#include <bits/stdc++.h>
// #include <ext/pb_ds/assoc_container.hpp>
// #include <ext/pb_ds/tree_policy.hpp>
// #include <ext/rope>
using namespace std;
// using namespace __gnu_pbds;
typedef long long ll;
typedef unsigned long long ull;
typedef unsigned int uint;
typedef long double ld;
typedef vector<int> VI;
typedef vector<vector<int>> VVI;
typedef vector<long long> VL;
typedef vector<vector<long long>> VVL;
typedef vector<char> VC;
typedef vector<vector<char>> VVC;
typedef vector<bool> VB;
typedef vector<vector<bool>> VVB;
typedef vector<double> VD;
typedef vector<vector<double>> VVD;
typedef pair<int, int> PII;
typedef pair<long long, long long> PLL;
typedef vector<pair<int, int>> VPI;
typedef vector<pair<long long, long long>> VPL;
#define LINE '\n'
#define SPACE ' '
#define PB push_back
#define FOR(i, a, b) for (int i = (a); i < (b); i++)
#define FORE(i, a, b) for (int i = (a); i <= (b); i++)
#define ALL(x) x.begin(), x.end()
#define RALL(x) x.rbegin(), x.rend()
#define kwad(a) ((a) * (a))
// zero indexed
template <class T>
struct segtree
{
const T def = 0;
int n;
vector<T> seg;
segtree(int _size) : n(_size), seg(2 * _size, def) {}
T merge(T a, T b)
{
return max(a, b);
}
void update(int pos, T val)
{
for (seg[pos += n] = val; pos /= 2;)
{
seg[pos] = merge(seg[pos * 2], seg[pos * 2 + 1]);
}
}
T query(int l, int r)
{ // get [l, r)
T a = def, b = def;
for (l += n, r += n; l < r; l /= 2, r /= 2)
{
if (l % 2)
a = merge(a, seg[l++]);
if (r % 2)
b = merge(b, seg[--r]);
}
return merge(a, b);
}
};
const ll MOD = 1e9 + 7;
template <class T>
void maxi(T &a, T b)
{
a = max(a, b);
}
template <class T>
void mini(T &a, T b)
{
a = min(a, b);
}
template <class T>
void addi(T &a, T b)
{
a = (a + b) % MOD;
}
template <class T>
void subi(T &a, T b)
{
a = (a - b + MOD) % MOD;
}
template <class T>
T add(T a, T b)
{
return (a + b) % MOD;
}
template <class T>
T sub(T a, T b)
{
return (a - b + MOD) % MOD;
}
template <class T>
T mul(T a, T b)
{
return ((a % MOD) * (b % MOD)) % MOD;
}
ll binpow(ll a, ll b, ll mod)
{
ll res = 1;
while (b > 0)
{
if (b & 1)
{
res = (res * a) % mod;
}
a = (a * a) % mod;
b >>= 1;
}
return res;
}
const int INF = 1e9;
const int MAX_N = 1e5 + 2;
vector<VPL> graph(MAX_N);
ll cost[3][MAX_N];
ll dp[2][MAX_N];
// 0 - from u
// 1 - from v
// 2 - from s
void djikstra1(int start, int i)
{
priority_queue<PLL, vector<PLL>, greater<PLL>> pq;
fill(cost[i], cost[i] + MAX_N, LLONG_MAX / 3);
pq.push({0, start});
cost[i][start] = 0;
while (!pq.empty())
{
auto [dist, node] = pq.top();
pq.pop();
for (auto [next, edge] : graph[node])
{
if (dist + edge < cost[i][next])
{
cost[i][next] = dist + edge;
pq.push({cost[i][next], next});
}
}
}
}
ll ans;
void djikstra2(int start, int end)
{
priority_queue<PLL, vector<PLL>, greater<PLL>> pq;
fill(dp[0], dp[0] + MAX_N, LLONG_MAX / 3);
fill(dp[1], dp[1] + MAX_N, LLONG_MAX / 3);
fill(cost[2], cost[2] + MAX_N, LLONG_MAX / 3);
pq.push({0, start});
cost[2][start] = 0;
dp[0][start] = cost[0][start];
dp[1][start] = cost[1][start];
while (!pq.empty())
{
auto [dist, node] = pq.top();
pq.pop();
for (auto [next, edge] : graph[node])
{
ll would_be = dist + edge;
if (would_be < cost[2][next])
{
cost[2][next] =would_be;
dp[0][next] = min(dp[0][node], cost[0][next]);
dp[1][next] = min(dp[1][node], cost[1][next]);
pq.push({cost[2][next], next});
}
else if (would_be == cost[2][next] &&
min(dp[0][node], cost[0][next]) + min(dp[1][node], cost[1][next]) <= dp[0][next] + dp[1][next])
{
dp[0][next] = min(dp[0][node], cost[0][next]);
dp[1][next] = min(dp[1][node], cost[1][next]);
}
}
}
mini(ans, dp[0][end] + dp[1][end]);
}
void solve()
{
int n, m, s, t, u, v;
cin >> n >> m >> s >> t >> u >> v;
FOR(i, 0, m)
{
int a, b, c;
cin >> a >> b >> c;
graph[a].PB({b, c});
graph[b].PB({a, c});
}
djikstra1(u, 0);
djikstra1(v, 1);
ans = cost[0][v];
djikstra2(s, t);
djikstra2(t, s);
cout << ans << LINE;
}
int main()
{
ios_base::sync_with_stdio(false);
cin.tie(nullptr);
int t = 1;
// cin >> t;
while (t--)
solve();
}
