#include <bits/stdc++.h>
using namespace std;
#define int long long
using ii = pair<int, int>;
#define F first
#define S second
#define REP(i, n) for(int i = 1; i <= n; i++)
#define FOR(i, a, b) for(auto i = a; i <= b; i++)
#define FORD(i, a, b) for(auto i = a; i >= b; i--)
template<class T> bool maximize(T& a, T b) { if(a < b) return a = b, 1; return 0; }
template<class T> bool minimize(T& a, T b) { if(a > b) return a = b, 1; return 0; }
mt19937 rng(time(0));
const int N = (int)1e5 + 7, INF = (int)7e18;
vector<ii> adj[N];
int dp[N][2];
int du[N], dv[N], d[N];
bool vis[N];
int n, m, s, t, l, r;
void Precompute(int start, int dist[])
{
priority_queue<ii> pq;
dist[start] = 0;
pq.push({0, start});
while(pq.size())
{
int u, f;
tie(f, u) = pq.top();
pq.pop();
f = -f;
if(dist[u] != f)
continue;
for(ii nxt : adj[u])
{
int v, w;
tie(v, w) = nxt;
if(minimize(dist[v], f + w))
pq.push({-dist[v], v});
}
}
}
int ans;
void Calc(int st, int en)
{
priority_queue<array<int, 3>> pq;
memset(dp, 0x3f, sizeof dp);
memset(vis, 0, sizeof vis);
fill(d, d + n + 1, INF);
d[st] = 0;
pq.push({0, st, 0});
while(pq.size())
{
int f, u, par;
array<int, 3> TOP = pq.top();
f = TOP[0];
u = TOP[1];
par = TOP[2];
pq.pop();
if(!vis[u])
{
vis[u] = 1;
d[u] = -f;
dp[u][0] = min(dp[par][0], du[u]);
dp[u][1] = min(dp[par][1], dv[u]);
for(ii nxt : adj[u])
{
int v, w;
tie(v, w) = nxt;
pq.push({f - w, v, u});
}
}else if(-f == d[u])
{
int f1 = min(dp[par][0], du[u]);
int f2 = min(dp[par][1], dv[u]);
if(f1 + f2 <= dp[u][0] + dp[u][1])
{
dp[u][0] = f1;
dp[u][1] = f2;
}
}
}
minimize(ans, dp[en][0] + dp[en][1]);
}
signed main(void)
{
cin.tie(nullptr)->sync_with_stdio(false);
#define TASK "CPASS"
if(fopen(TASK".INP", "r"))
{
freopen(TASK".INP", "r", stdin);
// freopen(TASK".OUT", "w", stdout);
}
cin >> n >> m;
cin >> s >> t;
cin >> l >> r;
REP(i, m)
{
int u, v, w;
cin >> u >> v >> w;
adj[u].push_back({v, w});
adj[v].push_back({u, w});
}
memset(du, 0x3f, sizeof du);
memset(dv, 0x3f, sizeof dv);
Precompute(l, du);
Precompute(r, dv);
ans = du[r];
Calc(s, t);
Calc(t, s);
cout << ans << '\n';
return 0;
}
/*
6 6
1 6
5 4
1 2 1
2 3 1
3 5 1
2 4 3
4 5 2
5 6 1
*/
