#include <bits/stdc++.h>
#define ii pair <int, int>
#define ll long long
#define llll pair <ll, ll>
#define ld long double
#define ull unsigned long long
#define el "\n"
#define sp " "
#define fi first
#define se second
#define pub push_back
#define puf push_front
#define pob pop_back
#define pof pop_front
#define __lcm(a, b) (a / __gcd(a, b) * b)
#define sq(x) (x) * (x)
#define sqr(x) sqrtl(x)
#define cbr(x) cbrtl(x)
#define sz(a) (ll)(a.size())
using namespace std;
const ld PI = acos(-1); const int INFI = 1e9 + 7; const ll INFL = 2e18 + 7;
int n, m, s, t, u, v, x[200005], y[200005], z[200005];
vector <pair <pair <int, ll>, int>> g[100005];
ll d[5][100005];
priority_queue <pair <pair <ll, int>, int>, vector <pair <pair <ll, int>, int>>, greater <pair <pair <ll, int>, int>>> pq;
void Dijkstra_1(int start, int id)
{
for (int i = 1; i <= n; i++) d[id][i] = INFL;
d[id][start] = 0;
pq.push({{0, start}, 1});
while (sz(pq))
{
pair <pair <ll, int>, int> temp = pq.top();
pq.pop();
for (pair <pair <int, ll>, int> i : g[temp.fi.se])
{
if (temp.fi.fi + i.fi.se < d[id][i.fi.fi])
{
d[id][i.fi.fi] = temp.fi.fi + i.fi.se;
pq.push({{temp.fi.fi + i.fi.se, i.fi.fi}, 1});
}
}
}
}
void Dijkstra_2(int start)
{
for (int i = 1; i <= n; i++)
{
for (int j = 1; j <= 4; j++) d[j][i] = INFL;
}
d[1][start] = 0;
pq.push({{0, start}, 1});
while (sz(pq))
{
pair <pair <ll, int>, int> temp = pq.top();
pq.pop();
//cout << temp.fi.fi << sp << temp.fi.se << sp << temp.se << el;
for (pair <pair <int, ll>, int> i : g[temp.fi.se])
{
if ((temp.se == 1 && i.se == 4) || ((temp.se == 2 || temp.se == 3) && (i.se != 4 && i.se != temp.se)) || (temp.se == 4 && i.se != 4)) continue;
if (temp.fi.fi + i.fi.se < d[i.se][i.fi.fi])
{
d[i.se][i.fi.fi] = temp.fi.fi + i.fi.se;
pq.push({{temp.fi.fi + i.fi.se, i.fi.fi}, i.se});
}
}
}
}
void Solve()
{
cin >> n >> m >> s >> t >> u >> v;
for (int i = 1; i <= m; i++)
{
cin >> x[i] >> y[i] >> z[i];
g[x[i]].pub({{y[i], z[i]}, 1});
g[y[i]].pub({{x[i], z[i]}, 1});
}
Dijkstra_1(s, 1);
Dijkstra_1(t, 2);
for (int i = 1; i <= m; i++)
{
g[x[i]].pub({{y[i], z[i]}, 4});
g[y[i]].pub({{x[i], z[i]}, 4});
if (d[1][x[i]] + z[i] + d[2][y[i]] == d[1][t])
{
g[x[i]].pub({{y[i], 0}, 2});
g[y[i]].pub({{x[i], 0}, 3});
}
else if (d[2][x[i]] + z[i] + d[1][y[i]] == d[1][t])
{
g[y[i]].pub({{x[i], 0}, 2});
g[x[i]].pub({{y[i], 0}, 3});
}
}
Dijkstra_2(u);
cout << min({d[1][v], d[2][v], d[3][v], d[4][v]});
}
int main()
{
ios_base::sync_with_stdio(0); cin.tie(NULL); cout.tie(0);
Solve();
return 0;
}
//coded by icyalmond
