//https://pastebin.com/jVURaNCJ
#include<bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
using namespace __gnu_pbds;
using namespace std;
#define N 100005
#define ff first
#define ss second
#define int long long
#define pb push_back
#define mp make_pair
#define pii pair<int,int>
#define piii pair<pair<int,int>,pair<int,int>>
#define vi vector<int>
#define mii map<int,int>
#define pqb priority_queue<int>
#define pqs priority_queue<int,vi,greater<int> >
#define setbits(x) __builtin_popcountll(x)
#define zrobits(x) __builtin_ctzll(x)
#define mod 1000000007
#define inf 1e18
#define ps(x,y) fixed<<setprecision(y)<<x
#define mk(arr,n,type) type *arr=new type[n];
#define w(x) int x; cin>>x; while(x--)
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
typedef tree<int, null_type, less<int>, rb_tree_tag, tree_order_statistics_node_update> pbds;
void c_p_c()
{
ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0);
}
int du[N];
int dv[N];
int ans = inf;
vector<pii>gr[N];
void dijkstra1(int node, int n, int dist[])
{
for (int i = 0; i <= n; i++)
dist[i] = inf;
dist[node] = 0;
priority_queue<pii, vector<pii>, greater<pii>>q;
q.push({dist[node], node});
int val;
while (!q.empty())
{
node = q.top().ss;
val = q.top().ff;
q.pop();
if (dist[node] < val)
continue;
for (auto child : gr[node])
{
if (dist[child.ff] > dist[node] + child.ss)
{
dist[child.ff] = dist[node] + child.ss;
q.push({dist[child.ff], child.ff});
}
}
}
}
int dist[N];
int dist2[2][N];
void dijkstra2(int node, int n, int end)
{
for (int i = 0; i <= n; i++)
{
dist[i] = dist2[0][i] = dist2[1][i] = inf;
}
dist[node] = 0;
priority_queue<pii, vector<pii>, greater<pii>>q;
q.push({0, node});
dist2[0][node] = du[node];
dist2[1][node] = dv[node];
while (!q.empty())
{
node = q.top().ss;
int val = q.top().ff;
q.pop();
for (auto child : gr[node])
{
int to_com = min( dist2[0][node], du[child.ff]) + min(dist2[1][node], dv[child.ff]);
if (dist[child.ff] > dist[node] + child.ss)
{
// cout << child.ff << endl;
dist[child.ff] = dist[node] + child.ss;
dist2[0][child.ff] = min(dist2[0][node], du[child.ff]);
dist2[1][child.ff] = min(dist2[1][node], dv[child.ff]);
q.push({dist[child.ff], child.ff});
}
else if (dist[child.ff] == dist[node] + child.ss && dist2[0][child.ff] + dist2[1][child.ff] > to_com)
{
dist2[0][child.ff] = min( dist2[0][node], du[child.ff]);
dist2[1][child.ff] = min(dist2[1][node], dv[child.ff]);
}
}
}
ans = min(ans, dist2[0][end] + dist2[1][end]);
//cout << dist2[0][7] << " " << dist2[1][7] << " " << dist2[0][2] << " " << dist2[1][2] << endl;
}
int32_t main()
{
c_p_c();
int n, m, s, t, u, v; cin >> n >> m >> s >> t >> u >> v;
for (int i = 0; i < m; i++)
{
int a, b, c; cin >> a >> b >> c;
gr[a].pb({b, c});
gr[b].pb({a, c});
}
dijkstra1(u, n, du);
dijkstra1(v, n, dv);
ans = dv[u];
dijkstra2(s, n, t);
dijkstra2(t, n, s);
cout << ans << '\n';
return 0;
}
