#include <bits/stdc++.h>
#define int long long
#define task "TUNNEL"
using namespace std;
template<class X, class Y>
bool minimize(X &a, Y b)
{
if (a > b)
{
return a = b, true;
}
return false;
}
template<class X, class Y>
bool maximize(X &a, Y b)
{
if (a < b)
{
return a = b, true;
}
return false;
}
const int SZ = 2e5 + 5;
int test = 1;
int n, m;
int a, b, c, d;
vector<pair<int, int>> adj[SZ];
int dpc[SZ], dpd[SZ], tmp[SZ], dp[2][SZ];
bool vis[SZ];
int res = 0;
void ReadData()
{
cin >> n >> m;
cin >> a >> b >> c >> d;
for (int i = 1; i <= m; i++) {
int u, v, w;
cin >> u >> v >> w;
adj[u].push_back({v, w});
adj[v].push_back({u, w});
}
}
void Prep1() {
for (int i = 0; i <= 2e5; i++) {
vis[i] = false;
}
priority_queue<pair<int, int>> pq;
pq.push({0, c});
while (!pq.empty()) {
pair<int, int> p = pq.top();
pq.pop();
if (!vis[p.second]) {
dpc[p.second] = -p.first;
vis[p.second] = true;
for (auto q : adj[p.second]) {
pq.push({p.first - q.second, q.first});
}
}
}
}
void Prep2() {
for (int i = 0; i <= 2e5; i++) {
vis[i] = false;
}
priority_queue<pair<int, int>> pq;
pq.push({0, d});
while (!pq.empty()) {
pair<int, int> p = pq.top();
pq.pop();
if (!vis[p.second]) {
dpd[p.second] = -p.first;
vis[p.second] = true;
for (auto q : adj[p.second]) {
pq.push({p.first - q.second, q.first});
}
}
}
}
void Dijkstra(int u, int v) {
for (int i = 0; i < 2; i++) {
for (int j = 0; j <= 2e5; j++) {
dp[i][j] = 1e18;
}
}
for (int i = 0; i <= 2e5; i++) {
vis[i] = false;
}
priority_queue<pair<int, pair<int, int>>> pq;
pq.push({0, {u, 0}});
while (!pq.empty()) {
pair<int, pair<int, int>> p = pq.top();
pq.pop();
if (!vis[p.second.first]) {
vis[p.second.first] = true;
tmp[p.second.first] = -p.first;
dp[0][p.second.first] = min(dpc[p.second.first], dp[0][p.second.second]);
dp[1][p.second.first] = min(dpd[p.second.first], dp[1][p.second.second]);
for (auto q : adj[p.second.first]) {
pq.push({p.first - q.second, {q.first, p.second.first}});
}
} else if (-p.first == tmp[p.second.first]) {
if (min(dpc[p.second.first], dp[0][p.second.second]) + min(dpd[p.second.first], dp[1][p.second.second]) <= dp[0][p.second.first] + dp[1][p.second.first]) {
dp[0][p.second.first] = min(dpc[p.second.first], dp[0][p.second.second]);
dp[1][p.second.first] = min(dpd[p.second.first], dp[1][p.second.second]);
}
}
}
res = min(res, dp[0][v] + dp[1][v]);
}
void Solve()
{
Prep1();
Prep2();
res = dpc[d];
Dijkstra(a, b);
Dijkstra(b, a);
cout << res;
}
signed main()
{
if (fopen(task".inp", "r"))
{
freopen(task".inp", "r", stdin);
freopen(task".out", "w", stdout);
}
ios_base::sync_with_stdio(false);
cin.tie(0);
//cin >> test;
while(test--)
{
ReadData();
Solve();
cout << "\n";
}
}
