/*
PROG: source
LANG: C++11
_____
.' '.
/ 0 0 \
| ^ |
| \ / |
\ '---' /
'._____.'
*/
#include <bits/stdc++.h>
#include <ext/pb_ds/tree_policy.hpp>
#include <ext/pb_ds/assoc_container.hpp>
using namespace std;
using namespace __gnu_pbds;
struct chash
{
int operator()(int x) const
{
x ^= (x >> 20) ^ (x >> 12);
return x ^ (x >> 7) ^ (x >> 4);
}
int operator()(long long x) const
{
return x ^ (x >> 32);
}
};
template<typename T> using orderedset = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
template<typename T> using hashtable = gp_hash_table<T, T, chash>;
template<class T>
void readi(T &x)
{
T input = 0;
bool negative = false;
char c = ' ';
while (c < '-')
{
c = getchar();
}
if (c == '-')
{
negative = true;
c = getchar();
}
while (c >= '0')
{
input = input * 10 + (c - '0');
c = getchar();
}
if (negative)
{
input = -input;
}
x = input;
}
template<class T>
void printi(T output)
{
if (output == 0)
{
putchar('0');
return;
}
if (output < 0)
{
putchar('-');
output = -output;
}
int aout[20];
int ilen = 0;
while(output)
{
aout[ilen] = ((output % 10));
output /= 10;
ilen++;
}
for (int i = ilen - 1; i >= 0; i--)
{
putchar(aout[i] + '0');
}
return;
}
template<class T>
void ckmin(T &a, T b)
{
a = min(a, b);
}
template<class T>
void ckmax(T &a, T b)
{
a = max(a, b);
}
template<class T>
T normalize(T x, T mod = 1000000007)
{
return (((x % mod) + mod) % mod);
}
long long randomizell(long long mod)
{
return ((1ll << 45) * rand() + (1ll << 30) * rand() + (1ll << 15) * rand() + rand()) % mod;
}
int randomize(int mod)
{
return ((1ll << 15) * rand() + rand()) % mod;
}
#define y0 ___y0
#define y1 ___y1
#define MP make_pair
#define MT make_tuple
#define PB push_back
#define PF push_front
#define LB lower_bound
#define UB upper_bound
#define fi first
#define se second
#define debug(x) cerr << #x << " = " << x << endl;
const long double PI = 4.0 * atan(1.0);
const long double EPS = 1e-10;
#define MAGIC 347
#define SINF 10007
#define CO 1000007
#define INF 1000000007
#define BIG 1000000931
#define LARGE 1696969696967ll
#define GIANT 2564008813937411ll
#define LLINF 2696969696969696969ll
#define MAXN 100013
typedef long long ll;
typedef long double ld;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
typedef pair<ll, int> pli;
typedef pair<ld, ld> pdd;
int N, M;
int S, T, U, V;
vector<pli> edge[MAXN];
ll distS[MAXN], distT[MAXN], distU[MAXN], distV[MAXN], big;
priority_queue<pli, vector<pli>, greater<pli> > pq;
ll ans = LLINF;
ll opt[MAXN];
bool seen[MAXN];
void solve(int u, bool flag)
{
if (seen[u])
{
return;
}
seen[u] = true;
// cerr << "solve " << u << ' ' << flag << endl;
for (pli p : edge[u])
{
ll ed = p.fi; int v = p.se;
// cerr << u << " -> " << v << ' ' << distS[v] << ' ' << ed << ' ' << distT[u] << endl;
if (distS[v] + ed + distT[u] == big)
{
solve(v, flag);
ckmin(opt[u], opt[v]);
}
}
// cerr << u << ' ' << opt[u] << endl;
if (flag)
{
// cerr << u << ' ' << distU[u] << ' ' << opt[u] << endl;
ckmin(ans, distU[u] + opt[u]);
}
else
{
// cerr << U << ' ' << distV[u] << ' ' << opt[u] << endl;
ckmin(ans, distV[u] + opt[u]);
}
return;
}
int32_t main()
{
ios_base::sync_with_stdio(0);
srand(time(0));
// cout << fixed << setprecision(10);
// cerr << fixed << setprecision(10);
if (fopen("input.in", "r"))
{
freopen ("input.in", "r", stdin);
freopen ("output.out", "w", stdout);
}
cin >> N >> M;
cin >> S >> T >> U >> V;
S--; T--; U--; V--;
for (int i = 0; i < M; i++)
{
int u, v; ll d;
cin >> u >> v >> d;
u--; v--;
edge[u].PB(MP(d, v));
edge[v].PB(MP(d, u));
}
for (int i = 0; i < N; i++)
{
distS[i] = LLINF; distT[i] = LLINF;
distU[i] = LLINF; distV[i] = LLINF;
}
distS[S] = 0;
pq.push(MP(0, S));
while(!pq.empty())
{
ll d = pq.top().fi; int u = pq.top().se;
pq.pop();
if (distS[u] != d)
{
continue;
}
for (pli p : edge[u])
{
ll ed = p.fi; int v = p.se;
if (distS[v] > d + ed)
{
distS[v] = d + ed;
pq.push({distS[v], v});
}
}
}
distT[T] = 0;
pq.push(MP(0, T));
while(!pq.empty())
{
ll d = pq.top().fi; int u = pq.top().se;
pq.pop();
if (distT[u] != d)
{
continue;
}
for (pli p : edge[u])
{
ll ed = p.fi; int v = p.se;
if (distT[v] > d + ed)
{
distT[v] = d + ed;
pq.push({distT[v], v});
}
}
}
distU[U] = 0;
pq.push(MP(0, U));
while(!pq.empty())
{
ll d = pq.top().fi; int u = pq.top().se;
pq.pop();
if (distU[u] != d)
{
continue;
}
for (pli p : edge[u])
{
ll ed = p.fi; int v = p.se;
if (distU[v] > d + ed)
{
distU[v] = d + ed;
pq.push({distU[v], v});
}
}
}
distV[V] = 0;
pq.push(MP(0, V));
while(!pq.empty())
{
ll d = pq.top().fi; int u = pq.top().se;
pq.pop();
if (distV[u] != d)
{
continue;
}
for (pli p : edge[u])
{
ll ed = p.fi; int v = p.se;
if (distV[v] > d + ed)
{
distV[v] = d + ed;
pq.push({distV[v], v});
}
}
}
big = distS[T];
// cerr << "ST=UV\n";
ans = distU[V];
for (int i = 0; i < N; i++)
{
seen[i] = false;
opt[i] = distU[i];
}
solve(T, 0);
// cerr << "ST=VU\n";
for (int i = 0; i < N; i++)
{
seen[i] = false;
opt[i] = distV[i];
}
solve(T, 1);
cout << ans << '\n';
// cerr << "time elapsed = " << (clock() / (CLOCKS_PER_SEC / 1000)) << " ms" << endl;
return 0;
}
