#include <algorithm>
#include <iostream>
using namespace std;
const int N = 100000;
const long long INF = 0x3f3f3f3f3f3f3f3fLL;
int *ej[N], *ew[N], eo[N], pq[N], iq[N + 1], pq_cnt, qu[N];
long long dd_s[N], dd_t[N], dd_u[N], dd_v[N], *dd;
void append(int i, int j, int w) {
int o = eo[i]++;
if (!o) {
ej[i] = (int *) malloc(sizeof *ej[i]);
ew[i] = (int *) malloc(sizeof *ew[i]);
} else if (!(o & o - 1)) {
ej[i] = (int *) realloc(ej[i], (o << 1) * sizeof *ej[i]);
ew[i] = (int *) realloc(ew[i], (o << 1) * sizeof *ew[i]);
}
ej[i][o] = j;
ew[i][o] = w;
}
bool lt(int i, int j) {
return dd[i] < dd[j];
}
int p2(int p) {
return (p <<= 1) > pq_cnt ? 0 : p ^ (p < pq_cnt && lt(iq[p ^ 1], iq[p]));
}
void pq_up(int i) {
int j, p, q;
for (p = pq[i]; (q = p >> 1) && lt(i, j = iq[q]); p = q)
iq[pq[j] = p] = j;
iq[pq[i] = p] = i;
}
void pq_dn(int i) {
int j, p, q;
for (p = pq[i]; (q = p2(p)) && lt(j = iq[q], i); p = q)
iq[pq[j] = p] = j;
iq[pq[i] = p] = i;
}
void pq_add_last(int i) {
iq[pq[i] = ++pq_cnt] = i;
}
int pq_remove_first() {
int i = iq[1], j = iq[pq_cnt--];
if (i != j)
pq[j] = 1, pq_dn(j);
pq[i] = 0;
return i;
}
void dijkstra(int n, int s) {
for (int i = 0; i < n; i++)
dd[i] = INF;
dd[s] = 0, pq_add_last(s);
for (int h = 0; h < n; h++) {
int i = qu[h] = pq_remove_first();
for (int o = 0; o < eo[i]; o++) {
int j = ej[i][o], w = ew[i][o];
long long d = dd[i] + w;
if (dd[j] > d) {
if (dd[j] == INF)
pq_add_last(j);
dd[j] = d, pq_up(j);
}
}
}
}
int main() {
ios_base::sync_with_stdio(false), cin.tie(NULL);
int n, m; cin >> n >> m;
int s, t; cin >> s >> t, s--, t--;
int u, v; cin >> u >> v, u--, v--;
while (m--) {
int i, j, w; cin >> i >> j >> w, i--, j--;
append(i, j, w), append(j, i, w);
}
dd = dd_t, dijkstra(n, t);
dd = dd_u, dijkstra(n, u);
dd = dd_v, dijkstra(n, v);
dd = dd_s, dijkstra(n, s);
long long ans = dd_u[v];
for (int h = 0; h < n; h++) {
int i = qu[h];
if (dd_s[i] + dd_t[i] == dd_s[t]) {
long long d_u = dd_u[i], d_v = dd_v[i];
for (int o = 0; o < eo[i]; o++) {
int j = ej[i][o], w = ew[i][o];
if (dd_s[j] + w == dd_s[i]) {
d_u = min(d_u, dd_u[j]);
d_v = min(d_v, dd_v[j]);
}
}
ans = min(ans, min(d_u + dd_v[i], dd_u[i] + d_v));
dd_u[i] = d_u, dd_v[i] = d_v;
}
}
cout << ans << '\n';
return 0;
}
