/*
* @Author: Twynzz
* @Last Modified by: Twynzz
* @Note For This Problem: https://wbd.ms/share/v2/aHR0cHM6Ly93aGl0ZWJvYXJkLm1pY3Jvc29mdC5jb20vYXBpL3YxLjAvd2hpdGVib2FyZHMvcmVkZWVtL2NmODRmYTFjYTY2NjRiNmViYjc1MzU1OTNjYmZjYzZhX0JCQTcxNzYyLTEyRTAtNDJFMS1CMzI0LTVCMTMxRjQyNEUzRF9iMDY2ZDUzNC1iMDIzLTQ1ZDQtOGNiNS03MDEwOWE0NjcwNTg=
*/
#include <bits/stdc++.h>
using namespace std;
// ------------ Define ------------
#define el "\n"
#define int long long
#define ld long double
#define str string
#define file(name) {freopen(name".inp","r",stdin);freopen(name".out","w",stdout);}
#define IOS {std::ios_base::sync_with_stdio(false);cin.tie(0);cout.tie(0);}
#define _TBN_ signed main()
#define setp(n) setprecision(n)<< fixed
#define fi first
#define se second
#define ii pair<int,int>
#define gcd(a,b) __gcd(a,b)
#define tup pair<int,ii>
#define pb push_back
#define pf push_front
#define eb emplace_back
#define sz(v) (int)v.size()
const int maxn = 1e6+9;
const long long oo = 1e18;
const int MOD = 1e9+7, Mod = 998244353;
const int base = 311;
template<class X>
bool maximize(X &a, const X &b)
{
if (a<b)
{
a = b;
return 1;
}
return 0;
}
template<class X>
bool minimize(X &a, const X &b)
{
if (a>b)
{
a = b;
return 1;
}
return 0;
}
namespace sub1
{
bool checkSub1();
void sub1();
}
namespace sub2
{
bool checkSub2();
void sub2();
}
namespace sub3
{
bool checkSub3();
void sub3();
}
int lcm(int a, int b)
{
return a/gcd(a,b)*b;
}
int sqr(int x) {return x*x;}
inline bool MASK(int mask, int bit) {return ((mask>>bit)&1);}
inline long long F(int n) {return n*(n+1)/2;}
inline int add(int a, int b, int m = MOD) {return ((a%m+b%m)%m+m)%m;}
inline int sub(int a, int b, int m = MOD) {return ((a-b)%m+m)%m;}
inline int mul(int a, int b, int m = MOD) {return ((a%m)*(b%m))%m;}
int dx[] = {1, 0};
int dy[] = {0, 1};
// ------------ Code ------------
int n, m, S, T, U, V;
vector<ii> adj[maxn];
_TBN_
{
IOS;
if (fopen("BOOKR.inp","r")) file("BOOKR");
cin >>n >>m >>S >>T >>U >>V;
for(int i = 1; i <= m; i++)
{
int u, v, c;
cin >>u >>v >>c;
adj[u].eb(v, c);
adj[v].eb(u, c);
}
for(int i = 1; i <= 1; i++)
{
if (sub1::checkSub1()) {sub1::sub1(); continue;}
// if (sub2::checkSub2()) {sub2::sub2(); continue;}
// if (sub3::checkSub3()) {sub3::sub3(); continue;}
}
return 0;
}
namespace sub1
{
bool checkSub1()
{
return 1;
}
int dis[4][maxn];
bool vis[maxn];
void dijk(int s, int id)
{
fill(dis[id] + 1, dis[id] + 1 + n, oo);
fill(vis + 1, vis + 1 + n, 0);
dis[id][s] = 0;
priority_queue<ii, vector<ii>, greater<ii>> q;
q.emplace(0, s);
while(!q.empty())
{
int u = q.top().se;
q.pop();
if (vis[u]) continue;
vis[u] = 1;
for(ii cur : adj[u])
{
int v = cur.fi, w = cur.se;
if (minimize(dis[id][v], dis[id][u] + w))
q.emplace(dis[id][v], v);
}
}
}
vector<int> e[maxn];
int dp[maxn][4], ans;
void dfs(int u)
{
dp[u][1] = dis[1][u]; // U -> V xuoi theo dijk
dp[u][2] = dis[2][u]; // V -> U xuoi theo dijk
vis[u] = 1;
if (u == T) return;
for(int v : e[u])
{
if (!vis[v]) dfs(v);
minimize(dp[u][1], dp[v][1]);
minimize(dp[u][2], dp[v][2]);
}
minimize(ans, dp[u][1] + dis[2][u]);
minimize(ans, dis[1][u] + dp[u][2]);
// cout<< u<< ' '<< dp[u][1]<< ' '<< dis[2][u]<< ' '<< ans<< el;
// cout<< u<< ' '<< dis[1][u]<< ' '<< dp[u][2]<< el;
}
void sub1()
{
dijk(S, 0);
dijk(U, 1);
dijk(V, 2);
dijk(T, 3);
for(int u = 1; u <= n; u++)
{
for(ii cur : adj[u])
{
int v = cur.fi, w = cur.se;
if (dis[0][u] + w + dis[3][v] == dis[0][T])
{
e[u].eb(v);
// cout<< u<< ' '<< v<< ' '<< w<< el;
}
}
}
ans = dis[1][V];
fill(vis + 1, vis + 1 + n, 0);
dfs(S);
cout<< ans<< el;
}
}
