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)

/**
 * code generated by JHelper
 * More info: https://github.com/AlexeyDmitriev/JHelper
 * @author zjsdut
 */

#include <bitset>
#include <iostream>
using std::to_string;
std::string to_string(const std::string &s) { return '"' + s + '"'; }

std::string to_string(const char *s) { return to_string((std::string) s); }

std::string to_string(bool b) { return (b ? "true" : "false"); }


template<size_t N>
std::string to_string(const std::bitset<N> &bs) {
  return bs.to_string();
}
// the declaration must goes before the definition!
template<typename A>
std::string to_string(const A &v);

template<typename A, typename B>
std::string to_string(const std::pair<A, B> &p) {
  return "(" + to_string(p.first) + ", " + to_string(p.second) + ")";
}

template<typename A>
std::string to_string(const A &v) {
  bool first = true;
  std::string res = "{";
  for (const auto &x : v) {
    if (!first) { res += ", "; }
    first = false;
    res += to_string(x);
  }
  res += "}";
  return res;
}



void debug_out() { std::cerr << std::endl; }

template<typename Head, typename... Tail>
void debug_out(const Head &H, const Tail &... T) {
  std::cerr << " " << to_string(H);
  debug_out(T...);
}

#if defined LOCAL
#define debug(...)                                                                                 \
  std::cerr << "\033[90m" << "[" << #__VA_ARGS__ << "]:", debug_out(__VA_ARGS__),              \
      std::cerr << "\033[0m"
#else
#define debug(...) 42
#endif

#include <vector>
#include <numeric>
#include <functional>
template <typename T> class BIT {
  using BinOp = std::function<T(T, T)>;
  BinOp bin_op;
  const T init;
  // 0-indexed
  std::vector<T> a;

public:
  explicit BIT(
      int n, BinOp op = [](T x, T y) { return x + y; }, T init = T{})
      : bin_op(std::move(op)), init(init), a(n, init) {}

  T prefix(int x) const {
    auto res = init;
    while (x >= 0) {
      res = bin_op(a[x], res);
      x = (x & (x + 1)) - 1;
    }
    return res;
  }

  void modify(int x, T v) {
    while (x < (int)a.size()) {
      a[x] = bin_op(a[x], v);
      x |= (x + 1);
    }
  }

  void clear() { fill(a.begin(), a.end(), init); }
};

#ifndef JHELPER_EXAMPLE_PROJECT_LIBRARY_IO_HPP_
#define JHELPER_EXAMPLE_PROJECT_LIBRARY_IO_HPP_

#include <iomanip>

struct fast_ios {
  fast_ios() {
    std::cin.tie(nullptr);
    std::ios::sync_with_stdio(false);
    std::cout << std::fixed << std::setprecision(10);
  };
} fast_ios_;

template<typename T>
std::istream &operator>>(std::istream &stream, std::vector<T> &vec) {
  for (auto &x : vec)
    stream >> x;
  return stream;
}

template<typename T, typename U>
std::istream &operator>>(std::istream &in, std::pair<T, U> &p) {
  in >> p.first >> p.second;
  return in;
}

void scan() {}

template<class T, class... Args>
void scan(T &a, Args &... rest) {
  std::cin >> a;
  scan(rest...);
}

template<typename T>
std::ostream &operator<<(std::ostream &stream, const std::vector<T> &vec) {
  bool first = true;
  for (const T &t : vec) {
    if (first) first = false;
    else std::cout << ' ';
    std::cout << t;
  }
  return stream;
}

template<typename T, typename U>
std::ostream &operator<<(std::ostream &out, const std::pair<T,U> &p) {
  out << p.first << ' ' << p.second;
  return out;
}

template<typename T>
void print(const std::vector<std::vector<T>> &t) {
  for (const auto &row : t) {
    std::cout << row << '\n';
  }
}

template<typename T>
void print(const T &t) { std::cout << t << ' '; }

template<typename T, typename... Args>
void print(const T &t, const Args &... rest) {
  print(t);
  print(rest...);
}

template<typename T>
void println(const T &t) { std::cout << t << '\n'; }

template<typename T, typename... Args>
void println(const T &t, const Args &... rest) {
  print(t);
  println(rest...);
}
#endif //JHELPER_EXAMPLE_PROJECT_LIBRARY_IO_HPP_

#ifndef ALGO_UTILS
#define ALGO_UTILS
#include <algorithm>
#include <cassert>
#include <queue>


#include <climits>
#include <map>
#include <set>
template<typename A, typename B>
bool chkmin(A &a, const B &b) {
  if (b < a) {
    a = b;
    return true;
  }
  return false;
}

template<typename A, typename B>
bool chkmax(A &a, const B &b) {
  if (b > a) {
    a = b;
    return true;
  }
  return false;
}

using ll = long long;
using ull = unsigned long long;
using vl = std::vector<ll>;
using vb = std::vector<bool>;
using vi = std::vector<int>;
using pii = std::pair<int, int>;
using pli = std::pair<ll, int>;
using pil = std::pair<int, ll>;
using pll = std::pair<ll, ll>;
using vpii = std::vector<pii>;
template<typename T>
using vv = std::vector<std::vector<T>>;
#define rng3(i, a, b) for (std::common_type<decltype(a), decltype(b)>::type i = a; i < b; ++i)
#define rng2(i, n) rng3(i, 0, n)
#define GET_MACRO(_1, _2, _3, NAME, ...) NAME
#define rng(...) GET_MACRO(__VA_ARGS__, rng3, rng2)(__VA_ARGS__)
#define up(i, a, b) for (std::common_type<decltype(a), decltype(b)>::type i = a; i <= b; ++i)
#define down(i, b, a) for (std::common_type<decltype(a), decltype(b)>::type i = b; i >= a; i--)
#define TOKENPASTE(x, y) x##y
#define TOKENPASTE2(x, y) TOKENPASTE(x, y)
#define rep(n)                                                                                     \
  for (int TOKENPASTE2(_iter_, __LINE__) = 0, TOKENPASTE2(_num_, __LINE__) = n;                    \
       TOKENPASTE2(_iter_, __LINE__) < TOKENPASTE2(_num_, __LINE__);                               \
       ++TOKENPASTE2(_iter_, __LINE__))
#define FOR(x, cont) for (const auto &x : cont)
#define For(x, cont) for (auto &x : cont)
#define ALL(x) begin(x), end(x)
#define pb push_back
#define mp make_pair
#define eb emplace_back
#define ep emplace
#define SZ(x) (int) (x).size()
#define UNIQ(vec) (vec).erase(std::unique(all(vec)), std::end(vec))
#define LB(cont, x) int(std::lower_bound(all(cont), x) - std::begin(cont))
#define UB(cont, x) int(std::upper_bound(all(cont), x) - std::begin(cont))
template<typename T, typename U = std::less<T>>
using pq = std::priority_queue<T, std::vector<T>, U>;
template<typename T, typename U>
T ceil(T x, U y) {
  assert(y > 0);
  if (x > 0) x += y - 1;
  return x / y;
}

template<typename T, typename U>
T floor(T x, U y) {
  assert(y > 0);
  if (x < 0) x -= y - 1;
  return x / y;
}
#endif
using namespace std;
//线段树是满二叉树：每个非叶子都有两个孩子。
//一棵有n个叶子的满二叉树共有2*n-1个节点。
class segtree {
  public:
  struct node {
    // don't forget to set default value (used for leaves)
    // not necessarily neutral element!
    int max = INT_MIN;
    void apply(int l, int r, int v) {
      max = v;
    }
  };
  node unite(const node &a, const node &b) const {
    node res;
    res.max = max(a.max, b.max);
    return res;
  }
  inline void push(int x, int l, int r) {
    //按先序遍历的顺序给节点编号。
    int y = (l + r) >> 1;
    int z = x + ((y - l + 1) << 1);
    // 左儿子编号是x+1,右儿子编号是z。
    // push from x into (x + 1) and z
//    ...
/*
    if (tree[x].add != 0) {
      tree[x + 1].apply(l, y, tree[x].add);
      tree[z].apply(y + 1, r, tree[x].add);
      tree[x].add = 0;
    }
*/
  }
  inline void pull(int x, int z) {
    tree[x] = unite(tree[x + 1], tree[z]);
  }
  int n;
  vector<node> tree;
  void build(int x, int l, int r) {
    if (l == r) {
      return;
    }
    int y = (l + r) >> 1;
    int z = x + ((y - l + 1) << 1);
    build(x + 1, l, y);
    build(z, y + 1, r);
    pull(x, z);
  }
  template <typename M>
  void build(int x, int l, int r, const vector<M> &v) {
    if (l == r) {
      tree[x].apply(l, r, v[l]);
      return;
    }
    int y = (l + r) >> 1;
    int z = x + ((y - l + 1) << 1);
    build(x + 1, l, y, v);
    build(z, y + 1, r, v);
    pull(x, z);
  }
  template <typename Callable>
  void build(int x, int l, int r, const Callable& f) {
    if (l == r) {
      tree[x].apply(l, r, f(l));
      return;
    }
    int y = (l + r) >> 1;
    int z = x + ((y - l + 1) << 1);
    build(x + 1, l, y, f);
    build(z, y + 1, r, f);
    pull(x, z);
  }
  node get(int x, int l, int r, int ll, int rr) {
    if (ll <= l && r <= rr) {
      return tree[x];
    }
    int y = (l + r) >> 1;
    int z = x + ((y - l + 1) << 1);
    push(x, l, r);
    node res{};
    if (rr <= y) {
      res = get(x + 1, l, y, ll, rr);
    } else {
      if (ll > y) {
        res = get(z, y + 1, r, ll, rr);
      } else {
        res = unite(get(x + 1, l, y, ll, rr), get(z, y + 1, r, ll, rr));
      }
    }
    pull(x, z);
    return res;
  }
  template <typename... M>
  void modify(int x, int l, int r, int ll, int rr, const M&... v) {
    if (ll <= l && r <= rr) {
      tree[x].apply(l, r, v...);
      return;
    }
    int y = (l + r) >> 1;
    int z = x + ((y - l + 1) << 1);
    push(x, l, r);
    if (ll <= y) {
      modify(x + 1, l, y, ll, rr, v...);
    }
    if (rr > y) {
      modify(z, y + 1, r, ll, rr, v...);
    }
    pull(x, z);
  }
  int find_first_knowingly(int x, int l, int r, const function<bool(const node&)> &f) {
    if (l == r) {
      return l;
    }
    push(x, l, r);
    int y = (l + r) >> 1;
    int z = x + ((y - l + 1) << 1);
    int res;
    if (f(tree[x + 1])) {
      res = find_first_knowingly(x + 1, l, y, f);
    } else {
      res = find_first_knowingly(z, y + 1, r, f);
    }
    pull(x, z);
    return res;
  }
  int find_first(int x, int l, int r, int ll, int rr, const function<bool(const node&)> &f) {
    if (ll <= l && r <= rr) {
      if (!f(tree[x])) {
        return -1;
      }
      return find_first_knowingly(x, l, r, f);
    }
    push(x, l, r);
    int y = (l + r) >> 1;
    int z = x + ((y - l + 1) << 1);
    int res = -1;
    if (ll <= y) {
      res = find_first(x + 1, l, y, ll, rr, f);
    }
    if (rr > y && res == -1) {
      res = find_first(z, y + 1, r, ll, rr, f);
    }
    pull(x, z);
    return res;
  }
  int find_last_knowingly(int x, int l, int r, const function<bool(const node&)> &f) {
    if (l == r) {
      return l;
    }
    push(x, l, r);
    int y = (l + r) >> 1;
    int z = x + ((y - l + 1) << 1);
    int res;
    if (f(tree[z])) {
      res = find_last_knowingly(z, y + 1, r, f);
    } else {
      res = find_last_knowingly(x + 1, l, y, f);
    }
    pull(x, z);
    return res;
  }
  int find_last(int x, int l, int r, int ll, int rr, const function<bool(const node&)> &f) {
    if (ll <= l && r <= rr) {
      if (!f(tree[x])) {
        return -1;
      }
      return find_last_knowingly(x, l, r, f);
    }
    push(x, l, r);
    int y = (l + r) >> 1;
    int z = x + ((y - l + 1) << 1);
    int res = -1;
    if (rr > y) {
      res = find_last(z, y + 1, r, ll, rr, f);
    }
    if (ll <= y && res == -1) {
      res = find_last(x + 1, l, y, ll, rr, f);
    }
    pull(x, z);
    return res;
  }
  segtree(int _n) : n(_n) {
    assert(n > 0);
    tree.resize(2 * n - 1);
    build(0, 0, n - 1);
  }
  template <typename M>
  segtree(const vector<M> &v) {
    n = v.size();
    assert(n > 0);
    tree.resize(2 * n - 1);
    build(0, 0, n - 1, v);
  }
  template <typename Callable>
  segtree(int _n, const Callable& f) : n(_n) {
    assert(n > 0);
    tree.resize(2 * n - 1);
    build(0, 0, n - 1, f);
  }
  node get(int ll, int rr) {
    assert(0 <= ll && ll <= rr && rr <= n - 1);
    return get(0, 0, n - 1, ll, rr);
  }
  node get(int p) {
    assert(0 <= p && p <= n - 1);
    return get(0, 0, n - 1, p, p);
  }
  template <typename... M>
  void modify(int ll, int rr, const M&... v) {
    assert(0 <= ll && ll <= rr && rr <= n - 1);
    modify(0, 0, n - 1, ll, rr, v...);
  }
  // find_first and find_last call all FALSE elements
  // to the left (right) of the sought position exactly once
  int find_first(int ll, int rr, const function<bool(const node&)> &f) {
    assert(0 <= ll && ll <= rr && rr <= n - 1);
    return find_first(0, 0, n - 1, ll, rr, f);
  }
  int find_last(int ll, int rr, const function<bool(const node&)> &f) {
    assert(0 <= ll && ll <= rr && rr <= n - 1);
    return find_last(0, 0, n - 1, ll, rr, f);
  }
};
class FBracketSequencing {
 public:
  static void solve(istream &, ostream &) {
    int n;
    scan(n);
    vector<string> s(n);
    scan(s);
    vi need_left(n);
    vi give_left(n);
    rng(i, 0, n) {
      int need_l = 0;
      int nl = 0;
      FOR(x, s[i]) {
        if (x == '(') ++nl;
        else {
          if (nl > 0) --nl;
          else
            ++need_l;
        }
      }
      need_left[i] = need_l;
      give_left[i] = nl;
    }
    // sum of need_left <= sum of give_left
    vi p(n);
    iota(ALL(p), 0);
    sort(ALL(p), [&](int i, int j) { return need_left[i] < need_left[j]; });
//    BIT<int> prefix_max(
//        n, [](int x, int y) { return max(x, y); }, INT_MIN);
//    map<int, set<pii>> delta;
    auto get_index = [&](int cnt) {
      return upper_bound(ALL(p), cnt, [&](int val, int index) { return val < need_left[index]; })
          - p.begin() - 1;
    };
    debug(n);
    segtree tree(n, [&](int i)->int{return give_left[p[i]] - need_left[p[i]];});
    debug(p);
    int n_left = 0;
    rep (n) {
      int r = get_index(n_left);
      if (r < 0) {
        println("No");
        return;
      }
      int max_delta = tree.get(0, r).max;
      if (max_delta == INT_MIN) {
        println("No");
        return;
      }
      n_left += max_delta;
      if (n_left < 0) {
        println("No");
        return;
      }
      int pos = tree.find_last(0, r, [max_delta](auto node){return node.max == max_delta;});
      tree.modify(pos, pos, INT_MIN);
    }
    println(n_left == 0 ? "Yes" : "No");
  }
};
/*
 * Make sure that your laptop is plugged in or the build may be slow.
 */

#define in std::cin
#define out std::cout
int main() {
  FBracketSequencing solver;
  solver.solve(in, out);
  return 0;
}