#include<bits/stdc++.h>
#include<ext/pb_ds/assoc_container.hpp>
#include<ext/pb_ds/tree_policy.hpp>
using namespace std;
using namespace __gnu_pbds;
typedef long long ll;
typedef long double ld;
#define pb push_back
#define pii pair<ll, ll>
#define pll pair<ll, ll>
#define pil pair<ll, ll>
#define pli pair<ll, ll>
#define st first
#define nd second
#define ordered_set tree<int, null_type, less<int>, rb_tree_tag, tree_order_statistics_node_update>
#define debug false
const int MAXN = 200 * 1000 + 1;
vector<pil> graf[MAXN];
ll odl[MAXN];
ll odlS[MAXN];
ll odlT[MAXN];
ll odlU[MAXN];
ll odlV[MAXN];
ll dp[MAXN][4];
vector<pli> vec;
priority_queue<pil> pq;
void djikstra (ll s) {
//memset(odl, ll(INT_MAX) * ll(MAXN), sizeof(odl));
for (int i = 1; i < MAXN; i ++) {
odl[i] = 1e18;
//cout << odl[i];
}
/*for (int i = 1; i <= 8; i ++) {
cout << odl[i] << " ";
}*/
odl[s] = 0;
pq.push({0, s});
while (!pq.empty()) {
ll v = pq.top().nd;
ll vodl = -pq.top().st;
pq.pop();
if (vodl > odl[v]) {
continue;
}
for (auto x : graf[v]) {
if (vodl + x.nd < odl[x.st]) {
odl[x.st] = vodl + x.nd;
pq.push({-odl[x.st], x.st});
}
}
}
}
int main () {
ios::sync_with_stdio(0); cin.tie(0); cout.tie(0);
ll n, m, S, T, U, V;
cin >> n >> m >> S >> T >> U >> V;
ll a, b;
ll c;
for (ll i = 0; i < m; i ++) {
cin >> a >> b >> c;
graf[a].pb({b, c});
graf[b].pb({a, c});
}
djikstra(S);
swap(odl, odlS);
djikstra(T);
swap(odl, odlT);
djikstra(U);
swap(odl, odlU);
djikstra(V);
swap(odl, odlV);
if (debug) {
cout << "odlS:\n";
for (ll i = 1; i <= n; i ++) {
cout << i << ": " << odlS[i] << "\n";
}
cout << "\n";
}
for (ll i = 1; i <= n; i ++) {
vec.pb({odlS[i], i});
}
sort(vec.begin(), vec.end());
//memset(dp, ll(INT_MAX) * ll(MAXN), sizeof(dp));
for (int i = 1; i <= n; i ++) {
for (int j = 0; j < 4; j ++) {
dp[i][j] = 1e18;
}
}
dp[S][0] = 0;
dp[S][1] = odlU[S];
dp[S][2] = odlV[S];
dp[S][3] = odlU[S] + odlV[S];
for (auto x : vec) {
ll v = x.nd;
for (auto x : graf[v]) {
if (odlS[v] == odlS[x.st] + x.nd) {
for (ll i = 0; i < 4; i ++) {
for (ll j = 0; j < 4; j ++) {
ll dod = 0;
if (j & 1) {
dod += odlU[v];
}
if (j & 2) {
dod += odlV[v];
}
if (odlU[x.st] == 1e18 || odlV[x.st] == 1e18 || dp[x.st][i] == 1e18) {
continue;
}
dp[v][i | j] = min(dp[v][i | j], dp[x.st][i] + dod);
}
}
}
}
}
cout << min(dp[T][3], odlU[V]) << "\n";
return 0;
}
