#include<bits/stdc++.h>
#define st first
#define nd second
#define pb push_back
#define ppb pop_back
#define umax(x,y) x=max(x,y)
#define umin(x,y) x=min(x,y)
#define ll long long
#define ii pair<int,int>
#define iii pair<int,ii>
#define sz(x) ((int) x.size())
#define orta ((bas+son)>>1)
#define all(x) x.begin(),x.end()
#define dbgs(x) cerr<<(#x)<<" --> "<<(x)<<" "
#define dbg(x) cerr<<(#x)<<" --> "<<(x)<<endl;getchar()
#define pw(x) (1<<(x))
#define inf 100000000000000
#define MOD 1000000007
#define N 100005
#define MAX 10000006
#define LOG 22
using namespace std;
struct state {
ll cost;
int from,now;
bool operator<(const state& oth) const {
return cost>oth.cost;
}
state(ll x,int y,int z) {
cost=x;
from=y;
now=z;
}
};
int n,m,S,T,U,V,x,y,z;
int mark[N],in[N];
ll up_min[2][N],SH[3][N];
ll ans=inf;
vector<int> graf1[N],graf2[N];
vector<ii> v[N];
void dfs_str(int node) {
// printf("Node --> %d\n",node);
// printf("up_min[0][%d] --> %lld up_min[1][%d] --> %lld\n",node,up_min[0][node],node,up_min[1][node]);
umin(ans,up_min[0][node]+SH[2][node]);
umin(ans,up_min[1][node]+SH[1][node]);
umin(up_min[0][node],SH[1][node]);
umin(up_min[1][node],SH[2][node]);
// printf("Changed up_min[0][%d] --> %lld up_min[1][%d] --> %lld\n",node,up_min[0][node],node,up_min[1][node]);
for(int go:graf1[node]) {
in[go]--;
umin(up_min[0][go],up_min[0][node]);
umin(up_min[1][go],up_min[1][node]);
if(!in[go] && mark[go]) {
dfs_str(go);
}
}
}
void dfs_rev(int node) {
// printf("Node Mark --> %d\n",node);
if(mark[node]) {
// printf("Returned --> %d\n",node);
return ;
}
mark[node]=1;
for(int go:graf2[node]) {
// printf("Cur Node --> %d\n",node);
dfs_rev(go);
}
}
void shp(int node,int wa,int add) {
priority_queue<state> Q;
Q.push(state(0,-1,node));
for(int i=1;i<=n;i++) SH[wa][i]=inf;
while(!Q.empty()) {
state result=Q.top();
Q.pop();
if(SH[wa][result.now]!=inf) {
if(SH[wa][result.now]==result.cost && add && result.from!=-1) {
graf1[result.from].pb(result.now);
graf2[result.now].pb(result.from);
}
continue ;
}
SH[wa][result.now]=result.cost;
if(result.from!=-1 && add) {
graf1[result.from].pb(result.now);
graf2[result.now].pb(result.from);
}
for(ii go:v[result.now]) {
Q.push(state(result.cost+go.nd,result.now,go.st));
}
}
}
int main() {
// freopen("input.txt","r",stdin);
scanf("%d %d",&n,&m);
scanf("%d %d",&S,&T);
scanf("%d %d",&U,&V);
for(int i=1;i<=m;i++) {
scanf("%d %d %d",&x,&y,&z);
v[x].pb({y,z});
v[y].pb({x,z});
}
shp(S,0,1); // from which array add edge?
shp(U,1,0);
shp(V,2,0);
/*for(int i=0;i<3;i++) {
if(i==0) printf("FROM S\n");
else if(i==1) printf("FROM U\n");
else printf("FROM V\n");
for(int j=1;j<=n;j++) printf("%d %lld\n",j,SH[i][j]);
}*/
dfs_rev(T);
for(int i=1;i<=n;i++) {
if(mark[i]) {
for(int go:graf1[i]) {
in[go]++;
}
}
up_min[0][i]=up_min[1][i]=inf;
}
dfs_str(S);
printf("%lld\n",min(ans,SH[1][V]));
}
