#include <bits/stdc++.h>
using namespace std;
#define int long long
#define F first
#define S second
#define pb push_back
#define all(a) a.begin(), a.end()
using namespace std;
typedef long long ll;
typedef pair<int, int> ii;
const int N = 2e5 + 5;
const int mod = 1e9 + 7;
int n, m, s, t, u, v;
bool vis[N];
vector<ii> g[N];
ll dp[2][N], res;
ll ds[N], dv[N], du[N];
void dijkstra(int st, ll d[])
{
for(int i = 0; i <= n; i++)
vis[i] = 0, d[i] = 1e17;
priority_queue<ii, vector<ii>, greater<ii>> q;
q.emplace(0, st);
d[st] = 0;
while(q.size())
{
int u = q.top().S;
int w = q.top().F;
q.pop();
if(w != d[u]) continue;
for(ii &x : g[u])
{
ll wv = w + x.S;
int v = x.F;
if(wv < d[v])
{
d[v] = wv;
q.emplace(wv, v);
}
}
}
}
void dijkstra2(int st, int ed)
{
for(int i = 0; i <= n; i++)
{
vis[i] = 0;
dp[0][i] = dp[1][i] = 1e17;
ds[i] = 1e17;
}
priority_queue<ii, vector<ii>, greater<ii>> q;
q.emplace(0, st);
ds[st] = 0;
while(q.size())
{
int u = q.top().S;
ll w = q.top().F;
q.pop();
if(w != ds[u]) continue;
for(ii &x : g[u])
{
ll wv = w + x.S;
int v = x.F;
if(wv < ds[v])
{
ds[v] = wv;
dp[0][v] = min(dp[0][u], du[v]);
dp[1][v] = min(dp[1][u], dv[v]);
q.emplace(w + x.S, v);
}
else if(wv == ds[v])
{
ll tmp1 = min(dp[0][u], du[v]);
ll tmp2 = min(dp[1][u], dv[v]);
if (tmp1 + tmp2 < dp[0][v] + dp[1][v])
{
dp[0][v] = tmp1;
dp[1][v] = tmp2;
}
}
}
}
res = min(res, dp[0][ed] + dp[1][ed]);
}
void solve()
{
cin >> n >> m >> s >> t >> u >> v;
for(int i = 1; i <= m; i++)
{
int u, v, w;
cin >> u >> v >> w;
g[u].pb(ii(v, w));
g[v].pb(ii(u, w));
}
dijkstra(u, du);
dijkstra(v, dv);
res = du[v];
dijkstra2(s, t);
dijkstra2(t, s);
cout << res;
}
signed main()
{
cin.tie(0)->sync_with_stdio(0);
int t = 1;
// cin >> t;
while (t--) solve();
return 0;
}
