#include <bits/stdc++.h>
#define ll long long
#define pb push_back
#define mp make_pair
using namespace std;
const int maxn = 100100;
ll dist[maxn][4], n, m, s, t, u, v;
ll dp[maxn][2];
bool visited[maxn];
vector<pair<int,int> > g[maxn];
/*
dist[i][0] - dist to i from u
dist[i][1] - dist to i from v
dist[i][2] - dist to i from s
dist[i][3] - dist to i from t
*/
void dijkstra(int start, int x) {
memset(visited,false,sizeof(visited));
for(int i=0;i<=n;i++) {
dist[i][x] = 10000000LL * INT_MAX;
}
dist[start][x] = 0LL;
//visited[start] = true;
priority_queue<pair<int,int>, vector<pair<int,int> >, greater<pair<int,int> > > pq;
pq.push(mp(0, start));
while(!pq.empty()) {
int curr = pq.top().second;
pq.pop();
if(visited[curr]) continue;
visited[curr] = true;
for(auto i:g[curr]) {
if(dist[curr][x] + i.second < dist[i.first][x] && !visited[i.first]) {
dist[i.first][x] = dist[curr][x] + i.second;
pq.push(mp(dist[i.first][x], i.first));
}
}
}
}
void get_dp(int start, int x) {
memset(visited,false,sizeof(visited));
for(int i=0;i<=n;i++) {
dp[i][x] = dist[i][1];
}
priority_queue<pair<int,int>, vector<pair<int,int> >, greater<pair<int,int> > > pq;
pq.push(mp(0, start));
int fx, sx, ffx;
if(x == 0) {
fx = 2;
sx = 3;
ffx = t;
}
else {
fx = 3;
sx = 2;
ffx = s;
}
while(!pq.empty()) {
int curr = pq.top().second;
pq.pop();
visited[curr] = true;
for(auto i:g[curr]) {
// check if this edge lies on some shortest path from s to v
if(dist[curr][fx] + dist[i.first][sx] + i.second == dist[ffx][fx] && !visited[i.first]) {
dp[i.first][x] = min(dp[curr][x], dp[i.first][x]);
pq.push(mp(dist[i.first][fx], i.first));
}
}
}
}
int main() {
cin>>n>>m;
cin>>s>>t;
cin>>u>>v;
int x, y, z;
for(int i=0;i<m;i++) {
cin>>x>>y>>z;
g[x].pb(mp(y,z));
g[y].pb(mp(x,z));
}
dijkstra(u, 0);
dijkstra(v, 1);
dijkstra(s, 2);
dijkstra(t, 3);
get_dp(s, 0);
get_dp(t, 1);
ll result = LLONG_MAX;
for(int i=1;i<=n;i++) {
result = min(result, dist[i][0] + min(dp[i][0], dp[i][1]));
}
cout<<result;
return 0;
}
