#include<bits/stdc++.h>
#define int long long
#define ii pair<int,int>
#define ff first
#define ss second
using namespace std;
const int maxn = 2e5 + 5;
int n, m, s, t, a, b, ans = 1e18;
int d[4][maxn], vis[maxn];
ii dp[maxn];
vector<ii> adj[maxn];
vector<int> dag[maxn];
void bfs(int x) /// dijkstra
{
int y;
if (x == t) y = 1;
else if (x == a) y = 2;
else y = 3;
memset(d[y], 0x3f, sizeof d[y]);
d[y][x] = 0;
priority_queue<ii, vector<ii>, greater<ii>> pq;
pq.emplace(0, x);
while (pq.size())
{
int u, v;
tie(v, u) = pq.top();
pq.pop();
if (v != d[y][u]) continue;
for (auto p : adj[u])
if (d[y][p.ff] > v + p.ss)
pq.emplace(d[y][p.ff] = v + p.ss, p.ff);
}
}
void dfs(int x)
{
if (vis[x]) return;
vis[x] = 1;
for (auto p : adj[x])
if (d[1][x] == d[1][p.ff] + p.ss)
dag[x].emplace_back(p.ff),
dfs(p.ff);
}
ii cal(int x)
{
if (vis[x]) return dp[x];
vis[x] = 1;
dp[x].ff = d[3][x];
dp[x].ss = d[2][x];
for (int i : dag[x])
{
int u, v;
tie(u, v) = cal(i);
dp[x].ff = min(dp[x].ff, u);
dp[x].ss = min(dp[x].ss, v);
}
ans = min(ans, d[2][x] + dp[x].ff);
ans = min(ans, d[3][x] + dp[x].ss);
return dp[x];
}
signed main()
{
ios_base::sync_with_stdio(false);
cin.tie(0); cout.tie(0);
// freopen("test.inp", "r", stdin);
// freopen("test.out", "w", stdout);
cin >> n >> m >> s >> t >> a >> b;
for (int i = 1, u, v, w; i <= m; i++)
cin >> u >> v >> w,
adj[u].emplace_back(v, w),
adj[v].emplace_back(u, w);
bfs(t);
bfs(a);
bfs(b);
dfs(s);
memset(vis, 0, sizeof vis);
cal(s);
ans = min(ans, d[2][b]);
cout << ans;
}
