#include <bits/stdc++.h>
#define respagold ios_base::sync_with_stdio(0), cin.tie(0);
#define int long long
#define ll long long
#define int2 __int128_t
#define FOR( i, x, n, d ) for( int i = x; i <= n; i += d )
#define FORR( i, x, n, d ) for( int i = x; i >= n; i -= d )
#define F first
#define S second
#define all(x) x.begin(), x.end()
#define sz(x) (int)(x.size())
#define pb push_back
#define ins insert
#define lb lower_bound
#define ub upper_bound
#define pii pair <int, int>
#define ppi pair <pair <int, int>, int>
#define pip pair <int, pair <int, int>>
#define mkp make_pair
using namespace std;
const int N = 1e5 + 12;
const int mod = 1e9 + 7;
const int inf = 1e18;
int n, m, ans, V, U, S, T, d1[N][2], d2[N][2], d[N];
vector <pii> g[N]; set <pii> st;
void djk1( int start, int tp )
{
FOR( i, 1, n, 1 ) d1[i][tp] = inf;
d1[start][tp] = 0, st.ins({0, start});
while( !st.empty() )
{
pii pp = *st.begin();
int v = pp.S; st.erase(pp);
for( auto i : g[v] )
{
int to = i.F, cost = i.S;
if( d1[v][tp] + cost < d1[to][tp] )
{
st.erase({ d1[to][tp], to });
d1[to][tp] = d1[v][tp] + cost;
st.ins({ d1[to][tp], to });
}
}
}
}
void djk2( int start )
{
FOR( i, 1, n, 1 ) d2[i][0] = d2[i][1] = d[i] = inf;
d2[start][0] = d1[start][0], d2[start][1] = d1[start][1];
d[start] = 0, st.ins({0, start});
while( !st.empty() )
{
pii pp = *st.begin();
int v = pp.S; st.erase(pp);
for( auto i : g[v] )
{
int to = i.F, cost = i.S;
if( d[v] + cost < d[to] )
{
st.erase({ d[to], to });
d[to] = d[v] + cost;
st.ins({ d[to], to });
d2[to][0] = min(d1[to][0], d2[v][0]);
d2[to][1] = min(d1[to][1], d2[v][1]);
}
else if( d[v] + cost == d[to] && min(d2[v][0], d1[to][0]) + min(d2[v][1], d1[to][1]) < d2[to][0] + d2[to][1] )
{
d2[to][0] = min(d2[v][0], d1[to][0]);
d2[to][1] = min(d2[v][1], d1[to][1]);
}
}
}
}
void solve()
{
cin >> n >> m >> S >> T >> U >> V;
FOR( i, 1, m, 1 )
{
int x, y, z;
cin >> x >> y >> z;
g[x].pb({ y, z });
g[y].pb({ x, z });
}
djk1(U, 0), djk1(V, 1);
ans = min(d1[V][0], d1[U][1]);
djk2(S); ans = min(ans, d2[T][0] + d2[T][1]);
djk2(T); ans = min(ans, d2[S][0] + d2[S][1]);
cout << ans << '\n';
}
signed main()
{
respagold;
int test = 1;
if( !test ) cin >> test;
while( test -- ) solve();
}
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