#include <bits/stdc++.h>
using namespace std;
const int MAX_N = 100000;
const long long INF = 1LL << 60;
vector<pair<int, int> > graph[1+MAX_N];
long long dist[2][1+MAX_N], dists[1+MAX_N];
long long dp[1+MAX_N][4];
bool viz[1+MAX_N];
void dijkstra(int n, int src, long long *dist) {
priority_queue<pair<long long, int> > pq;
for(int i = 1; i <= n; ++i)
dist[i] = INF;
dist[src] = 0;
pq.push(make_pair(0, src));
while(!pq.empty()) {
int nod = pq.top().second;
long long cost = -pq.top().first;
pq.pop();
if(cost == dist[nod]) {
for(auto it: graph[nod])
if(cost + it.second < dist[it.first]) {
dist[it.first] = cost + it.second;
pq.push(make_pair(-cost - it.second, it.first));
}
}
}
}
void computeDp(int nod) {
if(!viz[nod]) {
viz[nod] = true;
dp[nod][1] = dist[0][nod];
dp[nod][2] = dist[1][nod];
dp[nod][3] = dist[0][nod] + dist[1][nod];
for(auto it: graph[nod])
if(dists[nod] - it.second == dists[it.first]) {
computeDp(it.first);
dp[nod][1] = min(dp[nod][1], dp[it.first][1]);
dp[nod][2] = min(dp[nod][2], dp[it.first][2]);
dp[nod][3] = min(min(min(dp[nod][3],
dp[it.first][1] + dist[1][nod]),
dp[it.first][2] + dist[0][nod]),
dp[it.first][3]);
}
}
}
int main() {
#ifdef HOME
FILE *fin = fopen("input.in", "r");
FILE *fout = fopen("output.out", "w");
#else
FILE *fin = stdin;
FILE *fout = stdout;
#endif
priority_queue<int> pq;
int n, m, s, t, u, v;
int a, b, c;
fscanf(fin, "%d%d%d%d%d%d", &n, &m, &s, &t, &u, &v);
for(int i = 0; i < m; ++i) {
fscanf(fin, "%d%d%d", &a, &b, &c);
graph[a].push_back(make_pair(b, c));
graph[b].push_back(make_pair(a, c));
}
dijkstra(n, u, dist[0]);
dijkstra(n, v, dist[1]);
dijkstra(n, s, dists);
computeDp(t);
fprintf(fout, "%lld", min(dist[0][v], dp[t][3]));
fclose(fin);
fclose(fout);
return 0;
}
