#include<iostream>
#include<stdio.h>
#include<stdint.h>
#include<iomanip>
#include<algorithm>
#include<utility>
#include<vector>
#include<stack>
#include<queue>
#include<set>
#include<map>
#include<deque>
#include<math.h>
#include<assert.h>
#include<string.h>
using namespace std;
const int64_t INF = (int64_t) 1e18 + 100;
const int64_t mINF = (int64_t) 1e9 + 10;
const int64_t MOD = 998244353;
const int64_t MOD2 = 998244353;
const int nbit = 30;
const int ndig = 10;
const int nchar = 26;
const int p1 = 31;
const int p2 = 53;
const int D = 4;
int dr[D] = {-1, 0, 1, 0};
int dc[D] = {0, 1, 0, -1};
const int Dk = 8;
int drk[Dk] = {2, 2, -2, -2, 1, 1, -1, -1};
int dck[Dk] = {1, -1, 1, -1, 2, -2, 2, -2};
struct Node
{
int u;
int64_t w;
Node(int u_, int64_t w_) : u(u_), w(w_) {}
bool operator < (const Node& o) const
{
return w > o.w;
}
};
struct Node2
{
int u;
int p;
int64_t w;
Node2(int u_, int p_, int64_t w_) : u(u_), p(p_), w(w_) {}
bool operator < (const Node2& o) const
{
return w > o.w;
}
};
struct Edge
{
int v;
int w;
Edge(int v_, int w_) : v(v_), w(w_) {}
};
struct Solution
{
int n;
int m;
int64_t ans;
int st; int ed;
vector<int64_t> dis1;
vector<int64_t> dis2;
vector<vector<Edge> > adj;
Solution() {}
void solve()
{
int s; int t;
cin >> n >> m >> s >> t >> st >> ed;
s--; t--; st--; ed--;
adj.resize(n);
for(int i = 0; i < m; i++)
{
int u;
int v;
int w;
cin >> u >> v >> w;
u--; v--;
adj[u].push_back(Edge(v, w));
adj[v].push_back(Edge(u, w));
}
dis1.resize(n, INF);
dis2.resize(n, INF);
Dijkstra(st, dis1);
Dijkstra(ed, dis2);
ans = dis1[ed];
Dijkstra2(s, t);
Dijkstra2(t, s);
cout << ans << "\n";
}
void Dijkstra2(int s, int t)
{
vector<bool> vis(n, false);
vector<int64_t> dpu(n, INF);
vector<int64_t> dpv(n, INF);
vector<int64_t> dis(n, INF);
dis[s] = 0;
priority_queue<Node2> pq;
pq.push(Node2(s, -1, 0));
while(!pq.empty())
{
Node2 x = pq.top();
pq.pop();
int u = x.u;
if(!vis[u])
{
vis[u] = true; dis[u] = x.w;
dpu[u] = dis1[u];
if(x.p != -1) dpu[u] = min(dpu[u], dpu[x.p]);
dpv[u] = dis2[u];
if(x.p != -1) dpv[u] = min(dpv[u], dpv[x.p]);
for(int i = 0; i < (int) adj[u].size(); i++)
{
int v = adj[u][i].v;
int w = adj[u][i].w;
pq.push(Node2(v, u, x.w + w));
}
}
else if(vis[u] && dis[u] == x.w)
{
int64_t t1 = INF;
int64_t t2 = INF;
if(x.p != -1) t1 = dpu[x.p];
if(x.p != -1) t2 = dpv[x.p];
if(min(dis1[u], t1) + min(dis2[u], t2) <= dpu[u] + dpv[u])
{
dpu[u] = min(dis1[u], t1);
dpv[u] = min(dis2[u], t2);
}
}
}
ans = min(ans, dpu[t] + dpv[t]);
}
void Dijkstra(int s, vector<int64_t>& dis)
{
dis[s] = 0;
priority_queue<Node> pq;
pq.push(Node(s, 0));
while(!pq.empty())
{
Node x = pq.top();
pq.pop();
int u = x.u;
if(dis[u] != x.w) continue;
for(int i = 0; i < (int) adj[u].size(); i++)
{
int v = adj[u][i].v;
int w = adj[u][i].w;
if(dis[v] > dis[u] + w)
{
dis[v] = dis[u] + w;
pq.push(Node(v, dis[v]));
}
}
}
}
int modadd(int t1, int t2)
{
int res = t1 + t2;
if(res >= MOD) res -= MOD;
return res;
}
int modsub(int t1, int t2)
{
int res = t1 - t2;
if(res < 0) res += MOD;
return res;
}
int modmul(int t1, int t2)
{
int64_t res = 1LL * t1 * t2;
return res % MOD;
}
int Abs(int t1)
{
if(t1 < 0) return -t1;
return t1;
}
int MASK(int j)
{
return (1 << j);
}
bool BIT(int t1, int j)
{
return (t1 & MASK(j));
}
};
void __setup()
{
ios_base::sync_with_stdio(false);
cin.tie(NULL); cout.tie(NULL);
// freopen("in.txt", "r", stdin);
// freopen("out.txt", "w", stdout);
}
int main()
{
__setup();
int t = 1;
// cin >> t;
for(int i = 1; i <= t; i++)
{
Solution().solve();
}
return 0;
}
