#include <bits/stdc++.h>
#define ll long long
using namespace std;
int N, M;
ll DIST[5][100001], sol;
vector <pair <int, int>> VG[100001];
void Dijkstra(int node, ll dist, int i)
{
fill(DIST[i] + 1, DIST[i] + N + 1, 1e18);
DIST[i][node] = dist;
if(i == 2)
{
for(int j = 1; j <= N; j++) DIST[3][j] = DIST[0][j];
for(int j = 1; j <= N; j++) DIST[4][j] = DIST[1][j];
}
priority_queue <pair <ll, int>> H;
H.push({-dist, node});
while(H.size())
{
node = H.top().second;
dist = -H.top().first;
H.pop();
if(dist != DIST[i][node]) continue;
if(i == 2)
{
for(pair <int, int> p : VG[node])
{
if((DIST[i][node] - p.first) != DIST[i][p.second]) continue;
DIST[3][node] = min(DIST[3][p.second], DIST[3][node]);
DIST[4][node] = min(DIST[4][p.second], DIST[4][node]);
}
}
for(pair <int, int> p : VG[node])
{
if((DIST[i][node] + p.first) >= DIST[i][p.second]) continue;
DIST[i][p.second] = DIST[i][node] + p.first;
H.push({-DIST[i][p.second], p.second});
}
}
return;
}
bitset <100001> B;
void DFS(int node)
{
B[node] = 1;
sol = min({DIST[0][node] + DIST[4][node], DIST[1][node] + DIST[3][node], sol});
for(pair <int, int> p : VG[node])
{
if(B[p.second] || ((DIST[2][node] - p.first) != DIST[2][p.second])) continue;
DFS(p.second);
}
return;
}
int main()
{
ios_base::sync_with_stdio(0), cin.tie(0), cout.tie(0);
cin >> N >> M;
int s, t, s1, t1, u, v, w;
cin >> s >> t >> s1 >> t1;
for(int i = 1; i <= M; i++)
{
cin >> u >> v >> w;
VG[u].push_back({w, v});
VG[v].push_back({w, u});
}
Dijkstra(s1, 0, 0);
Dijkstra(t1, 0, 1);
Dijkstra(s, 0, 2);
sol = DIST[0][t1];
DFS(t);
cout << sol << '\n';
return 0;
}
