist[t][0]) {
result = min(result, d[i][0] + min(dp[i][0], dp[i][1]));
}
}
cout<<result;
}
int main() {
cin>>n>>m;
cin>>s>>t;
cin>>u>>v;
for(int i=0;i<m;i++) {
cin>>x>>y>>z;
g[x].pb(mp(y,z));
g[y].pb(mp(x,z));
}
dijkstra();
solve();
return 0;
}
