Language: C++

#define _CRT_SECURE_NO_WARNINGS
#define _USE_MATH_DEFINES
#pragma comment(linker, "/STACK:268435456")
#pragma warning( disable : 6031)
#pragma warning( disable : 4244)
#pragma warning( disable : 26451)
#ifndef _MSC_VER
#pragma GCC target ("sse4.2")
#endif
#ifdef _MSC_VER
#  include <intrin.h>
#  define __builtin_popcount __popcnt
#  define __builtin_popcountll __popcnt64
#endif
#include <cstdlib>
#include <cstdio>
#include <cstring>
#include <cstdint>
#include <climits>
#include <cassert>
#include <string>
#include <vector>
#include <iostream>
#include <map>
#include <stack>
#include <set>
#include <queue>
#include <numeric>
#include <algorithm>
#include <random>
#include <utility>
#include <bitset>
#include <cmath>
#include <sstream>
#include <functional>
#include <iomanip>
#include <random>
#include <unordered_map>
#include <unordered_set>
#include <chrono>

#define all(a) (a).begin(),(a).end()
#define sz(a) (int)(a).size()
#define eps (1e-15)

using namespace std;

mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());

typedef long long ll;
typedef vector<int> vi;
typedef vector< vi > vvi;
typedef vector<double> vd;
typedef vector< vd > vvd;
typedef vector< string > vs;
typedef pair< int, int > pii;
typedef pair<ll, ll> pll;
typedef vector< pii > vpii;
typedef vector< pll > vpll;
typedef vector<ll> vl;
typedef vector<vector<long long>> vvl;
typedef vector<bool> vb;
typedef vector<vb> vvb;
typedef tuple<int, int, int> tiii;
const long long mod = int(1e9) + 7;
const int INF = 1e9;
const ll LINF = 1e18;


int main() {
	ios_base::sync_with_stdio(0), cin.tie(0), cout.tie(0); cout << setprecision(18) << fixed;
#ifdef LOCAL_MACHINE
	freopen("input.txt", "rt", stdin);
	freopen("output.txt", "wt", stdout);
#endif
	int n;
	cin >> n;
	vpii a;
	for (int i = 0; i < n; i++)
	{
		string s;
		cin >> s;
		int closed_start = 0;

		int balance = 0;
		for (int i = 0; i < sz(s); i++)
		{
			if (s[i] == ')')
			{
				if (balance > 0)
					balance--;
				else
					closed_start++;
			}
			else
			{
				balance++;
			}
		}
		if (closed_start != 0 || balance != 0)
			a.emplace_back(closed_start, balance);

	}
	if (sz(a) == 0)
	{
		cout << "Yes";
		return 0;
	}
	int t = 0;
	for (int i = 0; i < sz(a); i++)
		t += a[i].second - a[i].first;
	if (t != 0)
	{
		cout << "No";
		return 0;
	}
	sort(all(a));
	if (a[0].first > 0)
	{
		cout << "No";
		return 0;
	}
	int balance = 0;
	vpii na;
	for (int i = 0; i < sz(a); i++)
	{
		if (a[i].first > 0)
		{
			for (int j = i; j < sz(a); j++)
			{
				na.push_back(a[j]);
			}
			break;
		}

		balance += a[i].second;
	}
	a = na;
	while (true)
	{
		bool found = false;
		vpii na;
		for (int i = 0; i < sz(a); i++)
		{
			if (balance < a[i].first)
			{
				for (int j = i; j < sz(a); j++)
					na.push_back(a[j]);
				break;
			}
			if (a[i].second - a[i].first < 0)
			{
				na.push_back(a[i]);
				continue;
			}
			balance += a[i].second - a[i].first;
			found = true;
		}
		a = na;

		sort(all(a));
		if (!found)
			break;
	}
	sort(all(a), [](const pii& l, const pii& r) {l.second - l.first < r.second - r.first; });
	for (int i = 0; i < sz(a); i++)
	{
		balance -= a[i].first;

		if (balance < 0)
		{
			cout << "No";
			return 0;
		}
		balance += a[i].second;
	}

	cout << (balance == 0 ? "Yes" : "No");




	return 0;
}


Compiler output:
In file included from /usr/include/c++/14/bits/stl_algobase.h:71,
                 from /usr/include/c++/14/string:51,
                 from a.cc:21:
/usr/include/c++/14/bits/predefined_ops.h: In instantiation of 'constexpr bool __gnu_cxx::__ops::_Iter_comp_iter<_Compare>::operator()(_Iterator1, _Iterator2) [with _Iterator1 = __gnu_cxx::__normal_iterator<std::pair<int, int>*, std::vector<std::pair<int, int> > >; _Iterator2 = __gnu_cxx::__normal_iterator<std::pair<int, int>*, std::vector<std::pair<int, int> > >; _Compare = main()::<lambda(const pii&, const pii&)>]':
/usr/include/c++/14/bits/stl_algo.h:1777:14:   required from 'void std::__insertion_sort(_RandomAccessIterator, _RandomAccessIterator, _Compare) [with _RandomAccessIterator = __gnu_cxx::__normal_iterator<pair<int, int>*, vector<pair<int, int> > >; _Compare = __gnu_cxx::__ops::_Iter_comp_iter<main()::<lambda(const pii&, const pii&)> >]'
 1777 |           if (__comp(__i, __first))
      |               ~~~~~~^~~~~~~~~~~~~~
/usr/include/c++/14/bits/stl_algo.h:1817:25:   required from 'void std::__final_insertion_sort(_RandomAccessIterator, _RandomAccessIterator, _Compare) [with _RandomAccessIterator = __gnu_cxx::__normal_iterator<pair<int, int>*, vector<pair<int, int> > >; _Compare = __gnu_cxx::__ops::_Iter_comp_iter<main()::<lambda(const pii&, const pii&)> >]'
 1817 |           std::__insertion_sort(__first, __first + int(_S_threshold), __comp);
      |           ~~~~~~~~~~~~~~~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
/usr/include/c++/14/bits/stl_algo.h:1908:31:   required from 'void std::__sort(_RandomAccessIterator, _RandomAccessIterator, _Compare) [with _RandomAccessIterator = __gnu_cxx::__normal_iterator<pair<int, int>*, vector<pair<int, int> > >; _Compare = __gnu_cxx::__ops::_Iter_comp_iter<main()::<lambda(const pii&, const pii&)> >]'
 1908 |           std::__final_insertion_sort(__first, __last, __comp);
      |           ~~~~~~~~~~~~~~~~~~~~~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~
/usr/include/c++/14/bits/stl_algo.h:4805:18:   required from 'void std::sort(_RAIter, _RAIter, _Compare) [with _RAIter = __gnu_cxx::__normal_iterator<pair<int, int>*, vector<pair<int, int> > >; _Compare = main()::<lambda(const pii&, const pii&)>]'
 4805 |       std::__sort(__first, __last, __gnu_cxx::__ops::__iter_comp_iter(__comp));
      |       ~~~~~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
a.cc:165:6:   required from here
  165 |         sort(all(a), [](const pii& l, const pii& r) {l.second - l.first < r.second - r.first; });
      |         ~~~~^~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
/usr/include/c++/14/bits/predefined_ops.h:158:30: error: void value not ignored as it ought to be
  158 |         { return bool(_M_comp(*__it1, *__it2)); }
      |                       ~~~~~~~^~~~~~~~~~~~~~~~
/usr/include/c++/14/bits/predefined_ops.h: In instantiation of 'bool __gnu_cxx::__ops::_Val_comp_iter<_Compare>::operator()(_Value&, _Iterator) [with _Value = std::pair<int, int>; _Iterator = __gnu_cxx::__normal_iterator<std::pair<int, int>*, std::vector<std::pair<int, int> > >; _Compare = main()::<lambda(const pii&, const pii&)>]':
/usr/include/c++/14/bits/stl_algo.h:1757:20:   required from 'void std::__unguarded_linear_insert(_RandomAccessIterator, _Compare) [with _RandomAccessIterator = __gnu_cxx::__normal_iterator<pair<int, int>*, vector<pair<int, int> > >; _Compare = __gnu_cxx::__ops::_Val_comp_iter<main()::<lambda(const pii&, const pii&)> >]'
 1757 |       while (__comp(__val, __next))
      |              ~~~~~~^~~~~~~~~~~~~~~
/usr/include/c++/14/bits/stl_algo.h:1785:36:   required from 'void std::__insertion_sort(_RandomAccessIterator, _RandomAccessIterator, _Compare) [with _RandomAccessIterator = __gnu_cxx::__normal_iterator<pair<int, int>*, vector<pair<int, int> > >; _Compare = __gnu_cxx::__ops::_Iter_comp_iter<main()::<lambda(const pii&, const pii&)> >]'
 1785 |             std::__unguarded_linear_insert(__i,
      |             ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~^~~~~
 1786 |                                 __gnu_cxx::__ops::__val_comp_iter(__comp));
      |                                 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
/usr/include/c++/14/bits/stl_algo.h:1817:25:   required from 'void std::__final_insertion_sort(_RandomAccessIterator, _RandomAccessIterator, _Compare) [with _RandomAccessIterator = __gnu_cxx::__normal_iterator<pair<int, int>*, vector<pair<int, int> > >; _Compare = __gnu_cxx::__ops::_Iter_comp_iter<main()::<lambda(const pii&, const pii&)> >]'
 1817 |           std::__insertion_sort(__first, __first + int(_S_threshold), __comp);
      |           ~~~~~~~~~~~~~~~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
/usr/include/c++/14/bits/stl_algo.h:1908:31:   required from 'void std::__sort(_RandomAccessIterator, _RandomAccessIterator, _Compare) [with _RandomAccessIterator = __gnu_cxx::__normal_iterator<pair<int, int>*, vector<pair<int, int> > >; _Compare = __gnu_cxx::__ops::_Iter_comp_iter<main()::<lambda(const pii&, const pii&)> >]'
 1908 |           std::__final_insertion_sort(__first, __last, __comp);
      |           ~~~~~~~~~~~~~~~~~~~~~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~
/usr/include/c++/14/bits/stl_algo.h:4805:18:   required from 'void std::sort(_RAIter, _RAIter, _Compare) [with _RAIter = __gnu_cxx::__normal_iterator<pair<int, int>*, vector<pair<int, int> > >; _Compare = main()::<lambda(const pii&, const pii&)>]'
 4805 |       std::__sort(__first, __last, __gnu_cxx::__ops::__iter_comp_iter(__comp));
      |       ~~~~~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
a.cc:165:6:   required from here
  165 |         sort(all(a), [](const pii& l, const pii& r) {l.second - l.first < r.second - r.first; });
      |         ~~~~^~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
/usr/include/c++/14/bits/predefined_ops.h:240:30: error: void value not ignored as it ought to be
  240 |         { return bool(_M_comp(__val, *__it)); }
      |                       ~~~~~~~^~~~~~~~~~~~~~
/usr/include/c++/14/bits/predefined_ops.h: In instantiation of 'bool __gnu_cxx::__ops::_Iter_comp_val<_Compare>::operator()(_Iterator, _Value&) [with _Iterator = __gnu_cxx::__normal_iterator<std::pair<int, int>*, std::vector<std::pair<int, int> > >; _Value = std::pair<int, int>; _Compare = main()::<lambda(const pii&, const pii&)>]':
/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<pair<int, int>*, vector<pair<int, int> > >; _Distance = long int; _Tp = pair<int, int>; _Compare = __gnu_cxx::__ops::_Iter_comp_val<main()::<lambda(const pii&, const pii&)> >]'
  140 |       while (__holeIndex > __topIndex && __comp(__first + __parent, __value))
      |                                          ~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~~~~~
/usr/include/c++/14/bits/stl_heap.h:247:23:   required from 'void std::__adjust_heap(_RandomAccessIterator, _Distance, _Distance, _Tp, _Compare) [with _RandomAccessIterator = __gnu_cxx::__normal_iterator<pair<int, int>*, vector<pair<int, int> > >; _Distance = long int; _Tp = pair<int, int>; _Compare = __gnu_cxx::__ops::_Iter_comp_iter<main()::<lambda(const pii&, const pii&)> >]'
  247 |       std::__push_heap(__first, __holeIndex, __topIndex,
      |       ~~~~~~~~~~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
  248 |                        _GLIBCXX_MOVE(__value), __cmp);
      |                        ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
/usr/include/c++/14/bits/stl_heap.h:356:22:   required from 'void std::__make_heap(_RandomAccessIterator, _RandomAccessIterator, _Compare&) [with _RandomAccessIterator = __gnu_cxx::__normal_iterator<pair<int, int>*, vector<pair<int, int> > >; _Compare = __gnu_cxx::__ops::_Iter_comp_iter<main()::<lambda(const pii&, const pii&)> >]'
  356 |           std::__adjust_heap(__first, __parent, __len, _GLIBCXX_MOVE(__value),
      |           ~~~~~~~~~~~~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
  357 |                              __comp);
      |                              ~~~~~~~
/usr/include/c++/14/bits/stl_algo.h:1593:23:   required from 'void std::__heap_select(_RandomAccessIterator, _RandomAccessIterator, _RandomAccessIterator, _Compare) [with _RandomAccessIterator = __gnu_cxx::__normal_iterator<pair<int, int>*, vector<pair<int, int> > >; _Compare = __gnu_cxx::__ops::_Iter_comp_iter<main()::<lambda(const pii&, const pii&)> >]'
 1593 |       std::__make_heap(__first, __middle, __comp);
      |       ~~~~~~~~~~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~~~
/usr/include/c++/14/bits/stl_algo.h:1868:25:   required from 'void std::__partial_sort(_RandomAccessIterator, _RandomAccessIterator, _RandomAccessIterator, _Compare) [with _RandomAccessIterator = __gnu_cxx::__normal_iterator<pair<int, int>*, vector<pair<int, int> > >; _Compare = __gnu_cxx::__ops::_Iter_comp_iter<main()::<lambda(const pii&, const pii&)> >]'
 1868 |       std::__heap_select(__first, __middle, __last, __comp);
      |       ~~~~~~~~~~~~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
/usr/include/c++/14/bits/stl_algo.h:1884:27:   required from 'void std::__introsort_loop(_RandomAccessIterator, _RandomAccessIterator, _Size, _Compare) [with _RandomAccessIterator = __gnu_cxx::__normal_iterator<pair<int, int>*, vector<pair<int, int> > >; _Size = long int; _Compare = __gnu_cxx::__ops::_Iter_comp_iter<main()::<lambda(const pii&, const pii&)> >]'
 1884 |               std::__partial_sort(__first, __last, __last, __comp);
      |               ~~~~~~~~~~~~~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
/usr/include/c++/14/bits/stl_algo.h:1905:25:   required from 'void std::__sort(_RandomAccessIterator, _RandomAccessIterator, _Compare) [with _RandomAccessIterator = __gnu_cxx::__normal_iterator<pair<int, int>*, vector<pair<int, int> > >; _Compare = __gnu_cxx::__ops::_Iter_comp_iter<main()::<lambda(const pii&, const pii&)> >]'
 1905 |           std::__introsort_loop(__first, __last,
      |           ~~~~~~~~~~~~~~~~~~~~~^~~~~~~~~~~~~~~~~
 1906 |                                 std::__lg(__last - __first) * 2,
      |