#include <bits/stdc++.h>
using namespace std;
//#define int long long
#define FILE "task"
#define pb push_back
#define endl '\n'
#define fi first
#define se second
#define ii pair<int, int>
#define FOR(i, l, r) for (int i = l; i <= r; i++)
#define FOD(i, l, r) for (int i = l; i >= r; i--)
#define ex exit(0)
#define pf push_front
#define pob pop_back
#define pof pop_front
#define ff fi.fi
//#define fs fi.se
#define ss se.se
#define sf se.fi
#define MASK(i) (1LL << i)
#define BASE 256
int const N = 1e5 + 5, mod = 1e9 + 7, M = 2e5 + 5, K = 34;
int n, m, x, y, s, t, in[N], flag[N];
int mark[N];
long long fs[N], ft[N], dp[N], ans = 1e18;
vector<ii> e[M];
vector<pair<ii, int>> c;
vector<ii> e2[M];
vector<int> topo;
queue<int> q;
void dijk(int s, long long f[N])
{
FOR(i, 1, n) f[i] = 1e18;
f[s] = 0;
priority_queue<ii, vector<ii>, greater<ii>> pq;
pq.push({0, s});
while(!pq.empty())
{
int u = pq.top().se;
int cost = pq.top().fi;
pq.pop();
if(cost > f[u]) continue;
for(auto x : e[u])
{
int v = x.fi, w = x.se;
if(f[v] > f[u] + w)
{
f[v] = f[u] + w;
pq.push({f[v], v});
}
}
}
}
void init()
{
cin >> n >> m >> s >> t >> x >> y;
FOR(i, 1, m)
{
int x, y, w; cin >> x >> y >> w;
e[x].pb({y, w});
e[y].pb({x, w});
c.pb({{x, y}, w});
}
FOR(i, 1, n)
{
sort(e[i].begin(), e[i].end());
e[i].erase(unique(e[i].begin(), e[i].end()), e[i].end());
}
}
void sub2()
{
if(x == y)
{
cout << 0; ex;
}
dijk(s, fs);
dijk(t, ft);
FOR(u, 1, n) {
for (auto& edge : e[u]) {
int v = edge.fi;
int w = edge.se;
if (fs[u] + w + ft[v] == fs[t]) {
e2[u].pb({v, w});
in[v]++; flag[u]++; flag[v]++;
}
}
}
// FOR(i, 1, n) cout << in[i] << endl;
// FOR(i, 1, n)
// {
// for(auto x : e2[i]) cout << i << " " << x.fi << " " << x.se;
// cout << endl;
// }
int topocnt = 0;
FOR(i, 1, n) if(!in[i] && flag[i] >= 1) q.push(i), mark[i] = ++topocnt;
while(!q.empty())
{
int u = q.front();
q.pop();
topo.pb(u);
for(auto x : e2[u])
{
int v = x.fi, w = x.se;
in[v]--;
if(!in[v]) q.push(v), mark[v] = ++topocnt;
}
}
// for(auto x : topo) cout << x << " ";
// cout << endl;
if(mark[x] > mark[y] && mark[x] && mark[y]) swap(x, y);
dijk(x, fs);
dijk(y, ft);
FOR(i, 1, n) dp[i] = 1e18;
FOD(i, topo.size() - 1, 0)
{
int u = topo[i];
dp[u] = ft[u];
for(auto x : e2[u])
{
int v = x.fi, w = x.se;
dp[u] = min(dp[u], dp[v]);
}
}
for(auto u : topo)
{
ans = min(ans, fs[u] + dp[u]);
// cout << fx[u] + dp[u] << " " << fx[u] << " " << dp[u] << endl;
}
FOR(i, 1, n) dp[i] = 1e18;
FOD(i, topo.size() - 1, 0)
{
int u = topo[i];
dp[u] = fs[u];
for(auto x : e2[u])
{
int v = x.fi, w = x.se;
dp[u] = min(dp[u], dp[v]);
}
}
for(auto u : topo)
{
ans = min(ans, ft[u] + dp[u]);
// cout << fx[u] + dp[u] << " " << fx[u] << " " << dp[u] << endl;
}
cout << min(ans, fs[y]);
}
signed main()
{
if (fopen(FILE ".inp", "r"))
{
freopen(FILE ".inp", "r", stdin);
freopen(FILE ".out", "w", stdout);
}
ios_base::sync_with_stdio(false);
cin.tie(0); cout.tie(0);
init();
sub2();
}
/*
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*/
