import java.util.*;
import java.io.*;
public class commuter_pass {
static ArrayList<Edge>[] graph;
static ArrayList<Integer>[] par;
static int n, m, s, t, u, v;
public static void main(String[] args) throws IOException {
BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
PrintWriter out = new PrintWriter(System.out);
StringTokenizer line = new StringTokenizer(in.readLine());
n = Integer.parseInt(line.nextToken());
m = Integer.parseInt(line.nextToken());
line = new StringTokenizer(in.readLine());
s = Integer.parseInt(line.nextToken()) - 1;
t = Integer.parseInt(line.nextToken()) - 1;
line = new StringTokenizer(in.readLine());
u = Integer.parseInt(line.nextToken()) - 1;
v = Integer.parseInt(line.nextToken()) - 1;
graph = new ArrayList[n];
par = new ArrayList[n];
for(int i = 0; i < n; i++) {
graph[i] = new ArrayList<Edge>();
par[i] = new ArrayList<Integer>();
}
for(int i = 0; i < m; i++) {
line = new StringTokenizer(in.readLine());
int a = Integer.parseInt(line.nextToken()) - 1;
int b = Integer.parseInt(line.nextToken()) - 1;
int c = Integer.parseInt(line.nextToken());
graph[a].add(new Edge(b, c));
graph[b].add(new Edge(a, c));
}
long[] dists = new long[n];
Arrays.fill(dists, -1);
PriorityQueue<Step> pq = new PriorityQueue<Step>();
pq.add(new Step(s, -1, 0));
while(pq.size() > 0) {
Step cur = pq.poll();
if(dists[cur.n] != -1) {
if(cur.d == dists[cur.n]) {
par[cur.n].add(cur.p);
}
continue;
}
par[cur.n].add(cur.p);
dists[cur.n] = cur.d;
for(Edge e : graph[cur.n]) {
pq.add(new Step(e.to, cur.n, cur.d + e.w));
}
}
boolean[] visited = new boolean[n];
genDAG(t, visited);
long res = Math.min(shortest_path(u, v), shortest_path(v, u));
out.println(res);
in.close();
out.close();
}
static long shortest_path(int source, int dest) {
long[][] dists = new long[n][3];
for(int i = 0; i < n; i++) {
Arrays.fill(dists[i], -1);
}
PriorityQueue<Step> pq = new PriorityQueue<Step>();
pq.add(new Step(source, -1, 0, 0));
while(pq.size() > 0) {
Step cur = pq.poll();
if(dists[cur.n][cur.t] != -1) {
continue;
}
dists[cur.n][cur.t] = cur.d;
for(Edge e : graph[cur.n]) {
if(e.w > 0) {
if(cur.t == 1) {
pq.add(new Step(e.to, cur.n, 2, cur.d + e.w));
}else {
pq.add(new Step(e.to, cur.n, cur.t, cur.d + e.w));
}
}else {
if(cur.t != 2) {
pq.add(new Step(e.to, cur.n, 1, cur.d));
}
}
}
}
long res = Long.MAX_VALUE;
for(int i = 0; i < 3; i++) {
if(dists[dest][i] != -1) {
res = Math.min(res, dists[dest][i]);
}
}
return res;
}
static void genDAG(int node, boolean[] visited) {
if(node == s || visited[node]) {
return;
}
visited[node] = true;
for(int prev : par[node]) {
graph[prev].add(new Edge(node, 0));
genDAG(prev, visited);
}
}
static class Step implements Comparable<Step> {
int n, p, t;
long d;
Step(int nn, int pp, long dd) {
n = nn;
p = pp;
d = dd;
}
Step(int nn, int pp, int tt, long dd) {
n = nn;
p = pp;
t = tt;
d = dd;
}
@Override
public int compareTo(Step o) {
if(d > o.d) return 1;
else if(d < o.d) return -1;
return 0;
}
}
static class Edge {
int to, w;
Edge(int t, int ww) {
to = t;
w = ww;
}
}
}
