#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
const int MAXN=1e5+5;
const ll INF=1e18;
vector<int> g[MAXN], pes[MAXN];
vector<int> dg[5][MAXN];
set<pair<ll, int> > s;
tuple<int, int, int> aresta[MAXN*2];
ll dist[5][MAXN], dp[2][MAXN];
int gin[2][MAXN];
int n, m, ori, dest, x, y;
void dijkstra(int ori, int k) {
for(int i=1; i<=n; i++) dist[k][i]= i==ori ? 0 : INF, s.insert({dist[k][i], i});
while(s.size()) {
int cur=s.begin()->second; s.erase(s.begin());
for(int i=0; i<g[cur].size(); i++) {
int viz=g[cur][i]; ll peso=pes[cur][i];
if(dist[k][viz]>dist[k][cur]+peso) {
s.erase({dist[k][viz], viz});
dist[k][viz]=dist[k][cur]+peso;
s.insert({dist[k][viz], viz});
}
}
}
}
void bfs(int k) {
queue<int> qu;
for(int i=1; i<=n; i++) if(gin[k][i]==0) qu.push(i);
while(qu.size()) {
int cur=qu.front(); qu.pop();
for(auto viz : dg[k][cur]) {
gin[k][viz]--;
if(gin[k][viz]==0) qu.push(viz);
dp[k][viz]=min(dp[k][viz], dp[k][cur]);
}
}
}
int main() {
scanf("%d %d", &n, &m);
scanf("%d %d", &ori, &dest);
scanf("%d %d", &x, &y);
for(int i=1; i<=m; i++) {
int a, b, c; scanf("%d %d %d", &a, &b, &c);
aresta[i]={a, b, c};
g[a].push_back(b); g[b].push_back(a);
pes[a].push_back(c); pes[b].push_back(c);
}
dijkstra(ori, 0); dijkstra(dest, 1);
dijkstra(x, 2); dijkstra(y, 3);
for(int i=1; i<=n; i++) dp[0][i]=dp[1][i]=dist[2][i];
for(int i=1; i<=m; i++) {
int a, b, c; tie(a, b, c)=aresta[i];
if(dist[0][a]+dist[1][b]+c!=dist[0][dest]&&dist[0][b]+dist[1][a]+c!=dist[0][dest]) continue;
if(dist[0][a]+c==dist[0][b]) {
dg[0][a].push_back(b); gin[0][b]++;
dg[1][b].push_back(a); gin[1][a]++;
}
if(dist[0][b]+c==dist[0][a]) {
dg[0][b].push_back(a); gin[0][a]++;
dg[1][a].push_back(b); gin[1][b]++;
}
}
bfs(0); bfs(1);
// for(int i=1; i<=n; i++) printf("%d: %lld %lld // %lld %lld\n", i, dist[0][i], dist[1][i], dist[2][i], dist[3][i]);
// for(int i=1; i<=n; i++) printf("dp[%d]= (%lld ; %lld)\n", i, dp[0][i], dp[1][i]);
ll respf=INF;
for(int i=1; i<=n; i++) respf=min(respf, dist[3][i]+min(dp[0][i], dp[1][i]));
printf("%lld\n", respf);
}
