Language: C++

#pragma GCC optimize("Ofast")
//#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native")

#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>

using namespace std;
template <class T>
using ordered_set = __gnu_pbds::tree<T, __gnu_pbds::null_type, less<T>, __gnu_pbds::rb_tree_tag, __gnu_pbds::tree_order_statistics_node_update>;
template <class T>
using ordered_multiset = __gnu_pbds::tree<T, __gnu_pbds::null_type, less_equal<T>, __gnu_pbds::rb_tree_tag, __gnu_pbds::tree_order_statistics_node_update>;

#define PI atan2(0, -1)
#define EPS 1e-9
#define INF 5e18
#define MOD 1000000007

#define all(x) begin(x), end(x)
#define pb push_back
#define mp make_pair
#define f first
#define s second
#define lb lower_bound
#define ub upper_bound

int N, arr [6010], suf [2010][6010];
unordered_map<pair<int, int>, int> dp [6010];

int solveIt(int curr, int a, int b){
    if(a < b) swap(a, b);
    if(curr == 3*N){
        return arr[curr] == a && arr[curr] == b;
    }
    auto dpit = dp[curr].find({a, b});
    if(dpit != dp[curr].end()){
        return dpit->s;
    }
    int tarr [5];
    tarr[0] = a;
    tarr[1] = b;
    for(int i = curr; i < curr+3; i++) tarr[i-curr+2] = arr[i];
    /*if(curr == 3){
        cout << "THREE ";
        for(int i = 0; i < 5; i++) cout << tarr[i] << ' ';
        cout << endl;
    }
    if(curr == 6){
        cout << "SIX ";
        for(int i = 0; i < 5; i++) cout << tarr[i] << ' ';
        cout << endl;
    }*/
    int ret = 0;
    for(int i = 0; i < 5; i++)
        for(int j = 0; j < i; j++) {
            int x = ((suf[tarr[i]][curr + 3] + (tarr[i] == tarr[j])) > 1 ? tarr[i] : 0);
            int y = ((suf[tarr[j]][curr + 3] + (tarr[i] == tarr[j])) > 1 ? tarr[j] : 0);
            //if(curr == 3 && x == 3 && y == 3){
            //    cout << "DOUBLE " << curr << ' ' << i << ' ' << j << endl;
            //    for(int a = 0; a < 5; a++) cout << tarr[a] << ' ';
            //    cout << endl;
            //}
            int prevy = -1;
            for (int k = 0; k < 5; k++) {
                if (k == i || k == j) continue;
                if (prevy == -1 || prevy == tarr[k]) prevy = tarr[k];
                else prevy = 0;
            }
            prevy = min(prevy, 1);
            ret = max(ret, solveIt(curr+3, x, y)+prevy);
            //cout << "STATE " << curr << ' ' << a << ' ' << b << endl;
            //cout << "NEXT " << curr+3 << ' ' << x << ' ' << y << endl;
        }
    return dp[curr][{a, b}] = ret;
}

int main(){
    //freopen("input.txt", "r", stdin); freopen("output.txt", "w", stdout);
    ios_base::sync_with_stdio(0); cin.tie(0); cout << fixed << setprecision(10);
    cin >> N; for(int i = 1; i <= 3*N; i++) cin >> arr[i];
    for(int i = 3*N; i > 0; i--){
        for(int j = 1; j <= N; j++) suf[j][i] = suf[j][i+1];
        suf[arr[i]][i]++;
    }
    cout << solveIt(3, arr[1], arr[2]) << '\n';
    return 0;
}

/******************************
Kateba ii dake no hanashi darou
Success is only a victory away
- No Game No Life Opening
******************************/


Compiler output:
a.cc:28:44: error: use of deleted function 'std::unordered_map<_Key, _Tp, _Hash, _Pred, _Alloc>::unordered_map() [with _Key = std::pair<int, int>; _Tp = int; _Hash = std::hash<std::pair<int, int> >; _Pred = std::equal_to<std::pair<int, int> >; _Alloc = std::allocator<std::pair<const std::pair<int, int>, int> >]'
   28 | unordered_map<pair<int, int>, int> dp [6010];
      |                                            ^
In file included from /usr/include/c++/14/unordered_map:41,
                 from /usr/include/c++/14/functional:63,
                 from /usr/include/x86_64-linux-gnu/c++/14/bits/stdc++.h:53,
                 from a.cc:4:
/usr/include/c++/14/bits/unordered_map.h:148:7: note: 'std::unordered_map<_Key, _Tp, _Hash, _Pred, _Alloc>::unordered_map() [with _Key = std::pair<int, int>; _Tp = int; _Hash = std::hash<std::pair<int, int> >; _Pred = std::equal_to<std::pair<int, int> >; _Alloc = std::allocator<std::pair<const std::pair<int, int>, int> >]' is implicitly deleted because the default definition would be ill-formed:
  148 |       unordered_map() = default;
      |       ^~~~~~~~~~~~~
/usr/include/c++/14/bits/unordered_map.h:148:7: error: use of deleted function 'std::_Hashtable<_Key, _Value, _Alloc, _ExtractKey, _Equal, _Hash, _RangeHash, _Unused, _RehashPolicy, _Traits>::_Hashtable() [with _Key = std::pair<int, int>; _Value = std::pair<const std::pair<int, int>, int>; _Alloc = std::allocator<std::pair<const std::pair<int, int>, int> >; _ExtractKey = std::__detail::_Select1st; _Equal = std::equal_to<std::pair<int, int> >; _Hash = std::hash<std::pair<int, int> >; _RangeHash = std::__detail::_Mod_range_hashing; _Unused = std::__detail::_Default_ranged_hash; _RehashPolicy = std::__detail::_Prime_rehash_policy; _Traits = std::__detail::_Hashtable_traits<true, false, true>]'
In file included from /usr/include/c++/14/bits/unordered_map.h:33:
/usr/include/c++/14/bits/hashtable.h:539:7: note: 'std::_Hashtable<_Key, _Value, _Alloc, _ExtractKey, _Equal, _Hash, _RangeHash, _Unused, _RehashPolicy, _Traits>::_Hashtable() [with _Key = std::pair<int, int>; _Value = std::pair<const std::pair<int, int>, int>; _Alloc = std::allocator<std::pair<const std::pair<int, int>, int> >; _ExtractKey = std::__detail::_Select1st; _Equal = std::equal_to<std::pair<int, int> >; _Hash = std::hash<std::pair<int, int> >; _RangeHash = std::__detail::_Mod_range_hashing; _Unused = std::__detail::_Default_ranged_hash; _RehashPolicy = std::__detail::_Prime_rehash_policy; _Traits = std::__detail::_Hashtable_traits<true, false, true>]' is implicitly deleted because the default definition would be ill-formed:
  539 |       _Hashtable() = default;
      |       ^~~~~~~~~~
/usr/include/c++/14/bits/hashtable.h:539:7: error: use of deleted function 'std::__detail::_Hashtable_base<_Key, _Value, _ExtractKey, _Equal, _Hash, _RangeHash, _Unused, _Traits>::_Hashtable_base() [with _Key = std::pair<int, int>; _Value = std::pair<const std::pair<int, int>, int>; _ExtractKey = std::__detail::_Select1st; _Equal = std::equal_to<std::pair<int, int> >; _Hash = std::hash<std::pair<int, int> >; _RangeHash = std::__detail::_Mod_range_hashing; _Unused = std::__detail::_Default_ranged_hash; _Traits = std::__detail::_Hashtable_traits<true, false, true>]'
In file included from /usr/include/c++/14/bits/hashtable.h:35:
/usr/include/c++/14/bits/hashtable_policy.h:1731:7: note: 'std::__detail::_Hashtable_base<_Key, _Value, _ExtractKey, _Equal, _Hash, _RangeHash, _Unused, _Traits>::_Hashtable_base() [with _Key = std::pair<int, int>; _Value = std::pair<const std::pair<int, int>, int>; _ExtractKey = std::__detail::_Select1st; _Equal = std::equal_to<std::pair<int, int> >; _Hash = std::hash<std::pair<int, int> >; _RangeHash = std::__detail::_Mod_range_hashing; _Unused = std::__detail::_Default_ranged_hash; _Traits = std::__detail::_Hashtable_traits<true, false, true>]' is implicitly deleted because the default definition would be ill-formed:
 1731 |       _Hashtable_base() = default;
      |       ^~~~~~~~~~~~~~~
/usr/include/c++/14/bits/hashtable_policy.h:1731:7: error: use of deleted function 'std::__detail::_Hash_code_base<_Key, _Value, _ExtractKey, _Hash, _RangeHash, _Unused, __cache_hash_code>::_Hash_code_base() [with _Key = std::pair<int, int>; _Value = std::pair<const std::pair<int, int>, int>; _ExtractKey = std::__detail::_Select1st; _Hash = std::hash<std::pair<int, int> >; _RangeHash = std::__detail::_Mod_range_hashing; _Unused = std::__detail::_Default_ranged_hash; bool __cache_hash_code = true]'
/usr/include/c++/14/bits/hashtable_policy.h: In instantiation of 'std::__detail::_Hashtable_ebo_helper<_Nm, _Tp, true>::_Hashtable_ebo_helper() [with int _Nm = 1; _Tp = std::hash<std::pair<int, int> >]':
/usr/include/c++/14/bits/hashtable_policy.h:1328:7:   required from here
 1328 |       _Hash_code_base() = default;
      |       ^~~~~~~~~~~~~~~
/usr/include/c++/14/bits/hashtable_policy.h:1245:49: error: use of deleted function 'std::hash<std::pair<int, int> >::hash()'
 1245 |       _Hashtable_ebo_helper() noexcept(noexcept(_Tp())) : _Tp() { }
      |                                                 ^~~~~
In file included from /usr/include/c++/14/string_view:50,
                 from /usr/include/c++/14/bits/basic_string.h:47,
                 from /usr/include/c++/14/string:54,
                 from /usr/include/c++/14/bitset:52,
                 from /usr/include/x86_64-linux-gnu/c++/14/bits/stdc++.h:52:
/usr/include/c++/14/bits/functional_hash.h:102:12: note: 'std::hash<std::pair<int, int> >::hash()' is implicitly deleted because the default definition would be ill-formed:
  102 |     struct hash : __hash_enum<_Tp>
      |            ^~~~
/usr/include/c++/14/bits/functional_hash.h:102:12: error: no matching function for call to 'std::__hash_enum<std::pair<int, int>, false>::__hash_enum()'
/usr/include/c++/14/bits/functional_hash.h:83:7: note: candidate: 'std::__hash_enum<_Tp, <anonymous> >::__hash_enum(std::__hash_enum<_Tp, <anonymous> >&&) [with _Tp = std::pair<int, int>; bool <anonymous> = false]'
   83 |       __hash_enum(__hash_enum&&);
      |       ^~~~~~~~~~~
/usr/include/c++/14/bits/functional_hash.h:83:7: note:   candidate expects 1 argument, 0 provided
/usr/include/c++/14/bits/functional_hash.h:102:12: error: 'std::__hash_enum<_Tp, <anonymous> >::~__hash_enum() [with _Tp = std::pair<int, int>; bool <anonymous> = false]' is private within this context
  102 |     struct hash : __hash_enum<_Tp>
      |            ^~~~
/usr/include/c++/14/bits/functional_hash.h:84:7: note: declared private here
   84 |       ~__hash_enum();
      |       ^
/usr/include/c++/14/bits/hashtable_policy.h:1245:49: note: use '-fdiagnostics-all-candidates' to display considered candidates
 1245 |       _Hashtable_ebo_helper() noexcept(noexcept(_Tp())) : _Tp() { }
      |                                                 ^~~~~
/usr/include/c++/14/bits/hashtable_policy.h:1328:7: note: 'std::__detail::_Hash_code_base<_Key, _Value, _ExtractKey, _Hash, _RangeHash, _Unused, __cache_hash_code>::_Hash_code_base() [with _Key = std::pair<int, int>; _Value = std::pair<const std::pair<int, int>, int>; _ExtractKey = std::__detail::_Select1st; _Hash = std::hash<std::pair<int, int> >; _RangeHash = std::__detail::_Mod_range_hashing; _Unused = std::__detail::_Default_ranged_hash; bool __cache_hash_code = true]' is implicitly deleted because the default definition would be ill-formed:
 1328 |       _Hash_code_base() = default;
      |       ^~~~~~~~~~~~~~~
/usr/include/c++/14/bits/hashtable_policy.h:1328:7: error: use of deleted function 'std::__detail::_Hashtable_ebo_helper<1, std::hash<std::pair<int, int> >, true>::~_Hashtable_ebo_helper()'
/usr/include/c++/14/bits/hashtable_policy.h:1242:12: note: 'std::__detail::_Hashtable_ebo_helper<1, std::hash<std::pair<int, int> >, true>::~_Hashtable_ebo_helper()' is implicitly deleted because the default definition would be ill-formed:
 1242 |     struct _Hashtable_ebo_helper<_Nm, _Tp, true>
      |            ^~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
/usr/include/c++/14/bits/hashtable_policy.h:1242:12: error: use of deleted function 'std::hash<std::pair<int, int> >::~hash()'
/usr/include/c++/14/bits/functional_hash.h:102:12: note: 'std::hash<std::pair<int, int> >::~hash()' is implicitly deleted because the default definition would be ill-formed:
  102 |     struct hash : __hash_enum<_Tp>
      |            ^~~~
/usr/include/c++/14/bits/functional_hash.h:102:12: error: 'std::__hash_enum<_Tp, <anonymous> >::~__hash_enum() [with _Tp = std::pair<int, int>; bool <anonymous> = false]' is private within this context
/usr/include/c++/14/bits/functional_hash.h:84:7: note: declared private here
   84 |       ~__hash_enum();
      |       ^
/usr/include/c++/14/bits/hashtable_policy.h:1731:7: note: use '-fdiagnostics-all-candidates' to display considered candidates
 1731 |       _Hashtable_base() = default;
      |       ^~~~~~~~~~~~~~~
/usr/include/c++/14/bits/hashtable_policy.h:1731:7: error: use of deleted function 'std::__detail::_Hash_code_base<std::pair<int, int>, std::pair<const std::pair<int, int>, int>, std::__detail::_Select1st, std::hash<std::pair<int, int> >, std::__detail::_Mod_range_hashing, std::__detail::_Default_ranged_hash, true>::~_Hash_code_base()'
/usr/include/c++/14/bits/hashtable_policy.h:1306:12: note: 'std::__detail::_Hash_code_base<std::pair<int, int>, std::pair<const std::pair<int, int>, int>, std::__detail::_Select1st, std::hash<std::pair<int, int> >, std::__detail::_Mod_range_hashing, std::__detail::_Default_ranged_hash, true>::~_Hash_code_base()' is implicitly deleted because the default definition would be ill-formed:
 1306 |     struct _Hash_code_base
      |            ^~~~~~~~~~~~~~~
/usr/include/c++/14/bits/hashtable_policy.h:1306:12: error: use of deleted function 'std::__detail::_Hashtable_ebo_helper<1, std::hash<std::pair<int, int> >, true>::~_Hashtable_ebo_helper()'
/usr/include/c++/14/bits/hashtable.h:539:7: note: use '-fdiagnostics-all-candidates' to display considered candidates
  539 |       _Hashtable() = default;
      |       ^~~~~~~~~~
/usr/include/c++/14/bits/hashtable.h:539:7: error: use of deleted function 'std::__detail::_Hashtable_base<std::pair<int, int>, std::p