//#define _GLIBCXX_DEBUG
#include <bits/stdc++.h>
using namespace std;
//randoms
mt19937 rnd(chrono::steady_clock::now().time_since_epoch().count());
#define ll long long
#define trace(x) cout << #x << " = " << (x) << endl;
#define all(x) x.begin(), (x).end()
#define rall(x) x.rbegin(), (x).rend()
#define unique(x) x.erase(unique(all(x)), (x).end())
#define ld long double
#define sz(s) (int) size(s)
const int N = 100001;
const ll infL = 1e18;
const int infI = 1e9 + 7;
const ll mod = 998244353;
ll dist[4][N]; //s, t, u, v
vector<pair<int, ll>> g[N];
vector<int> gr[N], tops;
bool VisT[N], used[N];
ll minU[N], minV[N];
void dfs(int v) {
used[v] = true;
for (int to : gr[v]) {
if (!used[to])
dfs(to);
}
tops.push_back(v);
}
int s, t, u, v, n;
void calcDist(int i) {
for (int j = 0; j < n; ++j)
dist[i][j] = infL;
if (i == 0) dist[i][s] = 0;
else if (i == 1) dist[i][t] = 0;
else if (i == 2) dist[i][u] = 0;
else dist[i][v] = 0;
set<pair<ll, int>> st;
for (int j = 0; j < n; ++j)
st.insert({dist[i][j], j});
while (!st.empty()) {
auto[w, V] = *st.begin();
st.erase(st.begin());
for (auto[to, W] : g[V]) {
ll val = W + w;
if (val < dist[i][to]) {
st.erase({dist[i][to], to});
dist[i][to] = val;
st.insert({dist[i][to], to});
}
}
}
}
int main() {
ios::sync_with_stdio(false);
cin.tie(nullptr);
int m;
cin >> n >> m >> s >> t >> u >> v;
--s, --t, --u, --v;
for (int i = 0; i < m; ++i) {
int a, b, w;
cin >> a >> b >> w;
--a, --b;
g[a].emplace_back(b, w);
g[b].emplace_back(a, w);
}
for (int i = 0; i < 4; ++i)
calcDist(i);
for (int i = 0; i < n; ++i) {
for (auto[to, W] : g[i]) {
if (dist[0][i] + W == dist[0][to]) {
gr[i].push_back(to);
}
}
}
for (int i = 0; i < n; ++i)
minU[i] = minV[i] = infL;
for (int i = 0; i < n; ++i) {
if (!used[i])
dfs(i);
}
ll ans = dist[2][v];
for (int x : tops) {
if (x == t) VisT[x] = true;
for (int to : gr[x]) {
if (VisT[to]) {
VisT[x] = true;
minU[x] = min(minU[x], minU[to]);
minV[x] = min(minV[x], minV[to]);
}
}
if (VisT[x]) {
ans = min({ans, minU[x] + dist[3][x], minV[x] + dist[2][x]});
minU[x] = min(minU[x], dist[2][x]);
minV[x] = min(minV[x], dist[3][x]);
}
}
cout << ans;
return 0;
}
