import java.io.*;
import java.util.*;
public class commuter_pass {
public static int num; public static int m; public static long ans;
public static int s; public static int t; public static int u; public static int v;
public static long[] udis; public static long[] vdis;
public static long[] dpU; public static long[] dpV; //The distances from U to node where node is end point of the current path (also the shortest by djikstra) from s to node
public static ArrayList<ArrayList<Pair>> adj;
public static void main(String[] args) throws IOException {
//FileReader file = new FileReader("/Users/owenzhou/Downloads/2018-ho-t4/in/01-02.txt");
BufferedReader scan = new BufferedReader(new InputStreamReader(System.in));
StringTokenizer l1 = new StringTokenizer(scan.readLine());
num = Integer.parseInt(l1.nextToken()); m = Integer.parseInt(l1.nextToken());
StringTokenizer l2 = new StringTokenizer(scan.readLine());
s = Integer.parseInt(l2.nextToken())-1; t = Integer.parseInt(l2.nextToken())-1;
StringTokenizer l3 = new StringTokenizer(scan.readLine());
u = Integer.parseInt(l3.nextToken())-1; v = Integer.parseInt(l3.nextToken())-1;
adj = new ArrayList<>();
for (int i = 0;i<num;i++)
adj.add(new ArrayList<>());
for (int i = 0;i<m;i++) {
StringTokenizer st = new StringTokenizer(scan.readLine());
int a = Integer.parseInt(st.nextToken())-1; int b = Integer.parseInt(st.nextToken())-1; int c = Integer.parseInt(st.nextToken());
adj.get(a).add(new Pair(b,c)); adj.get(b).add(new Pair(a,c));
}
dpU = new long[num]; dpV = new long[num]; Arrays.fill(dpU, Long.MAX_VALUE/2); Arrays.fill(dpV, Long.MAX_VALUE/2);
udis = dijkstra1(u); vdis = dijkstra1(v);
ans = udis[v]; dijkstra2();
System.out.println(ans);
}
public static void dijkstra2 () {
long[] dis = new long[num]; Arrays.fill(dis, Long.MAX_VALUE);
boolean[] visited = new boolean[num];
PriorityQueue<Node> pq = new PriorityQueue<>(Comparator.comparingLong(a->a.val));
pq.add(new Node(s,0, 0)); dis[s] = 0;
while (!pq.isEmpty()) {
Node curr = pq.poll(); int node = curr.n; long d = curr.val; int parent = curr.parent;
if (!visited[node]) {
visited[node] = true; dis[node] = d;
dpU[node] = Math.min(dpU[parent], udis[node]); dpV[node] = Math.min(dpV[parent], vdis[node]);
for (Pair next : adj.get(node)) {
if (next.n!=parent) pq.add(new Node(next.n,d+next.val,node));
}
} else if (dis[node]==d) {
dpU[node] = Math.min(dpU[node], dpU[parent]); dpV[node] = Math.min(dpV[node], dpV[parent]);
/*if (Math.min(udis[node], dpU[parent]) + Math.min(vdis[node], dpV[parent]) <=
dpU[node] + dpV[node]) {
dpU[node] = Math.min(udis[node], dpU[parent]);
dpV[node] = Math.min(vdis[node], dpV[parent]);
}*/
//No need to add extra vertices since we've already been here with dis = d.
}
}
ans = Math.min(ans, dpU[t]+dpV[t]);
}
public static long[] dijkstra1 (int start) {
long[] dis = new long[num]; Arrays.fill(dis, Long.MAX_VALUE);
PriorityQueue<Pair> pq = new PriorityQueue<>(Comparator.comparingLong(a->a.val));
pq.add(new Pair(start,0)); dis[start] = 0;
while (!pq.isEmpty()) {
Pair curr = pq.poll(); int node = curr.n; long d = curr.val;
if (dis[node]!=d) continue;
for (Pair v : adj.get(node)) {
int n = v.n; long w = v.val;
if (d+w<dis[n]) {
dis[n] = d+w;
pq.add(new Pair(n,dis[n]));
}
}
}
return dis;
}
public static class Pair {
int n; long val; //node to and value (weight or curr dis)
Pair (int n, long val) {
this.n = n; this.val = val;
}
}
public static class Node {
int n; long val; //node to and value (weight or curr dis)
int parent;
Node (int n, long val, int parent) {
this.n = n; this.val = val;
this.parent = parent;
}
}
}
