#include <iostream>
#include <algorithm>
#include <vector>
#include <queue>
#include <tuple>
using namespace std;
const int maxn = 100005;
const long long inf = (1LL << 62);
vector<pair<long long, long long>> g[maxn];
long long du[maxn];
long long dv[maxn];
long long ds[maxn];
long long dp[2][maxn];
long long ans = 0;
void dijkstra1(long long start_node, long long dist[])
{
fill(dist, dist + maxn, inf);
priority_queue<pair<long long, long long>> pq;
pq.push({0, start_node});
dist[start_node] = 0;
while (!pq.empty())
{
long long curr = -pq.top().first;
long long node = pq.top().second;
pq.pop();
if (dist[node] < curr) continue;
for (auto [v, w] : g[node])
{
long long path = curr + w;
if (dist[v] > path)
{
dist[v] = path;
pq.push({-path, v});
}
}
}
}
void dijkstra2(long long beg_node, long long end_node)
{
fill(dp[0], dp[0] + maxn, inf);
fill(dp[1], dp[1] + maxn, inf);
fill(ds, ds + maxn, inf);
priority_queue<pair<long long, long>> pq;
pq.push({0, beg_node});
dp[0][0] = inf;
dp[1][0] = inf;
while (!pq.empty())
{
long long curr = -pq.top().first;
long long node = pq.top().second;
pq.pop();
if (ds[node] < curr) continue;
for (auto [v, w] : g[node])
{
long long path = curr + w;
if (ds[v] > path)
{
ds[v] = path;
pq.push({-path, v});
dp[0][v] = min(du[v], dp[0][node]);
dp[1][v] = min(dv[v], dp[1][node]);
}
else if (ds[v] == path)
{
if (min(du[v], dp[0][node]) + min(dv[v], dp[1][node]) <= dp[0][node] + dp[1][node])
{
dp[0][node] = min(du[v], dp[0][node]);
dp[1][node] = min(dv[v], dp[1][node]);
}
}
}
}
ans = min(ans, dp[0][end_node] + dp[1][end_node]);
}
void fastIO()
{
ios_base::sync_with_stdio(0);
cin.tie(0);
cout.tie(0);
}
int main()
{
fastIO();
long long n, m, s, t, u, v;
cin >> n >> m >> s >> t >> u >> v;
for (int i = 1; i <= m; ++i)
{
long long x, y, w;
cin >> x >> y >> w;
g[x].push_back({y, w});
g[y].push_back({x, w});
}
dijkstra1(u, du);
dijkstra1(v, dv);
ans = du[v];
dijkstra2(s, t);
dijkstra2(t, s);
cout << ans << endl;
return 0;
}
