#include <bits/stdc++.h>
using namespace std;
#define faster ios_base::sync_with_stdio(0); cin.tie(0);
#define FOR(i,a,b) for(int i = a; i <= b; i++)
#define FOD(i,a,b) for(int i = a; i >= b; i--)
#define fi first
#define se second
#define pb push_back
#define ll long long
#define ull unsigned long long
#define lcm(a,b) (a*b)/__gcd(a,b)
#define ii pair<int,int>
#define iii pair<int,pair<int,int>>
#define iv pair<pair<int,int>,pair<int,int>>
const int inf = 1e9;
const ll INF = 1e18;
const int mod = 1e9 + 7;
const int N = 1e5 + 105;
const int dx[] = {-1,0,1,0};
const int dy[] = {0,1,0,-1};
const int dxx[] = {-1,-1,0,1,1,1,0,-1};
const int dyy[] = {0,1,1,1,0,-1,-1,-1};
int n, m, s, t, x, y;
ll ans;
vector<ii> g[N];
ll d[3][N], best[2][N];
void dijk(int type, int beg)
{
priority_queue<ii,vector<ii>,greater<ii>> pq;
FOR(i,1,n) d[type][i] = INF;
d[type][beg] = 0;
pq.push({0,beg});
while(!pq.empty())
{
int u = pq.top().se;
int cost = pq.top().fi;
pq.pop();
if(cost > d[type][u]) continue;
for(ii h : g[u])
{
int v = h.fi;
int l = h.se;
if(d[type][v] > d[type][u] + l)
{
d[type][v] = d[type][u] + l;
pq.push({d[type][v], v});
}
}
}
}
void dfs(int u)
{
best[0][u] = d[1][u];
best[1][u] = d[2][u];
for(ii h : g[u])
{
int v = h.fi;
if(d[0][v] + h.se == d[0][u])
{
dfs(v);
best[0][u] = min(best[0][u], best[0][v]);
best[1][u] = min(best[1][u], best[1][v]); }
}
ans = min(ans, d[1][u] + best[1][u]);
ans = min(ans, d[2][u] + best[0][u]);
}
void solve()
{
dijk(0,s);
dijk(1,x);
dijk(2,y);
ans = d[1][y];
dfs(t);
cout << ans;
}
void input()
{
//freopen("BUS.INP", "r", stdin);
//freopen("BUS.OUT", "w", stdout);
cin >> n >> m >> s >> t >> x >> y;
FOR(i,1,m)
{
int u, v, w;
cin >> u >> v >> w;
g[u].pb({v,w});
g[v].pb({u,w});
}
}
signed main()
{
faster
input();
solve();
}
