Language: C++

#include <bits/stdc++.h>
#define ll long long
#define INF 1000000005
#define MOD 1000000007
#define EPS 1e-10
#define rep(i,n) for(int i=0;i<(int)(n);++i)
#define rrep(i,n) for(int i=(int)(n)-1;i>=0;--i)
#define srep(i,s,t) for(int i=(int)(s);i<(int)(t);++i)
#define each(a,b) for(auto& (a): (b))
#define all(v) (v).begin(),(v).end()
#define len(v) (int)(v).size()
#define zip(v) sort(all(v)),v.erase(unique(all(v)),v.end())
#define cmx(x,y) x=max(x,y)
#define cmn(x,y) x=min(x,y)
#define fi first
#define se second
#define pb push_back
#define show(x) cout<<#x<<" = "<<(x)<<endl
#define spair(p) cout<<#p<<": "<<p.fi<<" "<<p.se<<endl
#define sar(a,n) cout<<#a<<":";rep(pachico,n)cout<<" "<<a[pachico];cout<<endl
#define svec(v) cout<<#v<<":";rep(pachico,v.size())cout<<" "<<v[pachico];cout<<endl
#define svecp(v) cout<<#v<<":";each(pachico,v)cout<<" {"<<pachico.first<<":"<<pachico.second<<"}";cout<<endl
#define sset(s) cout<<#s<<":";each(pachico,s)cout<<" "<<pachico;cout<<endl
#define smap(m) cout<<#m<<":";each(pachico,m)cout<<" {"<<pachico.first<<":"<<pachico.second<<"}";cout<<endl

using namespace std;

typedef pair<int,int> P;
typedef pair<ll,ll> pll;
typedef vector<int> vi;
typedef vector<vi> vvi;
typedef vector<ll> vl;
typedef vector<vl> vvl;
typedef vector<double> vd;
typedef vector<P> vp;
typedef vector<string> vs;

const int MAX_N = 100005;

template<class _Key, class _Tp, class _Hash> class UnorderedMapIterator;

template<class _Key, class _Tp, class _Hash = hash<_Key> >
class UnorderedMap
{
private:
    using iterator = UnorderedMapIterator<_Key, _Tp, _Hash>;
    using data_type = pair<_Key, _Tp>;
    using aligned_pointer = typename std::aligned_storage<sizeof(data_type), alignof(data_type)>::type;
    friend UnorderedMapIterator<_Key, _Tp, _Hash>;
    struct bucket {
        unsigned int _hash;
        int _dist;
        bool _last, _end;
        aligned_pointer _data_ptr;
        bucket() : _dist(-1), _last(false), _end(false){}
        inline void clear(){ _dist = -1; }
        inline void _delete(){ data_ptr()->~data_type(); }
        inline bool empty() const noexcept { return (_dist == -1); }
        inline data_type& data() noexcept {
            return *reinterpret_cast<data_type*>(&_data_ptr);
        }
        inline data_type* data_ptr() noexcept {
            return reinterpret_cast<data_type*>(&_data_ptr);
        }
        inline const _Key& get_key() noexcept { return data_ptr()->first; }
        inline void new_data(const data_type& data){
            new(&_data_ptr) data_type(data);
        }
        inline void _swap(unsigned int& hash, int& dist, data_type& _data){
            swap(_hash, hash), swap(_dist, dist), swap(data(), _data);
        }
    };
    inline static unsigned int ceilpow2(unsigned int u){
        --u, u |= u >> 1, u |= u >> 2, u |= u >> 4, u |= u >> 8;
        return (u | (u >> 16)) + 1;
    }
    inline static bucket *increment(bucket *cur) noexcept {
        for(++cur; !cur->_end; ++cur){
            if(!cur->empty()) break;
        }
        return cur;
    }
    inline bucket *next_bucket(bucket*& cur) const noexcept {
        return cur->_last ? _buckets : cur + 1;
    }
    inline unsigned int make_hash(const _Key& _key) const noexcept {
        return _key;
        // return rand1 ^ (_Hash()(_key) + rand2);
    }
    inline float load_factor() const noexcept {
        return (float)_data_count / _bucket_count;
    }
    // inline void make_random_number(){
    //     rand1 = random_device{}(), rand2 = 0x9e3779b9 + (rand1 << 6) + (rand1 >> 2);
    // }
    bucket *insert_impl(bucket *cur, unsigned int hash, int dist, data_type& data){
        bucket *ret = cur;
        bool flag = false;
        while(true){
            if(cur->empty()){
                cur->_hash = hash, cur->_dist = dist, cur->new_data(data);
                if(!flag) ret = cur, flag = true;
                break;
            }else if(dist > cur->_dist){
                cur->_swap(hash, dist, data);
                if(!flag) ret = cur, flag = true;
            }
            ++dist;
            cur = next_bucket(cur);
        }
        return ret;
    }
    bucket *_find(const _Key& _key, bool push=false){
        unsigned int hash = make_hash(_key);
        bucket *cur = _buckets + (hash & _mask);
        int dist = 0;
        while(dist <= cur->_dist){
            if(hash == cur->_hash && _key == cur->get_key()){
                return cur;
            }
            ++dist;
            cur = next_bucket(cur);
        }
        if(!push) return _buckets + _bucket_count;
        ++_data_count;
        if(rehash_check()){
            hash = make_hash(_key), cur = _buckets + (hash & _mask), dist = 0;
        }
        data_type tmp = data_type(_key, _Tp());
        return insert_impl(cur, hash, dist, tmp);
    }
    bucket *_insert(const _Key& _key, const _Tp& _value){
        ++_data_count;
        rehash_check();
        unsigned int hash = make_hash(_key);
        data_type tmp = data_type(_key, _value);
        return insert_impl(_buckets + (hash & _mask), hash, 0, tmp);
    }
    bucket *backward_shift(bucket *cur){
        cur->_delete();
        bucket *next = next_bucket(cur), *ret = cur;
        if(next->_dist < 1) return increment(cur);
        do {
            cur->_hash = next->_hash;
            cur->_dist = next->_dist - 1;
            cur->_data_ptr = next->_data_ptr;
            cur = next, next = next_bucket(cur);
        }while(next->_dist >= 1);
        cur->clear();
        return ret;
    }
    bucket *erase_impl(bucket *cur){
        assert(cur != _buckets + _bucket_count);
        --_data_count;
        cur->clear();
        return backward_shift(cur);
    }
    bucket *_erase(const _Key& _key){
        return erase_impl(_find(_key));
    }
    bool rehash_check(){
        if(load_factor() >= MAX_LOAD_FACTOR){
            rehash();
            return true;
        }else{
            return false;
        }
    }
    void move_data(data_type& data){
        unsigned int hash = make_hash(data.first);
        insert_impl(_buckets + (hash & _mask), hash, 0, data);
    }
    void rehash(){
        UnorderedMap new_unordered_map(_bucket_count * 2);
        new_unordered_map._data_count = _data_count;
        for(bucket *cur = _buckets; !cur->_end; ++cur){
            if(!cur->empty()){
                new_unordered_map.move_data(cur->data());
            }
        }
        swap(*this, new_unordered_map);
    }
    friend void swap(UnorderedMap& ump1, UnorderedMap& ump2){
        swap(ump1._bucket_count, ump2._bucket_count);
        swap(ump1._mask, ump2._mask);
        swap(ump1._data_count, ump2._data_count);
        // swap(ump1.rand1, ump2.rand1);
        // swap(ump1.rand2, ump2.rand2);
        swap(ump1._buckets, ump2._buckets);
    }

private:
    unsigned int _bucket_count, _mask, _data_count;
    // unsigned int rand1, rand2;
    bucket *_buckets;
public:
    static constexpr float MAX_LOAD_FACTOR = 0.5f;
    UnorderedMap(unsigned int bucket_size = 1u) noexcept
     : _bucket_count(ceilpow2(max(bucket_size, 1u))), _mask(_bucket_count - 1),
        _data_count(0u), _buckets(new bucket[_bucket_count + 1]){
        _buckets[_bucket_count - 1]._last = true, _buckets[_bucket_count]._end = true;
        // make_random_number();
    }
    // ~UnorderedMap(){ delete[] _buckets; }
    friend ostream& operator<< (ostream& os, UnorderedMap& ump) noexcept {
        for(data_type& val : ump) os << '{' << val.first << ',' << val.second << "} ";
        return os;
    }
    _Tp& operator[](const _Key& _key) noexcept {
        return _find(_key, true)->data_ptr()->second;
    }
    const _Tp& at(const _Key& _key){
        bucket *res = _find(_key);
        if(res == _buckets + _bucket_count) __throw_out_of_range(__N("Unordered_Map::at"));
        return res->data_ptr()->second;
    }
    void clear(){
        UnorderedMap new_unordered_map(1u);
        swap(*this, new_unordered_map);
    }
    size_t size() const noexcept { return _data_count; }
    size_t bucket_count() const noexcept { return _bucket_count; }
    bool empty() const noexcept { return (_data_count == 0); }
    iterator begin() const noexcept { return _buckets->empty() ? iterator(increment(_buckets)) : iterator(_buckets); }
    iterator end() const noexcept { return iterator(_buckets + _bucket_count); }
    iterator find(const _Key& _key){ return iterator(_find(_key)); }
    iterator insert(const _Key& _key, const _Tp& _value){
        return iterator(_insert(_key, _value));
    }
    iterator erase(const _Key& _key){ return iterator(_erase(_key)); }
    iterator erase(const iterator& itr){ return iterator(erase_impl(itr.bucket_ptr)); }
};

template<class _Key, class _Tp, class _Hash>
class UnorderedMapIterator {
private:
    friend UnorderedMap<_Key, _Tp, _Hash>;
    typename UnorderedMap<_Key, _Tp, _Hash>::bucket *bucket_ptr;
    using iterator_category = forward_iterator_tag;
    using data_type = pair<_Key, _Tp>;
    using difference_type = std::ptrdiff_t;
    using pointer = pair<_Key, _Tp>*;
    using reference = pair<_Key, _Tp>&;

private:
    UnorderedMapIterator(typename UnorderedMap<_Key, _Tp, _Hash>::bucket *_bucket_ptr)
        noexcept : bucket_ptr(_bucket_ptr){}
public:
    UnorderedMapIterator() noexcept : bucket_ptr(){}
    UnorderedMapIterator(const UnorderedMapIterator& itr) noexcept : bucket_ptr(itr.bucket_ptr){}
    UnorderedMapIterator& operator=(const UnorderedMapIterator& itr)
        & noexcept { return bucket_ptr = itr.bucket_ptr, *this; }
    UnorderedMapIterator& operator=(const UnorderedMapIterator&& itr)
        & noexcept { return bucket_ptr = itr.bucket_ptr, *this; }
    reference operator*() const { return bucket_ptr->data(); }
    pointer operator->() const { return bucket_ptr->data_ptr(); }
    UnorderedMapIterator& operator++() noexcept {
        return bucket_ptr = UnorderedMap<_Key, _Tp, _Hash>::increment(bucket_ptr), *this;
    }
    UnorderedMapIterator operator++(int) const noexcept {
        return UnorderedMapIterator(UnorderedMap<_Key, _Tp, _Hash>::increment(this->bucket_ptr));
    }
    bool operator==(const UnorderedMapIterator& itr) const noexcept { return !(*this != itr); };
    bool operator!=(const UnorderedMapIterator& itr) const noexcept { return bucket_ptr != itr.bucket_ptr; }
};

//0:red,1:blue
UnorderedMap<string,UnorderedMap<string,int> > mp[2];

int main()
{
    cin.tie(0);
    ios::sync_with_stdio(false);
    int n;
    cin >> n;
    n *= 2;
    string s;
    cin >> s;
    rep(i,(1 << (n-n/2))){
        string red,blue;
        rep(j,n-n/2){
            if((i >> j) & 1){
                red.pb(s[j+n/2]);
            }else{
                blue.pb(s[j+n/2]);
            }
        }
        reverse(all(blue));
        if(len(red) <= len(blue)){
            mp[0][blue][red]++;
        }else{
            mp[1][red][blue]++;
        }
    }
    ll ans = 0;
    rep(i,(1 << n/2)){
        string red, blue;
        rep(j,n/2){
            if((i >> j) & 1){
                red.pb(s[j]);
            }else{
                blue.pb(s[j]);
            }
        }
        reverse(all(blue));
        if(len(red) >= len(blue)){
            ans += mp[0][red][blue];
        }else{
            ans += mp[1][blue][red];
        }
    }
    cout << ans << "\n";
    return 0;
}


Compiler output:
a.cc: In instantiation of 'unsigned int UnorderedMap<_Key, _Tp, _Hash>::make_hash(const _Key&) const [with _Key = std::__cxx11::basic_string<char>; _Tp = UnorderedMap<std::__cxx11::basic_string<char>, int>; _Hash = std::hash<std::__cxx11::basic_string<char> >]':
a.cc:114:29:   required from 'UnorderedMap<_Key, _Tp, _Hash>::bucket* UnorderedMap<_Key, _Tp, _Hash>::_find(const _Key&, bool) [with _Key = std::__cxx11::basic_string<char>; _Tp = UnorderedMap<std::__cxx11::basic_string<char>, int>; _Hash = std::hash<std::__cxx11::basic_string<char> >]'
  114 |         unsigned int hash = make_hash(_key);
      |                             ^~~~~~~~~
a.cc:210:16:   required from '_Tp& UnorderedMap<_Key, _Tp, _Hash>::operator[](const _Key&) [with _Key = std::__cxx11::basic_string<char>; _Tp = UnorderedMap<std::__cxx11::basic_string<char>, int>; _Hash = std::hash<std::__cxx11::basic_string<char> >]'
  210 |         return _find(_key, true)->data_ptr()->second;
      |                ^~~~~
a.cc:290:23:   required from here
  290 |             mp[0][blue][red]++;
      |                       ^
a.cc:87:16: error: cannot convert 'const std::__cxx11::basic_string<char>' to 'unsigned int' in return
   87 |         return _key;
      |                ^~~~
a.cc: In instantiation of 'unsigned int UnorderedMap<_Key, _Tp, _Hash>::make_hash(const _Key&) const [with _Key = std::__cxx11::basic_string<char>; _Tp = int; _Hash = std::hash<std::__cxx11::basic_string<char> >]':
a.cc:114:29:   required from 'UnorderedMap<_Key, _Tp, _Hash>::bucket* UnorderedMap<_Key, _Tp, _Hash>::_find(const _Key&, bool) [with _Key = std::__cxx11::basic_string<char>; _Tp = int; _Hash = std::hash<std::__cxx11::basic_string<char> >]'
  114 |         unsigned int hash = make_hash(_key);
      |                             ^~~~~~~~~
a.cc:210:16:   required from '_Tp& UnorderedMap<_Key, _Tp, _Hash>::operator[](const _Key&) [with _Key = std::__cxx11::basic_string<char>; _Tp = int; _Hash = std::hash<std::__cxx11::basic_string<char> >]'
  210 |         return _find(_key, true)->data_ptr()->second;
      |                ^~~~~
a.cc:290:28:   required from here
  290 |             mp[0][blue][red]++;
      |                            ^
a.cc:87:16: error: cannot convert 'const std::__cxx11::basic_string<char>' to 'unsigned int' in return
   87 |         return _key;
      |                ^~~~