#include<bits/stdc++.h>
using namespace std;
#define int long long
const int MAXN = 2e5 + 5;
#define pii pair<int, int>
const int INF = 1e18;
int n, m;
int U, V, S, T;
vector<pii> adj[MAXN];
int du[MAXN];
int dv[MAXN];
int ds[MAXN];
int dp[2][MAXN];
void dijskstra1(int st, int d[])
{
for (int i = 1; i <= n; i++)
{
d[i] = INF;
}
d[st] = 0;
priority_queue<pii, vector<pii>, greater<pii>> pq;
pq.push({d[st], st});
while(!pq.empty())
{
auto[dist, u] = pq.top();
pq.pop();
if (dist > d[u]) continue;
for (auto[v, w] : adj[u])
{
if (d[v] > d[u] + w)
{
d[v] = d[u] + w;
pq.push({d[v], v});
}
}
}
}
int dijskstra2(int s, int t)
{
for (int i = 1; i <= n; i++)
{
dp[0][i] = INF;
dp[1][i] = INF;
ds[i] = INF;
}
ds[s] = 0;
dp[0][s] = du[s];
dp[1][s] = dv[s];
priority_queue<pii, vector<pii>, greater<pii>> pq;
pq.push({ds[s], s});
while(!pq.empty())
{
auto[dist, u] = pq.top();
pq.pop();
if (dist > ds[u]) continue;
for (auto[v, w] : adj[u])
{
if (ds[v] > ds[u] + w)
{
ds[v] = ds[u] + w;
dp[0][v] = min(dp[0][u], du[v]);
dp[1][v] = min(dp[1][u], dv[v]);
pq.push({ds[v], v});
}
else if (ds[v] == ds[u] + w)
{
int old_sum = dp[0][v] + dp[1][v];
int new_sum = min(dp[0][u], du[v]) + min(dp[1][u], dv[v]);
if (new_sum < old_sum)
{
dp[0][v] = min(dp[0][u], du[v]);
dp[1][v] = min(dp[1][u], dv[v]);
}
}
}
}
return dp[0][t] + dp[1][t];
}
signed main()
{
ios_base::sync_with_stdio(0);
cin.tie(0);
cout.tie(0);
cin >> n >> m;
cin >> S >> T;
cin >> U >> V;
for (int i = 1; i <= m; i++)
{
int u, v, c;
cin >> u >> v >> c;
adj[u].push_back({v, c});
adj[v].push_back({u, c});
}
dijskstra1(U, du);
dijskstra1(V, dv);
int res = du[V];
cout << min({res, dijskstra2(S, T), dijskstra2(T, S)});
}
