#include <iostream>
#include <vector>
#include <queue>
#include <utility>
#define pii pair<int, int>
#define piii pair<int, pii>
#define pll pair<long long, long long>
#define plll pair<long long, pll>
#define ff first
#define ss second
#define ee ss.ff
#define rr ss.ss
using namespace std;
vector<pii> gph[101010];
vector<int> agph[101010];
vector<int> bgph[101010];
bool vst[101010];
long long dist[101010];
long long dst[101010][4];
vector<int> pr[101010];
void dfs(int x)
{
if(vst[x]) return;
vst[x] = true;
for(auto y : pr[x]) if(y != -1)
{
agph[x].push_back(y);
bgph[y].push_back(x);
dfs(y);
}
}
int main()
{
ios_base::sync_with_stdio(false);
cin.tie(nullptr);
int n, m; cin >> n >> m;
int s, t, u, v; cin >> s >> t >> u >> v; --s; --t; --u; --v;
for(int i = 0; i < m; ++i)
{
int s, e, x; cin >> s >> e >> x; --s; --e;
gph[s].push_back({e, x});
gph[e].push_back({s, x});
}
{
for(int i = 0; i < n; ++i) dist[i] = -1;
priority_queue<plll, vector<plll>, greater<plll>> Q;
Q.push({0, {s, -1}});
while(Q.size())
{
auto x = Q.top(); Q.pop();
if(dist[x.ee] == -1 || dist[x.ee] == x.ff) pr[x.ee].push_back(x.rr);
if(dist[x.ee] != -1) continue;
dist[x.ee] = x.ff;
for(auto y : gph[x.ee]) Q.push({x.ff + y.ss, {y.ff, x.ee}});
}
dfs(t);
}
for(int i = 0; i < n; ++i) for(int j = 0; j < 4; ++j) dst[i][j] = -1;
priority_queue<plll, vector<plll>, greater<plll>> Q;
Q.push({0, {u, 0}});
while(Q.size())
{
auto x = Q.top(); Q.pop();
if(dst[x.ee][x.rr] != -1) continue;
dst[x.ee][x.rr] = x.ff;
if(x.rr == 0)
{
for(auto y : gph[x.ee]) Q.push({x.ff + y.ss, {y.ff, 0}});
for(auto y : agph[x.ee]) Q.push({x.ff, {y, 1}});
for(auto y : bgph[x.ee]) Q.push({x.ff, {y, 2}});
}
else if(x.rr == 1)
{
for(auto y : agph[x.ee]) Q.push({x.ff, {y, 1}});
for(auto y : gph[x.ee]) Q.push({x.ff + y.ss, {y.ff, 3}});
}
else if(x.rr == 2)
{
for(auto y : bgph[x.ee]) Q.push({x.ff, {y, 2}});
for(auto y : gph[x.ee]) Q.push({x.ff + y.ss, {y.ff, 3}});
}
else for(auto y : gph[x.ee]) Q.push({x.ff + y.ss, {y.ff, 3}});
}
long long ans = (long long)8e18;
for(int i = 0; i < 4; ++i) if(dst[v][i] != -1) ans = min(ans, dst[v][i]);
cout << ans;
}
