///TRAN THAI BAO :3
#include <iostream>
#include <cstdio>
#include <vector>
#include <queue>
using namespace std;
#define maxN 100007
#define oo 1e18
typedef pair<long long, long long> pii;
typedef pair<pii, long long> piii;
int n, m;
priority_queue<pii, vector<pii>, greater<pii> >pq;
priority_queue<piii, vector<piii>, greater<piii> >pq2;
vector<pii>orgAdj[maxN];
vector<piii>adj[maxN][4];
bool vis[maxN] = {false};
int S, T, X, Y;
long long orgMinD[maxN];
long long minD[maxN][4];
pii pre[maxN] = {{0, 0}};
void readData()
{
cin >> n >> m >> S >> T >> X >> Y;
int u, v, w;
for(int i = 0; i < m; i++)
{
cin >> u >> v >> w;
orgAdj[u].push_back({v, w});
orgAdj[v].push_back({u, w});
adj[u][0].push_back({{v, w}, 0});
adj[v][0].push_back({{u, w}, 0});
adj[u][3].push_back({{v, w}, 3});
adj[v][3].push_back({{u, w}, 3});
}
}
void dfsPre(int u)
{
vis[u] = true;
int v;
long long w;
for(int i = 0; i < orgAdj[u].size(); i++)
{
v = orgAdj[u][i].first;
w = orgAdj[u][i].second;
if(orgMinD[v] + w == orgMinD[u])
{
adj[v][1].push_back({{u, 0}, 1});
adj[u][2].push_back({{v, 0}, 2});
if(!vis[v])
dfsPre(v);
}
}
}
void dijkstra()
{
for(int i = 1; i <= n; i++)
orgMinD[i] = oo;
orgMinD[S] = 0;
pq.push({orgMinD[S], S});
while(!pq.empty())
{
int cur = pq.top().second;
long long w = pq.top().first;
pq.pop();
if(orgMinD[cur] != w) continue;
for(int i = 0; i < orgAdj[cur].size(); i++)
{
w = orgAdj[cur][i].second;
int v = orgAdj[cur][i].first;
if(orgMinD[v] > orgMinD[cur] + w)
{
orgMinD[v] = orgMinD[cur] + w;
pq.push({orgMinD[v], v});
}
}
}
dfsPre(T);
for(int i = 1; i <= n; i++)
{
adj[i][0].push_back({{i, 0}, 1});
adj[i][0].push_back({{i, 0}, 2});
adj[i][1].push_back({{i, 0}, 3});
adj[i][2].push_back({{i, 0}, 3});
}
}
void solve()
{
for(int i = 1; i <= n; i++)
{
minD[i][0] = oo;
minD[i][1] = oo;
minD[i][2] = oo;
minD[i][3] = oo;
}
minD[X][0] = 0;
pq2.push({{minD[X][0], X}, 0});
while(!pq2.empty())
{
int layer = pq2.top().second;
int cur = pq2.top().first.second;
long long w = pq2.top().first.first;
pq2.pop();
if(minD[cur][layer] != w) continue;
for(int i = 0; i < adj[cur][layer].size(); i++)
{
int v = adj[cur][layer][i].first.first;
w =adj[cur][layer][i].first.second;
int vLay = adj[cur][layer][i].second;
if(minD[v][vLay] > minD[cur][layer] + w)
{
minD[v][vLay] = minD[cur][layer]+w;
pq2.push({{minD[v][vLay], v}, vLay});
}
}
}
cout << minD[Y][3];
}
int main()
{
ios_base::sync_with_stdio(0);
cin.tie(0);
cout.tie(0);
readData();
dijkstra();
solve();
return 0;
}
