#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef pair<ll, int> pii;
const int maxn = 2e5+10;
const ll inf = 1e18+10;
struct Edge
{
int u, v, w;
} edge[maxn];
int n, m;
int S, T, U, V;
ll dist[4][maxn];
bool mark[maxn];
ll mn[maxn];
vector<int> dag[maxn], ord;
vector<pii> grafo[maxn];
void dijkstra(int q, int s)
{
for (int i = 1; i <= n; i++)
{
dist[q][i] = inf;
mark[i] = false;
}
priority_queue<pii, vector<pii>, greater<pii>> fila;
dist[q][s] = 0;
fila.push({dist[q][s], s});
while (!fila.empty())
{
int u = fila.top().second; fila.pop();
if (mark[u]) continue;
mark[u] = true;
for (auto pp: grafo[u])
{
int v = pp.first, w = pp.second;
if (dist[q][v] > dist[q][u] + 1ll*w)
{
dist[q][v] = dist[q][u] + 1ll*w;
fila.push({dist[q][v], v});
}
}
}
}
void dfs(int u)
{
mark[u] = true;
for (auto v: dag[u])
if (!mark[v])
dfs(v);
ord.push_back(u);
}
ll get_mn(int a, int b)
{
ll ans = inf;
for (auto u: ord)
{
mn[u] = dist[b][u];
for (auto v: dag[u])
mn[u] = min(mn[u], mn[v]);
ans = min(ans, dist[a][u] + mn[u]);
}
return ans;
}
int main(void)
{
scanf("%d %d %d %d %d %d", &n, &m, &S, &T, &U, &V);
for (int i = 1; i <= m; i++)
{
int u, v, w;
scanf("%d %d %d", &u, &v, &w);
grafo[u].push_back({v, w});
grafo[v].push_back({u, w});
edge[i] = {u, v, w};
}
dijkstra(0, S); dijkstra(1, T);
dijkstra(2, U); dijkstra(3, V);
for (int i = 1; i <= m; i++)
{
int u = edge[i].u, v = edge[i].v, w = edge[i].w;
if (dist[0][u] + 1LL*w + dist[1][v] == dist[0][T])
dag[u].push_back(v);
else if (dist[0][v] + 1LL*w + dist[1][u] == dist[0][T])
dag[v].push_back(u);
}
memset(mark, 0, sizeof mark);
for (int i = 1; i <= n; i++)
if (!mark[i])
dfs(i);
ll ans = min({dist[2][V], get_mn(2, 3), get_mn(3, 2)});
printf("%lld\n", ans);
}
