#include <bits/stdc++.h>
// author: aykhn
using namespace std;
typedef long long ll;
#define all(v) v.begin(), v.end()
#define pii pair<int, int>
#define mpr make_pair
#define eb emplace_back
#define pb push_back
#define ts to_string
#define fi first
#define se second
#define ins insert
#define int ll
#define inf 0x3F3F3F3F
#define infll 0x3F3F3F3F3F3F3F3FLL
#define bpc __builtin_popcount
const int MXN = 1e5 + 5;
int dist[2][MXN];
int d1[MXN];
array<array<int, 2>, 4> d[MXN];
vector<array<int, 2>> adj[MXN];
array<int, 2> comp(array<int, 2> a, array<int, 2> b, int t)
{
if (!t) return (a[0] + a[1] == b[0] + b[1] ? min(a, b) : (a[0] + a[1] < b[0] + b[1] ? a : b));
else if (t == 1)
{
swap(a[0], a[1]), swap(b[0], b[1]);
if (a > b) swap(a, b);
swap(a[0], b[0]), swap(b[0], b[1]);
return (a[0] + a[1] == b[0] + b[1] ? a : (a[0] + a[1] < b[0] + b[1] ? a : b));
}
else if (t == 2) return min(a, b);
else
{
swap(a[0], a[1]), swap(b[0], b[1]);
if (a > b) swap(a, b);
swap(a[0], a[1]);
return a;
}
}
void dijk(int s, int id)
{
for (int i = 0; i < MXN; i++) dist[id][i] = infll;
priority_queue<array<int, 2>, vector<array<int, 2>>, greater<array<int, 2>>> pq;
dist[id][s] = 0;
pq.push({0, s});
while (!pq.empty())
{
array<int, 2> f = pq.top();
pq.pop();
if (f[0] > dist[id][f[1]]) continue;
for (const array<int, 2> &v : adj[f[1]])
{
if (dist[id][v[0]] > f[0] + v[1])
{
dist[id][v[0]] = f[0] + v[1];
pq.push({dist[id][v[0]], v[0]});
}
}
}
}
signed main()
{
ios_base::sync_with_stdio(0);
cin.tie(nullptr);
int n, m, s, t, u, v;
cin >> n >> m >> s >> t >> u >> v;
while (m--)
{
int u, v, w;
cin >> u >> v >> w;
adj[u].pb({v, w});
adj[v].pb({u, w});
}
dijk(u, 0);
dijk(v, 1);
for (int i = 0; i < MXN; i++)
{
for (int j = 0; j < 4; j++) d[i][j] = {infll, infll};
d1[i] = infll;
}
priority_queue<array<int, 2>, vector<array<int, 2>>, greater<array<int, 2>>> pq;
d1[s] = 0;
d[s][0] = d[s][1] = d[s][2] = d[s][3] = {dist[0][s], dist[1][s]};
pq.push({0, s});
while (!pq.empty())
{
int f = pq.top()[1];
int w = pq.top()[0];
for (int i = 0; i < 4; i++) d[f][i][0] = min(d[f][i][0], dist[0][f]), d[f][i][1] = min(d[f][i][1], dist[1][f]);
pq.pop();
if (w > d1[f]) continue;
for (const array<int, 2> &v : adj[f])
{
if (d1[v[0]] > w + v[1])
{
d1[v[0]] = w + v[1];
d[v[0]] = d[f];
pq.push({d1[v[0]], v[0]});
}
else if (d1[v[0]] == w + v[1])
{
for (int i = 0; i < 4; i++) d[v[0]][i] = comp(d[f][3], comp(d[f][2], comp(d[f][1], comp(d[v[0]][i], d[f][0], 0), 0), 0), 0);
// pq.push({d1[v[0]], v[0]});
}
}
}
cout << min(d[t][0][0] + d[t][0][1], dist[0][v]) << '\n';
}
