#include <bits/stdc++.h>
using namespace std;
#define int long long
#define all(x) x.begin(), x.end()
const int INF = 1e18, MOD = 1e9 + 7, N = 1e5 + 1;
void setIO(string name = ""){
ios::sync_with_stdio(false);
cin.tie(0);
if(name.size()){
freopen((name + ".in").c_str(), "r", stdin);
freopen((name + ".out").c_str(), "w", stdout);
}
}
using pii = pair<int, int>;
vector<pii> adj[N];
int disu[N], disv[N], diss[N], vis[N], ans, dp[2][N];
void getdis(int start, int dis[]){
fill(vis, vis + N, false);
priority_queue<pii> pq;
pq.push({0, start});
dis[start] = 0;
while(!pq.empty()){
int c, cur;
tie(c, cur) = pq.top();
pq.pop();
if(!vis[cur]){
dis[cur] = -c;
vis[cur] = 1;
for(auto nxt : adj[cur])pq.push({c - nxt.first, nxt.second});
}
}
}
void dijkstra(int start, int end){
fill(vis, vis + N, false);
fill(dp[0], dp[0] + N, INF);
fill(dp[1], dp[1] + N, INF);
priority_queue<pair<int, pii>> pq;
pq.push({0, {start, 0}});
while(!pq.empty()){
int c, cur, par;
pii tmp;
tie(c, tmp) = pq.top();
tie(cur, par) = tmp;
pq.pop();
if(!vis[cur]){
vis[cur] = 1;
dp[0][cur] = min(disu[cur], dp[0][par]);
dp[1][cur] = min(disv[cur], dp[1][par]);
diss[cur] = -c;
for(auto nxt : adj[cur])pq.push({c - nxt.first, {nxt.second, cur}});
}else if(diss[cur] == -c){
if(min(disu[cur], dp[0][par]) + min(disv[cur], dp[1][par]) < dp[0][cur] + dp[1][cur]){
dp[0][cur] = min(disu[cur], dp[0][par]);
dp[1][cur] = min(disv[cur], dp[1][par]);
}
}
}
ans = min(ans, dp[0][end] + dp[1][end]);
}
signed main(){
setIO();
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;
adj[a].push_back({c, b});
adj[b].push_back({c, a});
}
getdis(u, disu);
getdis(v, disv);
ans = disu[v];
dijkstra(s, t);
dijkstra(t, s);
cout << ans;
}
