#include <bits/stdc++.h>
typedef long long ll;
using namespace std;
#define N 100005
struct A{
long long a,w,p;
bool operator<(const A& o)const{
return w>o.w;
}
};
priority_queue<A> q;
vector<A> g[N];
vector<pair<ll, ll>> graph[100001];
vector<vector<long long>> dis(2,vector<long long>(N,1e18));
ll ds[100001], dp[2][100001], ans;
bool visited[100001];
void dijk(int idx,int s){
q.push({s,0});
dis[idx][s]=0;
while(!q.empty()){
auto [a,w,p]=q.top();
q.pop();
if(w>dis[idx][a])continue;
for(auto x:g[a]){
if(w+x.w<dis[idx][x.a])q.push({x.a,w+x.w}),dis[idx][x.a]=w+x.w;
}
}
}
void dijkstra2(ll start, ll end) {
fill(dp[0], dp[0] + 100001, LLONG_MAX / 2);
fill(dp[1], dp[1] + 100001, LLONG_MAX / 2);
fill(visited, visited + 100001, false);
priority_queue<pair<ll, pair<ll, ll>>> pq;
pq.push({0, {start, 0}});
dp[0][0] = dp[1][0] = LLONG_MAX/ 2;
while (!pq.empty()) {
ll c, node, par;
pair<ll, ll> p;
tie(c, p) = pq.top();
tie(node, par) = p;
pq.pop();
if (!visited[node]) {
visited[node] = true;
ds[node] = -c;
dp[0][node] = min(dis[0][node], dp[0][par]);
dp[1][node] = min(dis[1][node], dp[1][par]);
for (auto i : graph[node]) pq.push({c - i.second, {i.first, node}});
} else if (-c == ds[node]) {
if (min(dis[0][node], dp[0][par]) + min(dis[1][node], dp[1][par]) <= dp[0][node] + dp[1][node]) {
dp[0][node] = min(dis[0][node], dp[0][par]);
dp[1][node] = min(dis[1][node], dp[1][par]);
}
}
}
ans = min(ans, dp[0][end] + dp[1][end]);
}
int main() {
int n,m,s,t,u,v,i,a,b;
long long w;
scanf("%d %d %d %d %d %d",&n,&m,&s,&t,&u,&v);
for(i=1;i<=m;i++){
scanf("%d %d %lld",&a,&b,&w);
g[a].push_back({b,w});
g[b].push_back({a,w});
}
dijk(0,u);
dijk(1,v);
ans = dis[0][v];
dijkstra2(s, t);
dijkstra2(t, s);
printf("%lld",ans);
return 0;
}
