/*
███████╗██████╗ █████╗
██╔════╝██╔══██╗██╔══██╗
███████╗██████╔╝███████║ --- incredible
██╔════╝██╔═══╝ ██╔══██║
███████╗██║ ██║ ██║
╚══════╝╚═╝ ╚═╝ ╚═╝
*/
#include<bits/stdc++.h>
#pragma GCC target("avx2")
#pragma GCC optimize("O3")
#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native")
#define sz() size()
#define all(v) (v).begin(),(v).end()
#define F first
#define S second
#define pb push_back
#define popb pop_back
#define ss sort
#define rr reverse
#define pii pair <int, int>
#define pll pair <ll, ll>
using namespace std;
using ld = long double;
using ll = long long;
const int N = 3e5+10;
const ll inf = 1e18;
const int Mod = 1e9+7;
const int P = 273;
int n, m, S, T, U, V;
ll dp[2][N], dist[4][N], res;
vector <pii> g[N];
vector <int> g1[N];
vector <int> p[N];
bool used[N];
void djk(int v, int type)
{
for (int i = 1; i <= n; ++i) dist[type][i] = inf;
set <pll> st;
st.insert({0, v});
dist[type][v] = 0;
while (!st.empty())
{
auto [d, u] = *st.begin();
st.erase(st.begin());
if (dist[type][u] < d) continue;
for (auto [to, w] : g[u])
{
if (dist[type][to] > d + w)
{
dist[type][to] = d + w;
st.insert({dist[type][to], to});
if (type == 0)
{
p[to].clear();
p[to].pb(u);
}
} else if (type == 0 && dist[type][to] == d + w) p[to].pb(u);
}
}
}
void dfs(int v)
{
used[v] = true;
dp[0][v] = dist[2][v];
dp[1][v] = dist[3][v];
for (auto to : g1[v])
{
if (!used[to]) dfs(to);
dp[0][v] = min(dp[0][v], dp[0][to]);
dp[1][v] = min(dp[1][v], dp[1][to]);
}
res = min({res, dist[2][v] + dp[1][v], dist[3][v] + dp[0][v]});
// cout << v << ": ";
// cout << dist[2][v] + dp[1][v] << " " << dist[3][v] + dp[0][v] << "\n";
}
void Erali_is_the_best(int testCase)
{
cin >> n >> m >> S >> T >> U >> V;
for (int i = 1, u, v, w; i <= m; ++i)
{
cin >> u >> v >> w;
g[u].pb({v, w});
g[v].pb({u, w});
}
djk(S, 0);
djk(T, 1);
djk(U, 2);
djk(V, 3);
for (int i = 1; i <= n; ++i)
for (auto [to, w] : g[i])
if (dist[0][i] + dist[1][to] + w == dist[0][T])
g1[i].pb(to);
res = dist[2][V];
dfs(S);
cout << res << "\n";
}
int32_t main()
{
ios_base::sync_with_stdio(false);
cin.tie(nullptr);
// freopen("cardgame.in","r",stdin);
// freopen("cardgame.out","w",stdout);
int tt = 1;
// cin >> tt;
for (int test = 1; test <= tt; ++test)
{
Erali_is_the_best(test);
}
}
