Submission #490988

#TimeUsernameProblemLanguageResultExecution timeMemory
490988Mike4235Toys (CEOI18_toy)C++17
Compilation error
0 ms0 KiB
#pragma GCC optimize("Ofast") #pragma GCC optimize("unroll-loops") #pragma GCC target("avx,avx2,fma") #include <bits/stdc++.h> #define for1(i,a,b) for (int i = a; i <= b; i++) #define for2(i,a,b) for (int i = a; i >= b; i--) // #define int long long #define sz(a) (int)a.size() #define pii pair<int,int> #define pb push_back /* __builtin_popcountll(x) : Number of 1-bit __builtin_ctzll(x) : Number of trailing 0 */ const long double PI = 3.1415926535897932384626433832795; const int INF = 1000000000000000000; const int MOD = 1000000007; const int MOD2 = 1000000009; const long double EPS = 1e-6; using namespace std; const int MX = 1e5; int n; unordered_map<int, vector<pii>> mp; unordered_map<pii, bool> flag; set<int> se; vector<pii> d[MX + 5]; void solve(int x, int sum) { if (flag[{x, sum}]) return; flag[{x, sum}] = 1; se.insert(sum + x - 1); if (x <= MX) { for (auto p : d[x]) solve(p.first, sum + p.second - 1); return; } if (mp.find(x) != mp.end()) { for (auto p : mp[x]) solve(p.first, sum + p.second - 1); } else { for (int i = 2; i * i <= x; i++) if (x % i == 0) { if (i * i == x) { mp[x].push_back({i, i}); solve(i, sum + i - 1); } else { int j = x / i; mp[x].push_back({i, j}); mp[x].push_back({j, i}); solve(i, sum + j - 1); solve(j, sum + i - 1); } } } } signed main() { ios_base::sync_with_stdio(false); cin.tie(NULL); cout.tie(NULL); // freopen("cf.inp", "r", stdin); // freopen("cf.out", "w", stdout); for1(i,1,MX) { for (int j = i * 2, cnt = 2; j <= MX; j += i, cnt++) d[j].push_back({i, cnt}); } cin >> n; solve(n, 0); cout << sz(se) << "\n"; for (auto x : se) cout << x << " "; }

Compilation message (stderr)

toy.cpp:21:17: warning: overflow in conversion from 'long int' to 'int' changes value from '1000000000000000000' to '-1486618624' [-Woverflow]
   21 | const int INF = 1000000000000000000;
      |                 ^~~~~~~~~~~~~~~~~~~
toy.cpp:32:26: error: use of deleted function 'std::unordered_map<_Key, _Tp, _Hash, _Pred, _Alloc>::unordered_map() [with _Key = std::pair<int, int>; _Tp = bool; _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>, bool> >]'
   32 | unordered_map<pii, bool> flag;
      |                          ^~~~
In file included from /usr/include/c++/10/unordered_map:47,
                 from /usr/include/c++/10/functional:61,
                 from /usr/include/c++/10/pstl/glue_algorithm_defs.h:13,
                 from /usr/include/c++/10/algorithm:74,
                 from /usr/include/x86_64-linux-gnu/c++/10/bits/stdc++.h:65,
                 from toy.cpp:5:
/usr/include/c++/10/bits/unordered_map.h:141:7: note: 'std::unordered_map<_Key, _Tp, _Hash, _Pred, _Alloc>::unordered_map() [with _Key = std::pair<int, int>; _Tp = bool; _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>, bool> >]' is implicitly deleted because the default definition would be ill-formed:
  141 |       unordered_map() = default;
      |       ^~~~~~~~~~~~~
/usr/include/c++/10/bits/unordered_map.h:141:7: error: use of deleted function 'std::_Hashtable<_Key, _Value, _Alloc, _ExtractKey, _Equal, _H1, _H2, _Hash, _RehashPolicy, _Traits>::_Hashtable() [with _Key = std::pair<int, int>; _Value = std::pair<const std::pair<int, int>, bool>; _Alloc = std::allocator<std::pair<const std::pair<int, int>, bool> >; _ExtractKey = std::__detail::_Select1st; _Equal = std::equal_to<std::pair<int, int> >; _H1 = std::hash<std::pair<int, int> >; _H2 = std::__detail::_Mod_range_hashing; _Hash = 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++/10/unordered_map:46,
                 from /usr/include/c++/10/functional:61,
                 from /usr/include/c++/10/pstl/glue_algorithm_defs.h:13,
                 from /usr/include/c++/10/algorithm:74,
                 from /usr/include/x86_64-linux-gnu/c++/10/bits/stdc++.h:65,
                 from toy.cpp:5:
/usr/include/c++/10/bits/hashtable.h:451:7: note: 'std::_Hashtable<_Key, _Value, _Alloc, _ExtractKey, _Equal, _H1, _H2, _Hash, _RehashPolicy, _Traits>::_Hashtable() [with _Key = std::pair<int, int>; _Value = std::pair<const std::pair<int, int>, bool>; _Alloc = std::allocator<std::pair<const std::pair<int, int>, bool> >; _ExtractKey = std::__detail::_Select1st; _Equal = std::equal_to<std::pair<int, int> >; _H1 = std::hash<std::pair<int, int> >; _H2 = std::__detail::_Mod_range_hashing; _Hash = 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:
  451 |       _Hashtable() = default;
      |       ^~~~~~~~~~
/usr/include/c++/10/bits/hashtable.h:451:7: error: use of deleted function 'std::__detail::_Hashtable_base<_Key, _Value, _ExtractKey, _Equal, _H1, _H2, _Hash, _Traits>::_Hashtable_base() [with _Key = std::pair<int, int>; _Value = std::pair<const std::pair<int, int>, bool>; _ExtractKey = std::__detail::_Select1st; _Equal = std::equal_to<std::pair<int, int> >; _H1 = std::hash<std::pair<int, int> >; _H2 = std::__detail::_Mod_range_hashing; _Hash = std::__detail::_Default_ranged_hash; _Traits = std::__detail::_Hashtable_traits<true, false, true>]'
In file included from /usr/include/c++/10/bits/hashtable.h:35,
                 from /usr/include/c++/10/unordered_map:46,
                 from /usr/include/c++/10/functional:61,
                 from /usr/include/c++/10/pstl/glue_algorithm_defs.h:13,
                 from /usr/include/c++/10/algorithm:74,
                 from /usr/include/x86_64-linux-gnu/c++/10/bits/stdc++.h:65,
                 from toy.cpp:5:
/usr/include/c++/10/bits/hashtable_policy.h:1791:5: note: 'std::__detail::_Hashtable_base<_Key, _Value, _ExtractKey, _Equal, _H1, _H2, _Hash, _Traits>::_Hashtable_base() [with _Key = std::pair<int, int>; _Value = std::pair<const std::pair<int, int>, bool>; _ExtractKey = std::__detail::_Select1st; _Equal = std::equal_to<std::pair<int, int> >; _H1 = std::hash<std::pair<int, int> >; _H2 = std::__detail::_Mod_range_hashing; _Hash = std::__detail::_Default_ranged_hash; _Traits = std::__detail::_Hashtable_traits<true, false, true>]' is implicitly deleted because the default definition would be ill-formed:
 1791 |     _Hashtable_base() = default;
      |     ^~~~~~~~~~~~~~~
/usr/include/c++/10/bits/hashtable_policy.h:1791:5: error: use of deleted function 'std::__detail::_Hash_code_base<_Key, _Value, _ExtractKey, _H1, _H2, std::__detail::_Default_ranged_hash, true>::_Hash_code_base() [with _Key = std::pair<int, int>; _Value = std::pair<const std::pair<int, int>, bool>; _ExtractKey = std::__detail::_Select1st; _H1 = std::hash<std::pair<int, int> >; _H2 = std::__detail::_Mod_range_hashing]'
/usr/include/c++/10/bits/hashtable_policy.h:1368:7: note: 'std::__detail::_Hash_code_base<_Key, _Value, _ExtractKey, _H1, _H2, std::__detail::_Default_ranged_hash, true>::_Hash_code_base() [with _Key = std::pair<int, int>; _Value = std::pair<const std::pair<int, int>, bool>; _ExtractKey = std::__detail::_Select1st; _H1 = std::hash<std::pair<int, int> >; _H2 = std::__detail::_Mod_range_hashing]' is implicitly deleted because the default definition would be ill-formed:
 1368 |       _Hash_code_base() = default;
      |       ^~~~~~~~~~~~~~~
/usr/include/c++/10/bits/hashtable_policy.h:1368:7: error: use of deleted function '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++/10/bits/hashtable_policy.h:1112:7: note: 'std::__detail::_Hashtable_ebo_helper<_Nm, _Tp, true>::_Hashtable_ebo_helper() [with int _Nm = 1; _Tp = std::hash<std::pair<int, int> >]' is implicitly deleted because the default definition would be ill-formed:
 1112 |       _Hashtable_ebo_helper() = default;
      |       ^~~~~~~~~~~~~~~~~~~~~
/usr/include/c++/10/bits/hashtable_policy.h:1112:7: error: use of deleted function 'std::hash<std::pair<int, int> >::hash()'
In file included from /usr/include/c++/10/string_view:42,
                 from /usr/include/c++/10/bits/basic_string.h:48,
                 from /usr/include/c++/10/string:55,
                 from /usr/include/c++/10/bits/locale_classes.h:40,
                 from /usr/include/c++/10/bits/ios_base.h:41,
                 from /usr/include/c++/10/ios:42,
                 from /usr/include/c++/10/istream:38,
                 from /usr/include/c++/10/sstream:38,
                 from /usr/include/c++/10/complex:45,
                 from /usr/include/c++/10/ccomplex:39,
                 from /usr/include/x86_64-linux-gnu/c++/10/bits/stdc++.h:54,
                 from toy.cpp:5:
/usr/include/c++/10/bits/functional_hash.h:101:12: note: 'std::hash<std::pair<int, int> >::hash()' is implicitly deleted because the default definition would be ill-formed:
  101 |     struct hash : __hash_enum<_Tp>
      |            ^~~~
/usr/include/c++/10/bits/functional_hash.h:101:12: error: no matching function for call to 'std::__hash_enum<std::pair<int, int>, false>::__hash_enum()'
/usr/include/c++/10/bits/functional_hash.h:82:7: note: candidate: 'std::__hash_enum<_Tp, <anonymous> >::__hash_enum(std::__hash_enum<_Tp, <anonymous> >&&) [with _Tp = std::pair<int, int>; bool <anonymous> = false]'
   82 |       __hash_enum(__hash_enum&&);
      |       ^~~~~~~~~~~
/usr/include/c++/10/bits/functional_hash.h:82:7: note:   candidate expects 1 argument, 0 provided
/usr/include/c++/10/bits/functional_hash.h:101:12: error: 'std::__hash_enum<_Tp, <anonymous> >::~__hash_enum() [with _Tp = std::pair<int, int>; bool <anonymous> = false]' is private within this context
  101 |     struct hash : __hash_enum<_Tp>
      |            ^~~~
/usr/include/c++/10/bits/functional_hash.h:83:7: note: declared private here
   83 |       ~__hash_enum();
      |       ^
In file included from /usr/include/c++/10/bits/hashtable.h:35,
                 from /usr/include/c++/10/unordered_map:46,
                 from /usr/include/c++/10/functional:61,
                 from /usr/include/c++/10/pstl/glue_algorithm_defs.h:13,
                 from /usr/include/c++/10/algorithm:74,
                 from /usr/include/x86_64-linux-gnu/c++/10/bits/stdc++.h:65,
                 from toy.cpp:5:
/usr/include/c++/10/bits/hashtable_policy.h:1112:7: error: use of deleted function 'std::hash<std::pair<int, int> >::~hash()'
 1112 |       _Hashtable_ebo_helper() = default;
      |       ^~~~~~~~~~~~~~~~~~~~~
In file included from /usr/include/c++/10/string_view:42,
                 from /usr/include/c++/10/bits/basic_string.h:48,
                 from /usr/include/c++/10/string:55,
                 from /usr/include/c++/10/bits/locale_classes.h:40,
                 from /usr/include/c++/10/bits/ios_base.h:41,
                 from /usr/include/c++/10/ios:42,
                 from /usr/include/c++/10/istream:38,
                 from /usr/include/c++/10/sstream:38,
                 from /usr/include/c++/10/complex:45,
                 from /usr/include/c++/10/ccomplex:39,
                 from /usr/include/x86_64-linux-gnu/c++/10/bits/stdc++.h:54,
                 from toy.cpp:5:
/usr/include/c++/10/bits/functional_hash.h:101:12: note: 'std::hash<std::pair<int, int> >::~hash()' is implicitly deleted because the default definition would be ill-formed:
  101 |     struct hash : __hash_enum<_Tp>
      |            ^~~~
/usr/include/c++/10/bits/functional_hash.h:101:12: 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++/10/bits/functional_hash.h:83:7: note: declared private here
   83 |       ~__hash_enum();
      |       ^
In file included from /usr/include/c++/10/bits/hashtable.h:35,
                 from /usr/include/c++/10/unordered_map:46,
                 from /usr/include/c++/10/functional:61,
                 from /usr/include/c++/10/pstl/glue_algorithm_defs.h:13,
                 from /usr/include/c++/10/algorithm:74,
                 from /usr/include/x86_64-linux-gnu/c++/10/bits/stdc++.h:65,
                 from toy.cpp:5:
/usr/include/c++/10/bits/hashtable_policy.h:1368:7: error: use of deleted function 'std::__detail::_Hashtable_ebo_helper<1, std::hash<std::pair<int, int> >, true>::~_Hashtable_ebo_helper()'
 1368 |       _Hash_code_base() = default;
      |       ^~~~~~~~~~~~~~~
/usr/include/c++/10/bits/hashtable_policy.h:1109:12: 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:
 1109 |     struct _Hashtable_ebo_helper<_Nm, _Tp, true>
      |            ^~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
/usr/include/c++/10/bits/hashtable_policy.h:1109:12: error: use of deleted function 'std::hash<std::pair<int, int> >::~hash()'
/usr/include/c++/10/bits/hashtable_policy.h:1791:5: error: use of deleted function 'std::__detail::_Hash_code_base<std::pair<int, int>, std::pair<const std::pair<int, int>, bool>, std::__detail::_Select1st, std::hash<std::pair<int, int> >, std::__detail::_Mod_range_hashing, std::__detail::_Default_ranged_hash, true>::~_Hash_code_base()'
 1791 |     _Hashtable_base() = default;
      |     ^~~~~~~~~~~~~~~
/usr/include/c++/10/bits/hashtable_policy.h:1341:12: note: 'std::__detail::_Hash_code_base<std::pair<int, int>, std::pair<const std::pair<int, int>, bool>, 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:
 1341 |     struct _Hash_code_base<_Key, _Value, _ExtractKey, _H1, _H2,
      |            ^~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
 1342 |       _Default_ranged_hash, true>
      |       ~~~~~~~~~~~~~~~~~~~~~~~~~~~
/usr/include/c++/10/bits/hashtable_policy.h:1341:12: error: use of deleted function 'std::__detail::_Hashtable_ebo_helper<1, std::hash<std::pair<int, int> >, true>::~_Hashtable_ebo_helper()'
In file included from /usr/include/c++/10/unordered_map:46,
                 from /usr/include/c++/10/functional:61,
                 from /usr/include/c++/10/pstl/glue_algorithm_defs.h:13,
                 from /usr/include/c++/10/algorithm:74,
                 from /usr/include/x86_64-linux-gnu/c++/10/bits/stdc++.h:65,
                 from toy.cpp:5:
/usr/include/c++/10/bits/hashtable.h:451:7: error: use of deleted function 'std::__detail::_Hashtable_base<std::pair<int, int>, std::pair<const std::pair<int, int>, bool>, std::__detail::_Select1st, std::equal_to<std::pair<int, int> >, std::hash<std::pair<int, int> >, std::__detail::_Mod_range_hashing, std::__detail::_Default_ranged_hash, std::__detail::_Hashtable_traits<true, false, true> >::~_Hashtable_base()'
  451 |       _Hashtable() = default;
      |       ^~~~~~~~~~
In file included from /usr/include/c++/10/bits/hashtable.h:35,
                 from /usr/include/c++/10/unordered_map:46,
                 from /usr/include/c++/10/functional:61,
                 from /usr/include/c++/10/pstl/glue_algorithm_defs.h:13,
                 from /usr/include/c++/10/algorithm:74,
                 from /usr/include/x86_64-linux-gnu/c++/10/bits/stdc++.h:65,
                 from toy.cpp:5:
/usr/include/c++/10/bits/hashtable_policy.h:1725:10: note: 'std::__detail::_Hashtable_base<std::pair<int, int>, std::pair<const std::pair<int, int>, bool>, std::__detail::_Select1st, std::equal_to<std::pair<int, int> >, std::hash<std::pair<int, int> >, std::__detail::_Mod_range_hashing, std::__detail::_Default_ranged_hash, std::__detail::_Hashtable_traits<true, false, true> >::~_Hashtable_base()' is implicitly deleted because the default definition would be ill-formed:
 1725 |   struct _Hashtable_base
      |          ^~~~~~~~~~~~~~~
/usr/include/c++/10/bits/hashtable_policy.h:1725:10: error: use of deleted function 'std::__detail::_Hash_code_base<std::pair<int, int>, std::pair<const std::pair<int, int>, bool>, 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++/10/bits/hashtable_policy.h: In instantiation of 'std::__detail::_Hash_code_base<_Key, _Value, _ExtractKey, _H1, _H2, std::__detail::_Default_ranged_hash, true>::__hash_code std::__detail::_Hash_code_base<_Key, _Value, _ExtractKey, _H1, _H2, std::__detail::_Default_ranged_hash, true>::_M_hash_code(const _Key&) const [with _Key = std::pair<int, int>; _Value = std::pair<const std::pair<int, int>, bool>; _ExtractKey = std::__detail::_Select1st; _H1 = std::hash<std::pair<int, int> >; _H2 = std::__detail::_Mod_range_hashing; std::__detail::_Hash_code_base<_Key, _Value, _ExtractKey, _H1, _H2, std::__detail::_Default_ranged_hash, true>::__hash_code = long unsigned int]':
/usr/include/c++/10/bits/hashtable_policy.h:734:45:   required from 'std::__detail::_Map_base<_Key, _Pair, _Alloc, std::__detail::_Select1st, _Equal, _H1, _H2, _Hash, _RehashPolicy, _Traits, true>::mapped_type& std::__detail::_Map_base<_Key, _Pair, _Alloc, std::__detail::_Select1st, _Equal, _H1, _H2, _Hash, _RehashPolicy, _Traits, true>::operator[](std::__detail::_Map_base<_Key, _Pair, _Alloc, std::__detail::_Select1st, _Equal, _H1, _H2, _Hash, _RehashPolicy, _Traits, true>::key_type&&) [with _Key = std::pair<int, int>; _Pair = std::pair<const std::pair<int, int>, bool>; _Alloc = std::allocator<std::pair<const std::pair<int, int>, bool> >; _Equal = std::equal_to<std::pair<int, int> >; _H1 = std::hash<std::pair<int, int> >; _H2 = std::__detail::_Mod_range_hashing; _Hash = std::__detail::_Default_ranged_hash; _RehashPolicy = std::__detail::_Prime_rehash_policy; _Traits = std::__detail::_Hashtable_traits<true, false, true>; std::__detail::_Map_base<_Key, _Pair, _Alloc, std::__detail::_Select1st, _Equal, _H1, _H2, _Hash, _RehashPolicy, _Traits, true>::mapped_type = bool; std::__detail::_Map_base<_Key, _Pair, _Alloc, std::__detail::_Select1st, _Equal, _H1, _H2, _Hash, _RehashPolicy, _Traits, true>::key_type = std::pair<int, int>]'
/usr/include/c++/10/bits/unordered_map.h:988:20:   required from 'std::unordered_map<_Key, _Tp, _Hash, _Pred, _Alloc>::mapped_type& std::unordered_map<_Key, _Tp, _Hash, _Pred, _Alloc>::operator[](std::unordered_map<_Key, _Tp, _Hash, _Pred, _Alloc>::key_type&&) [with _Key = std::pair<int, int>; _Tp = bool; _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>, bool> >; std::unordered_map<_Key, _Tp, _Hash, _Pred, _Alloc>::mapped_type = bool; std::unordered_map<_Key, _Tp, _Hash, _Pred, _Alloc>::key_type = std::pair<int, int>]'
toy.cpp:37:22:   required from here
/usr/include/c++/10/bits/hashtable_policy.h:1377:16: error: static assertion failed: hash function must be invocable with an argument of key type
 1377 |  static_assert(__is_invocable<const _H1&, const _Key&>{},
      |                ^~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
/usr/include/c++/10/bits/hashtable_policy.h:1379:16: error: no match for call to '(const std::hash<std::pair<int, int> >) (const std::pair<int, int>&)'
 1379 |  return _M_h1()(__k);
      |         ~~~~~~~^~~~~
In file included from /usr/include/c++/10/unordered_map:46,
                 from /usr/include/c++/10/functional:61,
                 from /usr/include/c++/10/pstl/glue_algorithm_defs.h:13,
                 from /usr/include/c++/10/algorithm:74,
                 from /usr/include/x86_64-linux-gnu/c++/10/bits/stdc++.h:65,
                 from toy.cpp:5:
/usr/include/c++/10/bits/hashtable.h: In instantiation of 'std::_Hashtable<_Key, _Value, _Alloc, _ExtractKey, _Equal, _H1, _H2, _Hash, _RehashPolicy, _Traits>::~_Hashtable() [with _Key = std::pair<int, int>; _Value = std::pair<const std::pair<int, int>, bool>; _Alloc = std::allocator<std::pair<const std::pair<int, int>, bool> >; _ExtractKey = std::__detail::_Select1st; _Equal = std::equal_to<std::pair<int, int> >; _H1 = std::hash<std::pair<int, int> >; _H2 = std::__detail::_Mod_range_hashing; _Hash = std::__detail::_Default_ranged_hash; _RehashPolicy = std::__detail::_Prime_rehash_policy; _Traits = std::__detail::_Hashtable_traits<true, false, true>]':
/usr/include/c++/10/bits/unordered_map.h:102:11:   required from here
/usr/include/c++/10/bits/hashtable.h:1389:5: error: use of deleted function 'std::__detail::_Hashtable_base<std::pair<int, int>, std::pair<const std::pair<int, int>, bool>, std::__detail::_Select1st, std::equal_to<std::pair<int, int> >, std::hash<std::pair<int, int> >, std::__detail::_Mod_range_hashing, std::__detail::_Default_ranged_hash, std::__detail::_Hashtable_traits<true, false, true> >::~_Hashtable_base()'
 1389 |     }
      |     ^