Problem:
Score : 600 points

Problem Statement

A bracket sequence is a string that is one of the following:

An empty string;

The concatenation of (, A, and ) in this order, for some bracket sequence A ;

The concatenation of A and B in this order, for some non-empty bracket sequences A and B /

Given are N strings S_i. Can a bracket sequence be formed by concatenating all the N strings in some order?

Constraints

1 \leq N \leq 10^6

The total length of the strings S_i is at most 10^6.

S_i is a non-empty string consisting of ( and ).

Input

Input is given from Standard Input in the following format:

N
S_1
:
S_N

Output

If a bracket sequence can be formed by concatenating all the N strings in some order, print Yes; otherwise, print No.

Sample Input 1

2
)
(()

Sample Output 1

Yes

Concatenating (() and ) in this order forms a bracket sequence.

Sample Input 2

2
)(
()

Sample Output 2

No

Sample Input 3

4
((()))
((((((
))))))
()()()

Sample Output 3

Yes

Sample Input 4

3
(((
)
)

Sample Output 4

No

Solution in C++ (GCC 9.2.1) (judge verdict: Wrong Answer)

#pragma GCC optimize ("O3")
#include "bits/stdc++.h"

using namespace std;
using ll = long long int;

#define all(v) (v).begin(),(v).end()
#define repeat(cnt,l) for(typename remove_const<typename remove_reference<decltype(l)>::type>::type cnt={};(cnt)<(l);++(cnt))
#define rrepeat(cnt,l) for(auto cnt=(l)-1;0<=(cnt);--(cnt))
#define iterate(cnt,b,e) for(auto cnt=(b);(cnt)!=(e);++(cnt))
#define diterate(cnt,b,e) for(auto cnt=(b);(cnt)!=(e);--(cnt))
const long long MD = 1000000007ll; const long double PI = 3.1415926535897932384626433832795L;
template<typename T1, typename T2> inline ostream& operator <<(ostream &o, const pair<T1, T2> p) { o << '(' << p.first << ':' << p.second << ')'; return o; }
template<typename T> inline T& chmax(T& to, const T& val) { return to = max(to, val); }
template<typename T> inline T& chmin(T& to, const T& val) { return to = min(to, val); }
void bye(string s, int code = 0) { cout << s << endl; exit(code); }
mt19937_64 randdev(8901016);
template<typename T, typename Random = decltype(randdev), typename enable_if<is_integral<T>::value>::type* = nullptr>
inline T rand(T l, T h, Random& rand = randdev) { return uniform_int_distribution<T>(l, h)(rand); }
template<typename T, typename Random = decltype(randdev), typename enable_if<is_floating_point<T>::value>::type* = nullptr>
inline T rand(T l, T h, Random& rand = randdev) { return uniform_real_distribution<T>(l, h)(rand); }

template <typename I>
struct MyRangeFormat{ I b,e; MyRangeFormat(I _b, I _e):b(_b),e(_e){} };
template<typename I>
static ostream& operator<<(ostream& o, const MyRangeFormat<I>& f) {
  o << "[ "; iterate(i,f.b,f.e) o<<*i<<' ';
  return o << ']';
}
template <typename I>
struct MyMatrixFormat{
  const I& p; long long n, m;
  MyMatrixFormat(const I& _p, long long _n, long long _m):p(_p),n(_n),m(_m){}
};
template<typename I>
static ostream& operator<<(ostream& o, const MyMatrixFormat<I>& f) {
  o<<'\n';
  repeat(i,(f.n)) {
    repeat(j,f.m) o<<f.p[i][j]<<' ';
    o<<'\n';
  }
  return o;
}
struct LOG_t { ~LOG_t() { cout << endl; } };
#define LOG (LOG_t(),cout<<'L'<<__LINE__<<": ")
#define FMTA(m,w) (MyRangeFormat<decltype(m+0)>(m,m+w))
#define FMTR(b,e) (MyRangeFormat<decltype(e)>(b,e))
#define FMTV(v) FMTR(v.begin(),v.end())
#define FMTM(m,h,w) (MyMatrixFormat<decltype(m+0)>(m,h,w))

#if defined(_WIN32) || defined(_WIN64)
#define getc_x _getc_nolock
#define putc_x _putc_nolock
#elif defined(__GNUC__)
#define getc_x getc_unlocked
#define putc_x putc_unlocked
#else
#define getc_x getc
#define putc_x putc
#endif
class MaiScanner {
  FILE* fp_;
  constexpr bool isvisiblechar(char c) noexcept { return (0x21<=(c)&&(c)<=0x7E); }
public:
  inline MaiScanner(FILE* fp):fp_(fp){}
  template<typename T> void input_integer(T& var) noexcept {
    var = 0; T sign = 1;
    int cc = getc_x(fp_);
    for (; cc < '0' || '9' < cc; cc = getc_x(fp_))
      if (cc == '-') sign = -1;
    for (; '0' <= cc && cc <= '9'; cc = getc_x(fp_))
      var = (var << 3) + (var << 1) + cc - '0';
    var = var * sign;
  }
  inline int c() noexcept { return getc_x(fp_); }
  template<typename T, typename enable_if<is_integral<T>::value, nullptr_t>::type = nullptr>
  inline MaiScanner& operator>>(T& var) noexcept { input_integer<T>(var); return *this; }
  inline MaiScanner& operator>>(string& var) {
    int cc = getc_x(fp_);
    for (; !isvisiblechar(cc); cc = getc_x(fp_));
    for (; isvisiblechar(cc); cc = getc_x(fp_))
      var.push_back(cc);
    return *this;
  }
  template<typename IT> inline void in(IT begin, IT end) { for (auto it = begin; it != end; ++it) *this >> *it; }
};
class MaiPrinter {
  FILE* fp_;
public:
  inline MaiPrinter(FILE* fp):fp_(fp){}
  template<typename T>
  void output_integer(T var) noexcept {
    if (var == 0) { putc_x('0', fp_); return; }
    if (var < 0)
      putc_x('-', fp_),
      var = -var;
    char stack[32]; int stack_p = 0;
    while (var)
      stack[stack_p++] = '0' + (var % 10),
      var /= 10;
    while (stack_p)
      putc_x(stack[--stack_p], fp_);
  }
  inline MaiPrinter& operator<<(char c) noexcept { putc_x(c, fp_); return *this; }
  template<typename T, typename enable_if<is_integral<T>::value, nullptr_t>::type = nullptr>
  inline MaiPrinter& operator<<(T var) noexcept { output_integer<T>(var); return *this; }
  inline MaiPrinter& operator<<(char* str_p) noexcept { while (*str_p) putc_x(*(str_p++), fp_); return *this; }
  inline MaiPrinter& operator<<(const string& str) {
    const char* p = str.c_str();
    const char* l = p + str.size();
    while (p < l) putc_x(*p++, fp_);
    return *this;
  }
  template<typename IT> void join(IT begin, IT end, char sep = ' ') { for (bool b = 0; begin != end; ++begin, b = 1) b ? *this << sep << *begin : *this << *begin; }
};
MaiScanner scanner(stdin);
MaiPrinter printer(stdout);



//

int N;

//

// array<int, 2> V[1000100];

int cplus[1000100];
// int minus[1000100];

int main() {
  
  scanner >> N;
  
  int depth = 0;
  int start = 0;
  int lvltotal = 0;
  
  vector<pair<int, int>> pminus; pminus.reserve(100000);
  
  repeat(i, N) {
    string s; scanner >> s;
    int low = 0;
    int lvl = 0;
    for (auto c : s) {
      lvl += (c == '(') - (c == ')');
      chmin(low, lvl);
    }
    // V[i] = {low,lvl};
    lvltotal += lvl;
    // 初期値不要
    if (low == 0) start += lvl;
    else if (lvl > 0) {
      cplus[-low] += lvl;
    }
    else {
      // minus[-low] += lvl;
      // low is negative
      pminus.emplace_back(lvl, low);
    }
    chmax(depth, -low);
  }
  if (lvltotal != 0) bye("No");
  
  // sort(V, V+N);
  
  // {
  //   int lvl = 0;
  //   rrepeat(i, N) {
  //     if (lvl + V[i][0] < 0) bye("No");
  //     lvl += V[i][1];
  //   }
  // }
  {
    int lvl = start;
    repeat(i, depth+1) {
      if (lvl < i) bye("No");
      lvl += cplus[i];
    }
    sort(all(pminus));
    for (auto p : pminus) {
      // LOG << p << lvl;
      if (-p.second > lvl) bye("No");
      lvl += p.first;
    }
  }
  cout << "Yes" << endl;
  
  return 0;
}