#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef pair<ll, ll> pll;
const int MAXN = 2e5 + 10;
const ll INF = 4e18;
ll n, m, s, t, s1, e1, h[4][MAXN], dp1[MAXN], dp2[MAXN];
vector<int> num;
bool seen[4][MAXN];
vector<pll> adj[MAXN];
void input() {
cin >> n >> m >> s >> t >> s1 >> e1;
for (int i = 0; i < m; i++) {
int x, y, z;
cin >> x >> y >> z;
adj[x].push_back({y, z});
adj[y].push_back({x, z});
}
}
void dij1(int c) {
priority_queue<pll, vector<pll>, greater<pll>> q;
if (c == 0)
q.push({0, s});
else if (c == 1)
q.push({0, s1});
else if (c == 2)
q.push({0, e1});
else
q.push({0, t});
while (!q.empty()) {
ll u = q.top().second, d = q.top().first;
q.pop();
if (!seen[c][u]) {
if (c == 0)
num.push_back(u);
seen[c][u] = true;
h[c][u] = d;
for (auto p : adj[u]) {
int v = p.first, w = p.second;
if (!seen[c][v])
q.push({d + w, v});
}
}
}
}
void calcDp() {
for (auto u : num) {
dp1[u] = h[2][u];
for (auto p : adj[u]) {
int v = p.first, w = p.second;
if ((h[0][v] + w + h[3][u]) == h[0][t])
dp1[u] = min(dp1[u], dp1[v]);
}
}
reverse(num.begin(), num.end());
for (auto u : num) {
dp2[u] = h[2][u];
for (auto p : adj[u]) {
int v = p.first, w = p.second;
if ((h[0][u] + w + h[3][v]) == h[0][t])
dp2[u] = min(dp2[u], dp2[v]);
}
}
}
ll findAns() {
ll res = INF;
for (int i = 1; i <= n; i++)
res = min(res, h[1][i] + min(dp1[i], dp2[i]));
return res;
}
int main() {
ios::sync_with_stdio(false); cin.tie(0);
input();
dij1(0);
dij1(1);
dij1(2);
dij1(3);
calcDp();
cout << findAns() << endl;
return 0;
}
