//package ojuz;
import java.io.*;
import java.util.*;
import java.util.function.BiFunction;
import java.util.function.IntFunction;
public class commuter_pass {
public static final PriorityQueue<Token> pq = new PriorityQueue<>(Comparator.comparingLong((Token i) -> i.cost).thenComparingInt(i -> i.node));
public static void main(String[] args) throws IOException {
BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));
String[] first = reader.readLine().split(" ");
int n = Integer.parseInt(first[0]), m = Integer.parseInt(first[1]);
first = reader.readLine().split(" ");
int s = Integer.parseInt(first[0]) - 1, t = Integer.parseInt(first[1]) - 1;
first = reader.readLine().split(" ");
int u = Integer.parseInt(first[0]) - 1, v = Integer.parseInt(first[1]) - 1;
Graph g = new Graph(n, 2 * m);
for (int i = 0; i < m; i++) {
String[] edge = reader.readLine().split(" ");
int a = Integer.parseInt(edge[0]) - 1, b = Integer.parseInt(edge[1]) - 1, w = Integer.parseInt(edge[2]);
g.add(a, b, w);
g.add(b, a, w);
}
IntFunction<long[]> find = start -> {
pq.clear();
pq.add(new Token(start, 0, -1));
long[] dist = new long[n];
Arrays.fill(dist, Long.MAX_VALUE / 2);
while (!pq.isEmpty()) {
Token val = pq.poll();
if (dist[val.node] <= val.cost) continue;
dist[val.node] = val.cost;
for (int i = g.head[val.node]; i != -1; i = g.edges[i][1]) {
pq.add(new Token(g.edges[i][0], g.edges[i][2] + val.cost, -1));
}
}
return dist;
};
long[] distU = find.apply(u);
long[] distV = find.apply(v);
BiFunction<Integer, long[], long[][]> findMin = (start, dists) -> {
pq.clear();
pq.add(new Token(start, 0, dists[start]));
long[] dist = new long[n];
long[] mins = new long[n];
Arrays.fill(dist, Long.MAX_VALUE / 2);
Arrays.fill(mins, Long.MAX_VALUE / 2);
while (!pq.isEmpty()) {
Token val = pq.poll();
if (dist[val.node] < val.cost) continue;
if (dist[val.node] == val.cost) throw new RuntimeException();
dist[val.node] = val.cost;
mins[val.node] = Math.min(dists[val.node], val.min);
while (!pq.isEmpty() && pq.peek().node == val.node && pq.peek().cost == val.cost) mins[val.node] = Math.min(mins[val.node], pq.poll().min);
for (int i = g.head[val.node]; i != -1; i = g.edges[i][1] ) {
pq.add(new Token(g.edges[i][0], g.edges[i][2] + val.cost, mins[val.node]));
}
}
return new long[][] { dist, mins };
};
long[][] distS = findMin.apply(s, distU);
long[][] distT = findMin.apply(t, distU);
long ans = Long.MAX_VALUE;
long distST = distS[0][t];
if (distST != distT[0][s]) throw new RuntimeException();
for (int i = 0; i < n; i++) {
if (distST == distS[0][i] + distT[0][i]) {
ans = Math.min(ans, distS[1][i] + distV[i]);
ans = Math.min(ans, distT[1][i] + distV[i]);
}
}
System.out.println(Math.min(ans, distU[v]));
}
static class Graph {
public final int[][] edges;
public final int[] head;
public int ptr;
public Graph(int n, int m) {
this.edges = new int[m][3];
this.head = new int[n];
Arrays.fill(head, -1);
}
public void add(int a, int b, int w) {
edges[ptr][0] = b;
edges[ptr][1] = head[a];
edges[ptr][2] = w;
head[a] = ptr++;
}
}
static class Token {
public final int node;
public final long cost, min;
public Token(int n, long w, long m) {
this.node = n;
this.cost = w;
this.min = m;
}
}
}
