#include <bits/stdc++.h>
using namespace std;
const int N = (int)2e5 + 10;
const long long LINF = (long long) 1e18;
int n, m;
int s, t, u, v;
long long d[4][N];
vector<pair<long long, int> > g[N];
pair<long long, int> ord[N];
long long dp[N][4];
void djikstra(int type, int s_point) {
for (int i = 1; i <= n; i++) {
d[type][i] = LINF;
}
d[type][s_point] = 0;
set<pair<long long, int> > st;
st.insert(make_pair(d[type][s_point], s_point));
while (!st.empty()) {
int cur = st.begin()->second;
st.erase(st.begin());
for (auto go : g[cur]) {
if (d[type][cur] + go.second < d[type][go.first]) {
st.erase(make_pair(d[type][go.first], go.first));
d[type][go.first] = d[type][cur] + go.second;
st.insert(make_pair(d[type][go.first], go.first));
}
}
}
}
int main() {
#ifdef local
freopen("input.txt", "r", stdin);
#endif // local
scanf("%d%d%d%d%d%d", &n, &m, &s, &t, &u, &v);
while (m--) {
int x, y, c;
scanf("%d%d%d", &x, &y, &c);
g[x].push_back(make_pair(y, c));
g[y].push_back(make_pair(x, c));
}
djikstra(0, s);
djikstra(1, t);
djikstra(2, u);
djikstra(3, v);
long long ans = d[2][v];
ans = min(ans, d[2][s] + d[1][v]); // u->s...t->v
ans = min(ans, d[2][t] + d[0][v]); // u->t...s->v
for (int i = 1; i <= n; i++) {
ord[i] = make_pair(d[0][i], i);
dp[i][1] = LINF;
dp[i][2] = LINF;
dp[i][3] = LINF;
}
sort(ord + 1, ord + n + 1);
for (int ptr = 1; ptr <= n; ptr++) {
int i = ord[ptr].second;
// cout << "ptr " << ptr << " ord " << i << "\n";
if (d[0][i] + d[1][i] == d[0][t]) {
dp[i][1] = d[2][i];
dp[i][2] = d[3][i];
dp[i][3] = d[2][i] + d[3][i];
for (auto it : g[i]) {
if (d[0][it.first] + it.second == d[0][i]) {
dp[i][1] = min(dp[it.first][1], dp[i][1]);
dp[i][2] = min(dp[it.first][2], dp[i][2]);
dp[i][3] = min(dp[it.first][3], dp[i][3]);
dp[i][3] = min(d[2][i] + dp[it.first][2], dp[i][3]);
dp[i][3] = min(d[3][i] + dp[it.first][1], dp[i][3]);
}
}
}
ans = min(ans, dp[i][3]);
}
cout << ans;
return 0;
}
