#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
struct Arete
{
ll v, c;
};
struct Situation
{
ll u, dis;
bool operator<(Situation other) const
{
return (dis > other.dis or (dis == other.dis and u > other.u));
}
};
const int MAXN = 1e5;
const ll INF = 1e18;
const int U = 0;
const int V = 1;
const int S = 2;
const int T = 3;
vector<Arete> G[MAXN];
ll dis[4][MAXN];
ll uv_from_st[4][4][MAXN];
ll u_from_s[MAXN], v_from_s[MAXN], u_from_t[MAXN];
int special_nodes[4];
int nb_noeuds, nb_aretes;
int u, v, s, t;
void read_input(void)
{
cin >> nb_noeuds >> nb_aretes;
cin >> s >> t;
cin >> u >> v;
s--, t--, u--, v--;
special_nodes[U] = u, special_nodes[V] = v, special_nodes[S]=s, special_nodes[T]=t;
for (int i(0); i < nb_aretes; ++i)
{
int a, b;
ll c;
cin >> a >> b >> c;
G[a-1].push_back({b-1, c});
G[b-1].push_back({a-1, c});
}
}
void run_dis(int from)
{
for (int i(0); i < nb_noeuds; ++i)
dis[from][i] = INF;
dis[from][special_nodes[from]] = 0;
priority_queue<Situation> Q;
Q.push({special_nodes[from], 0});
while (!Q.empty())
{
auto node = Q.top();
Q.pop();
int x = node.u;
ll d = node.dis;
if (d > dis[from][x])
continue;
for (auto e : G[x])
if (d + e.c < dis[from][e.v])
{
dis[from][e.v] = d+e.c;
Q.push({e.v, d+e.c});
}
}
}
void run_weird_dis(int from, int to)
{
for (int i(0); i < nb_noeuds; ++i)
uv_from_st[from][to][i] = INF;
uv_from_st[from][to][special_nodes[from]] = dis[from][special_nodes[to]];
priority_queue<Situation> Q;
Q.push({special_nodes[from], uv_from_st[from][to][special_nodes[from]]});
while (!Q.empty())
{
auto node = Q.top();
Q.pop();
int x = node.u;
ll d = node.dis;
if (uv_from_st[from][to][x] < d)
continue ;
for (auto e : G[x])
if (dis[from][e.v] == dis[from][x] + e.c && uv_from_st[from][to][e.v] > uv_from_st[from][to][x])
{
uv_from_st[from][to][e.v] = min(uv_from_st[from][to][x], dis[to][e.v]);
Q.push({e.v, uv_from_st[from][to][e.v]});
}
}
}
int main(void)
{
ios_base::sync_with_stdio(false); cin.tie(0); cout.tie(0);
read_input();
for (int i(0); i < 4; ++i)
run_dis(i);
for (int from(2); from < 4; ++from)
for (int to(0); to < 2; ++to)
run_weird_dis(from, to);
ll shortest = dis[U][v];
for (int x(0); x < nb_noeuds; ++x)
{
if (dis[S][x] + dis[T][x] == dis[S][t])
{
shortest = min(shortest, min(uv_from_st[S][U][x] + dis[V][x], uv_from_st[T][V][x] + dis[U][x]));
shortest = min(shortest, min(uv_from_st[S][V][x] + dis[U][x], uv_from_st[T][U][x] + dis[V][x]));
}
}
cout << shortest << endl;
}
