#include<bits/stdc++.h>
using namespace std;
#define task "NETWORK"
#define se second
#define fi first
#define ll long long
#define ii pair<ll, ll>
const long mxN = 2e5 + 7;
const ll inf = 1e18;
int m, n, p[3];
vector<ii> w[mxN];
ll dp[10][mxN], mn[2][mxN];
void Dij(bool id)
{
for (int i = 1; i <= n; i++)
mn[id][i] = inf;
mn[id][p[id]] = 0;
priority_queue<ii, vector<ii>, greater<ii>> pq;
pq.push({0, p[id]});
while (pq.size())
{
ii j = pq.top();
pq.pop();
if (j.fi != mn[id][j.se])
continue;
for (ii i : w[j.se])
{
if (j.fi + i.se < mn[id][i.fi])
{
mn[id][i.fi] = j.fi + i.se;
pq.push({j.fi + i.se, i.fi});
}
}
}
}
void Solve(int stt)
{
for (int i = 1; i <= n; i++)
{
for (int u = 1; u <= 4; u++)
dp[u][i] = inf;
}
dp[4][stt] = 0;
priority_queue<ii, vector<ii>, greater<ii>> pq;
pq.push({0, stt});
while (pq.size())
{
ii j = pq.top();
pq.pop();
if (j.fi != dp[4][j.se])
continue;
for (int i = 0; i <= 1; i++)
{
for (int u = 0; u < 4; u++)
dp[u | (1 << i)][j.se] = min(dp[u | (1 << i)][j.se], dp[u][j.se] + mn[i][j.se]);
}
for (ii i : w[j.se])
{
if (j.fi + i.se < dp[4][i.fi])
{
for (int u = 1; u < 4; u++)
dp[u][i.fi] = inf;
dp[4][i.fi] = j.fi + i.se;
pq.push({j.fi + i.se, i.fi});
}
if (j.fi + i.se == dp[4][i.fi])
{
for (int u = 1; u < 4; u++)
dp[u][i.fi] = min(dp[u][i.fi], dp[u][j.se]);
}
}
}
}
int main()
{
ios_base::sync_with_stdio(false);
cin.tie(NULL);
cout.tie(NULL);
cin >> n >> m;
int stt, en;
cin >> stt >> en;
cin >> p[0] >> p[1];
for (int i = 1; i <= m; i++)
{
int u, v, dis;
cin >> u >> v >> dis;
w[u].push_back({v, dis});
w[v].push_back({u, dis});
}
for (int i = 0; i <= 1; i++)
Dij(i);
Solve(stt);
cout << min(mn[0][p[1]], dp[3][en]);
}
