#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
const long long INF = 2000000000000000000LL;
const int maxN = 1e5 + 4;
const int LOG = 18;
const int dx[] = {1,-1,0,0};
const int dy[] = {0,0,1,-1};
const int MOD = 1e9 + 7;
const int base = 311;
int n, m, s, t, x, y;
vector<pair<int,int>> E[maxN], G[4 * maxN];
ll D[2][maxN], P[4 * maxN];
void dijk(int st, int k)
{
for (int i = 1; i <= n; ++i) D[k][i] = 1e18;
D[k][st] = 0;
priority_queue<pair<ll,int>, vector<pair<ll,int>>, greater<pair<ll,int>>> q;
q.push({0, st});
while(!q.empty())
{
pair<ll,int> h = q.top(); q.pop();
int u = h.second;
ll w = h.first;
if (w > D[k][u]) continue;
for (pair<int,int> x : E[u])
{
int v = x.first, weight = x.second;
if (D[k][v] > D[k][u] + weight)
{
D[k][v] = D[k][u] + weight;
q.push({D[k][v], v});
}
}
}
}
int main()
{
ios_base::sync_with_stdio(false);
cin.tie(NULL); cout.tie(NULL);
// freopen(".INP","r",stdin);
// freopen(".OUT","w",stdout);
cin >> n >> m >> s >> t >> x >> y;
for (int i = 1; i <= m; ++i)
{
int u, v, w; cin >> u >> v >> w;
E[u].push_back({v, w});
E[v].push_back({u, w});
}
dijk(s, 0);
dijk(t, 1);
for (int u = 1; u <= n; ++u)
{
G[u].push_back({n + u, 0});
G[u].push_back({2 * n + u, 0});
G[n + u].push_back({3 * n + u, 0});
G[2 * n + u].push_back({3 * n + u, 0});
for (pair<int,int> x : E[u])
{
int v = x.first, w = x.second;
if (D[0][u] + w + D[1][v] == D[0][t])
{
G[n + u].push_back({n + v, 0});
G[2 * n + v].push_back({2 * n + u, 0});
}
G[u].push_back({v, w});
G[3 * n + u].push_back({3 * n + v, w});
}
}
for (int i = 1; i <= 4 * n; ++i) P[i] = 1e18;
P[x] = 0;
priority_queue<pair<ll,int>, vector<pair<ll,int>>, greater<pair<ll,int>>> q;
q.push({0, x});
while(!q.empty())
{
pair<ll,int> h = q.top(); q.pop();
ll w = h.first;
int u = h.second;
if (w > P[u]) continue;
for (pair<int,int> x : G[u])
{
int v = x.first, weight = x.second;
if (P[v] > P[u] + weight)
{
P[v] = P[u] + weight;
q.push({P[v], v});
}
}
}
cout << P[3 * n + y];
return 0;
}
