#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
const int MAXN=1e5+5;
const ll INF=1e18;
set<pair<ll, int> > s;
vector<int> g[6][MAXN], pes[6][MAXN];
tuple<int, int, int> aresta[MAXN*2];
ll dist[6][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[k][cur].size(); i++) {
int viz=g[k][cur][i]; ll peso=pes[k][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 liga(int a, int b, int c, int k) {
// if(k>=2) printf("liga %d %d %d %d\n", a, b, c, k);
g[k][a].push_back(b);
pes[k][a].push_back(c);
}
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);
liga(a, b, c, 0); liga(b, a, c, 0);
liga(a, b, c, 1); liga(b, a, c, 1);
aresta[i]={a, b, c};
}
dijkstra(ori, 0);
dijkstra(dest, 1);
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]) {
liga(a, b, c, 2), liga(b, a, c, 2);
liga(a, b, c, 3), liga(b, a, c, 3);
}
else if(dist[0][a]+c==dist[0][b]) {
liga(a, b, 0, 2); liga(b, a, c, 2);
liga(a, b, 0, 3); liga(b, a, c, 3);
}
else if(dist[0][b]+c==dist[0][a]) {
liga(a, b, c, 2); liga(b, a, 0, 2);
liga(a, b, c, 3); liga(b, a, 0, 3);
}
}
dijkstra(x, 2);
dijkstra(y, 3);
// for(int i=1; i<=n; i++) printf("%d: %d %d // %d %d\n", i, dist[0][i], dist[1][i], dist[2][i], dist[3][i]);
ll respf=min(dist[2][y], dist[3][x]);
printf("%lld\n", respf);
}
