#include <iostream>
#include <iomanip>
#include <cstdlib>
#include <algorithm>
#include <fstream>
#include <cstdio>
#include <cmath>
#include <cstring>
#include <string>
#include <ctime>
#include <queue>
#include <stack>
#include <vector>
#include <map>
#include <set>
#include <deque>
#include <cassert>
#include <unordered_map>
#include <bitset>
#include <unordered_set>
using namespace std;
#define pb push_back
#define pp pop_back
#define f first
#define s second
#define mp make_pair
const int N = (int) 1e6 + 123;
int n, m;
int S, T, U, V;
int edgeFrom[N];
int edgeTo[N];
int edgeWeight[N];
vector<int> g[N];
vector<int> dag[N];
long long d[4][N];
void dijkstra(long long *dist, int start) {
for (int i = 1; i <= n; i++) dist[i] = (long long) 1e18;
dist[start] = 0;
set<pair<long long, int>> s;
s.insert(make_pair(0, start));
while (!s.empty()) {
int v = s.begin() -> second;
s.erase(s.begin());
for (int edge : g[v]) {
int to = ((edgeFrom[edge] ^ edgeTo[edge]) ^ v);
if (dist[to] > dist[v] + edgeWeight[edge]) {
s.erase(make_pair(dist[to], to));
dist[to] = dist[v] + edgeWeight[edge];
s.insert(make_pair(dist[to], to));
}
}
}
}
bool used[N];
long long minU[N];
long long minV[N];
long long ans = 1e18;
void dfs(int v) {
if (used[v]) return;
used[v] = true;
minU[v] = d[2][v];
minV[v] = d[3][v];
for (auto to : dag[v]) {
dfs(to);
minU[v] = min(minU[v], minU[to]);
minV[v] = min(minV[v], minV[to]);
}
ans = min(ans, d[2][v] + minV[v]);
ans = min(ans, d[3][v] + minU[v]);
}
int main() {
#ifdef LOCAL
freopen("input.txt", "r", stdin);
#endif
ios_base::sync_with_stdio(0);
cin.tie(0);
cin >> n >> m;
cin >> S >> T;
cin >> U >> V;
for (int i = 1; i <= m; i++) {
cin >> edgeFrom[i] >> edgeTo[i] >> edgeWeight[i];
g[edgeFrom[i]].push_back(i);
g[edgeTo[i]].push_back(i);
}
dijkstra(d[0], S);
dijkstra(d[1], T);
dijkstra(d[2], U);
dijkstra(d[3], V);
long long shortest = d[0][T];
for (int i = 1; i <= m; i++) {
if (d[0][edgeFrom[i]] + edgeWeight[i] + d[1][edgeTo[i]] == shortest) {
dag[edgeFrom[i]].push_back(edgeTo[i]);
dag[edgeTo[i]].push_back(edgeFrom[i]);
} else if (d[0][edgeTo[i]] + edgeWeight[i] + d[1][edgeFrom[i]] == shortest) {
dag[edgeTo[i]].push_back(edgeFrom[i]);
dag[edgeFrom[i]].push_back(edgeTo[i]);
}
}
dfs(S);
cout << ans;
return 0;
}
