Language: C++

#include <bits/stdc++.h>
#define rep(i, n) for (int i = 0; i < (n); ++i)
#define repr(i, n) for (int i = (n); i >= 0; --i)
#define FOR(i, m, n) for (int i = (m); i < (n); ++i)
#define FORR(i, m, n) for (int i = (m); i >= (n); --i)
#define equals(a, b) (fabs((a) - (b)) < EPS)
using namespace std;
typedef long long ll;
typedef unsigned long long ull;
typedef long double ld;
const ll mod = 1000000007;
//const ll mod = 998244353;
const int inf = 1e9 + 10;
const ll INF = 1e18;
const ld EPS = 1e-10;
const int dx[8] = {1, 0, -1, 0, 1, -1, -1, 1};
const int dy[8] = {0, 1, 0, -1, 1, 1, -1, -1};
template<class T> bool chmax(T &a, const T &b) { if (a<b) { a=b; return 1; } return 0; }
template<class T> bool chmin(T &a, const T &b) { if (a>b) { a=b; return 1; } return 0; }

struct Info {
  int a, b;

  Info(int a = 0,int b = 0): a(a), b(b) {}

  bool operator < (const Info & i) const {
    if (b != i.b) return b < i.b;
    else return a > i.a;
  }
};

struct Info2 {
  int a, b;

  Info2(int a = 0,int b = 0): a(a), b(b) {}

  bool operator < (const Info & i) const {
    if (a != i.a) return a < i.a;
    else return b > i.b;
  }
};

int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  cout << fixed << setprecision(25);

  int n;
  cin >> n;
  vector<string> s(n);
  rep(i, n) cin >> s[i];
  
  vector<Info> p(n);
  int suml = 0, sumr = 0;
  rep(i, n) {
    int l = 0, r = 0;
    rep(j, s[i].length()) {
      if (s[i][j] == '(') {
        l++;
      }
      else {
        r++;
        chmax(p[i].b, r - l);
      }
    }
    p[i].a = l - r;
    suml += l;
    sumr += r;
  }
  if (suml != sumr) {
    cout << "No" << '\n';
    return 0;
  }
  sort(p.begin(), p.end());
  int res = 0, idx = 0;
  priority_queue<Info2> pq;
  rep(i, n) {
    while (idx < n && p[idx].b <= res) {
      pq.push({p[idx].a, p[idx].b});
      idx++;
    }
    if (pq.empty()) {
      cout << "No" << '\n';
      return 0;
    }
    if (res < pq.top().b) {
      cout << "No" << '\n';
      return 0;
    }
    res += pq.top().a;
    pq.pop();
  }
  cout << "Yes" << '\n';

  








  
  return 0;
}


Compiler output:
In file included from /usr/include/c++/14/string:49,
                 from /usr/include/c++/14/bitset:52,
                 from /usr/include/x86_64-linux-gnu/c++/14/bits/stdc++.h:52,
                 from a.cc:1:
/usr/include/c++/14/bits/stl_function.h: In instantiation of 'constexpr bool std::less<_Tp>::operator()(const _Tp&, const _Tp&) const [with _Tp = Info2]':
/usr/include/c++/14/bits/predefined_ops.h:196:23:   required from 'bool __gnu_cxx::__ops::_Iter_comp_val<_Compare>::operator()(_Iterator, _Value&) [with _Iterator = __gnu_cxx::__normal_iterator<Info2*, std::vector<Info2, std::allocator<Info2> > >; _Value = Info2; _Compare = std::less<Info2>]'
  196 |         { return bool(_M_comp(*__it, __val)); }
      |                       ~~~~~~~^~~~~~~~~~~~~~
/usr/include/c++/14/bits/stl_heap.h:140:48:   required from 'void std::__push_heap(_RandomAccessIterator, _Distance, _Distance, _Tp, _Compare&) [with _RandomAccessIterator = __gnu_cxx::__normal_iterator<Info2*, vector<Info2, allocator<Info2> > >; _Distance = long int; _Tp = Info2; _Compare = __gnu_cxx::__ops::_Iter_comp_val<less<Info2> >]'
  140 |       while (__holeIndex > __topIndex && __comp(__first + __parent, __value))
      |                                          ~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~~~~~
/usr/include/c++/14/bits/stl_heap.h:216:23:   required from 'void std::push_heap(_RAIter, _RAIter, _Compare) [with _RAIter = __gnu_cxx::__normal_iterator<Info2*, vector<Info2, allocator<Info2> > >; _Compare = less<Info2>]'
  216 |       std::__push_heap(__first, _DistanceType((__last - __first) - 1),
      |       ~~~~~~~~~~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
  217 |                        _DistanceType(0), _GLIBCXX_MOVE(__value), __cmp);
      |                        ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
/usr/include/c++/14/bits/stl_queue.h:747:16:   required from 'void std::priority_queue<_Tp, _Sequence, _Compare>::push(value_type&&) [with _Tp = Info2; _Sequence = std::vector<Info2, std::allocator<Info2> >; _Compare = std::less<Info2>; value_type = Info2]'
  747 |         std::push_heap(c.begin(), c.end(), comp);
      |         ~~~~~~~~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~~
a.cc:79:14:   required from here
   79 |       pq.push({p[idx].a, p[idx].b});
      |       ~~~~~~~^~~~~~~~~~~~~~~~~~~~~~
/usr/include/c++/14/bits/stl_function.h:405:20: error: no match for 'operator<' (operand types are 'const Info2' and 'const Info2')
  405 |       { return __x < __y; }
      |                ~~~~^~~~~
a.cc:37:8: note: candidate: 'bool Info2::operator<(const Info&) const'
   37 |   bool operator < (const Info & i) const {
      |        ^~~~~~~~
a.cc:37:33: note:   no known conversion for argument 1 from 'const Info2' to 'const Info&'
   37 |   bool operator < (const Info & i) const {
      |                    ~~~~~~~~~~~~~^
In file included from /usr/include/c++/14/bits/stl_algobase.h:64,
                 from /usr/include/c++/14/algorithm:60,
                 from /usr/include/x86_64-linux-gnu/c++/14/bits/stdc++.h:51:
/usr/include/c++/14/bits/stl_pair.h:1045:5: note: candidate: 'template<class _T1, class _T2> constexpr bool std::operator<(const pair<_T1, _T2>&, const pair<_T1, _T2>&)'
 1045 |     operator<(const pair<_T1, _T2>& __x, const pair<_T1, _T2>& __y)
      |     ^~~~~~~~
/usr/include/c++/14/bits/stl_pair.h:1045:5: note:   template argument deduction/substitution failed:
/usr/include/c++/14/bits/stl_function.h:405:20: note:   'const Info2' is not derived from 'const std::pair<_T1, _T2>'
  405 |       { return __x < __y; }
      |                ~~~~^~~~~
In file included from /usr/include/c++/14/bits/stl_algobase.h:67:
/usr/include/c++/14/bits/stl_iterator.h:448:5: note: candidate: 'template<class _Iterator> constexpr bool std::operator<(const reverse_iterator<_Iterator>&, const reverse_iterator<_Iterator>&)'
  448 |     operator<(const reverse_iterator<_Iterator>& __x,
      |     ^~~~~~~~
/usr/include/c++/14/bits/stl_iterator.h:448:5: note:   template argument deduction/substitution failed:
/usr/include/c++/14/bits/stl_function.h:405:20: note:   'const Info2' is not derived from 'const std::reverse_iterator<_Iterator>'
  405 |       { return __x < __y; }
      |                ~~~~^~~~~
/usr/include/c++/14/bits/stl_iterator.h:493:5: note: candidate: 'template<class _IteratorL, class _IteratorR> constexpr bool std::operator<(const reverse_iterator<_Iterator>&, const reverse_iterator<_IteratorR>&)'
  493 |     operator<(const reverse_iterator<_IteratorL>& __x,
      |     ^~~~~~~~
/usr/include/c++/14/bits/stl_iterator.h:493:5: note:   template argument deduction/substitution failed:
/usr/include/c++/14/bits/stl_function.h:405:20: note:   'const Info2' is not derived from 'const std::reverse_iterator<_Iterator>'
  405 |       { return __x < __y; }
      |                ~~~~^~~~~
/usr/include/c++/14/bits/stl_iterator.h:1694:5: note: candidate: 'template<class _IteratorL, class _IteratorR> constexpr bool std::operator<(const move_iterator<_IteratorL>&, const move_iterator<_IteratorR>&)'
 1694 |     operator<(const move_iterator<_IteratorL>& __x,
      |     ^~~~~~~~
/usr/include/c++/14/bits/stl_iterator.h:1694:5: note:   template argument deduction/substitution failed:
/usr/include/c++/14/bits/stl_function.h:405:20: note:   'const Info2' is not derived from 'const std::move_iterator<_IteratorL>'
  405 |       { return __x < __y; }
      |                ~~~~^~~~~
/usr/include/c++/14/bits/stl_iterator.h:1760:5: note: candidate: 'template<class _Iterator> constexpr bool std::operator<(const move_iterator<_IteratorL>&, const move_iterator<_IteratorL>&)'
 1760 |     operator<(const move_iterator<_Iterator>& __x,
      |     ^~~~~~~~
/usr/include/c++/14/bits/stl_iterator.h:1760:5: note:   template argument deduction/substitution failed:
/usr/include/c++/14/bits/stl_function.h:405:20: note:   'const Info2' is not derived from 'const std::move_iterator<_IteratorL>'
  405 |       { return __x < __y; }
      |                ~~~~^~~~~