#include <bits/stdc++.h>
#define fi first
#define se second
#define ll long long
using namespace std;
const int N = 1e5 + 100;
ll n, m, S, T, U, V;
ll dis[N][3];
bool dd[N][2];
vector < pair <ll, ll> > adj[N];
void Dijkstra(int type, int batdau)
{
for (int i = 1; i <= n; i++)
dis[i][type] = 1e18;
dis[batdau][type] = 0;
priority_queue < pair<ll, ll> > inside;
inside.push({-dis[batdau][type], batdau});
while (inside.size() != 0)
{
pair <ll, ll> cur = inside.top(); inside.pop();
int u = cur.se;
ll kk = -cur.fi;
if (dis[u][type] < kk)
continue;
for (int i = 0; i < adj[u].size(); i++)
{
pair <ll, ll> tmp = adj[u][i];
int v = tmp.fi;
ll val = tmp.se;
if (kk + val < dis[v][type])
{
dis[v][type] = kk + val;
inside.push({-dis[v][type], v});
}
}
}
}
void dfs(int u, int type)
{
dd[u][type] = true;
for (int i = 0; i < adj[u].size(); i++)
{
pair <ll, ll> tmp = adj[u][i];
int v = tmp.fi;
long long val = tmp.se;
if (dis[u][2] - val == dis[v][2] && dd[v][type] == false)
dfs(v, type);
}
}
void sub1()
{
Dijkstra(2, S);
Dijkstra(1, V);
dfs(T, 0);
long long ans = dis[U][1];
for (int i = 1; i <= n; i++)
if (dd[i][0] == true)
ans = min(ans, dis[i][1]);
cout << ans;
}
void sub3()
{
Dijkstra(2, S);
Dijkstra(0, U);
Dijkstra(1, V);
dfs(T, 0);
long long ans = dis[U][1];
for (int i = 1; i <= n; i++)
if (dd[i][0] == true)
{
for (int j = 1; j <= n; j++)
dd[j][1] = false;
dfs(i, 1);
for (int j = 1; j <= n; j++)
if (dd[j][1] == true)
{
ans = min(ans, dis[i][0] + dis[j][1]);
ans = min(ans, dis[i][1] + dis[j][0]);
}
}
cout << ans;
}
set < pair<ll, ll> > xoa;
void dfs2(int u, int type)
{
dd[u][type] = true;
for (int i = 0; i < adj[u].size(); i++)
{
pair <ll, ll> tmp = adj[u][i];
int v = tmp.fi;
long long val = tmp.se;
if (dis[u][2] - val == dis[v][2] && dd[v][type] == false)
{
dfs2(v, type);
adj[u][i] = {v, 0};
xoa.insert({v, u});
}
}
}
void sub2()
{
Dijkstra(2, S);
dfs2(T, 0);
for (int i = 1; i <= n; i++)
{
for (int j = 0; j < adj[i].size(); j++)
{
pair<ll, ll> tmp = adj[i][j];
if (xoa.find({i, tmp.fi}) != xoa.end())
adj[i][j] = {tmp.fi, 0};
}
}
Dijkstra(0, U);
long long ans = dis[V][0];
cout << ans;
}
int main()
{
ios_base::sync_with_stdio(false);
cin.tie(NULL); cout.tie(NULL);
cin >> n >> m;
cin >> S >> T;
cin >> U >> V;
for (int i = 1; i <= m; i++)
{
ll a, b, c;
cin >> a >> b >> c;
adj[a].push_back({b, c});
adj[b].push_back({a, c});
}
if (S == U)
sub1();
else
if (n <= 300)
sub3();
else
sub2();
return 0;
};
