#include <bits/stdc++.h>
using namespace std;
template <class T>
inline void mn(T& x, const T& y) {
  if (y < x) x = y;
}
template <class T>
inline void mx(T& x, const T& y) {
  if (x < y) x = y;
}
template <class T>
inline int sz(const T& x) {
  return x.size();
}
const int N = 24;
const vector<vector<int> >& f(int n);
vector<vector<int> > F[N + 1];
vector<int> goal;
int used[N + 1];
int n;
inline void gen(int init, int left, int sum, int last,
                vector<vector<int> >& var, vector<vector<int> >& dest) {
  if (var.size() == 0) {
    return;
  }
  if (left == 0) {
    if (sum == 0) {
      if (init != n) {
        for (int i = 0; i < var.size(); ++i) {
          dest.push_back(move(var[i]));
        }
      } else {
        for (auto& con : var) {
          sort(con.begin(), con.end());
          if (con == goal) {
            cout << "YES" << endl;
            exit(0);
          }
        }
      }
    }
    return;
  }
  for (int curr = last; left * curr <= sum; ++curr) {
    const auto& add = f(curr);
    if (add.size() == 0) {
      continue;
    }
    vector<vector<int> > next_var;
    for (const auto& x : var) {
      for (const auto& y : add) {
        vector<int> curr_var = x;
        copy(y.begin(), y.end(), back_inserter(curr_var));
        next_var.push_back(move(curr_var));
      }
    }
    gen(init, left - 1, sum - curr, curr, next_var, dest);
  }
}
vector<vector<int> > ONE(1, vector<int>(1, 1));
vector<vector<int> > ZERO;
const vector<vector<int> >& f(int n) {
  if (n == 1) return ONE;
  if (n == 2 || !used[n]) return ZERO;
  if (!F[n].empty()) return F[n];
  for (int children = 2; children < n; ++children) {
    vector<vector<int> > st(1, vector<int>(1, n));
    gen(n, children, n - 1, 1, st, F[n]);
  }
  return F[n];
}
int main() {
  ios_base::sync_with_stdio(false);
  cin >> n;
  if (n == 1) {
    cout << "YES" << endl;
    return 0;
  }
  goal.resize(n);
  for (int i = 0; i < (n); ++i) {
    cin >> goal[i];
    used[goal[i]]++;
  }
  sort(goal.begin(), goal.end());
  f(n);
  cout << "NO" << endl;
  return 0;
}

### Prompt

Please create a solution in cpp to the following problem:

Iahub and Iahubina went to a picnic in a forest full of trees. Less than 5 minutes passed before Iahub remembered of trees from programming. Moreover, he invented a new problem and Iahubina has to solve it, otherwise Iahub won't give her the food. 

Iahub asks Iahubina: can you build a rooted tree, such that

  * each internal node (a node with at least one son) has at least two sons; 
  * node i has ci nodes in its subtree? 



Iahubina has to guess the tree. Being a smart girl, she realized that it's possible no tree can follow Iahub's restrictions. In this way, Iahub will eat all the food. You need to help Iahubina: determine if there's at least one tree following Iahub's restrictions. The required tree must contain n nodes.

Input

The first line of the input contains integer n (1 ≤ n ≤ 24). Next line contains n positive integers: the i-th number represents ci (1 ≤ ci ≤ n).

Output

Output on the first line "YES" (without quotes) if there exist at least one tree following Iahub's restrictions, otherwise output "NO" (without quotes). 

Examples

Input

4
1 1 1 4


Output

YES

Input

5
1 1 5 2 1


Output

NO

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
template <class T>
inline void mn(T& x, const T& y) {
  if (y < x) x = y;
}
template <class T>
inline void mx(T& x, const T& y) {
  if (x < y) x = y;
}
template <class T>
inline int sz(const T& x) {
  return x.size();
}
const int N = 24;
const vector<vector<int> >& f(int n);
vector<vector<int> > F[N + 1];
vector<int> goal;
int used[N + 1];
int n;
inline void gen(int init, int left, int sum, int last,
                vector<vector<int> >& var, vector<vector<int> >& dest) {
  if (var.size() == 0) {
    return;
  }
  if (left == 0) {
    if (sum == 0) {
      if (init != n) {
        for (int i = 0; i < var.size(); ++i) {
          dest.push_back(move(var[i]));
        }
      } else {
        for (auto& con : var) {
          sort(con.begin(), con.end());
          if (con == goal) {
            cout << "YES" << endl;
            exit(0);
          }
        }
      }
    }
    return;
  }
  for (int curr = last; left * curr <= sum; ++curr) {
    const auto& add = f(curr);
    if (add.size() == 0) {
      continue;
    }
    vector<vector<int> > next_var;
    for (const auto& x : var) {
      for (const auto& y : add) {
        vector<int> curr_var = x;
        copy(y.begin(), y.end(), back_inserter(curr_var));
        next_var.push_back(move(curr_var));
      }
    }
    gen(init, left - 1, sum - curr, curr, next_var, dest);
  }
}
vector<vector<int> > ONE(1, vector<int>(1, 1));
vector<vector<int> > ZERO;
const vector<vector<int> >& f(int n) {
  if (n == 1) return ONE;
  if (n == 2 || !used[n]) return ZERO;
  if (!F[n].empty()) return F[n];
  for (int children = 2; children < n; ++children) {
    vector<vector<int> > st(1, vector<int>(1, n));
    gen(n, children, n - 1, 1, st, F[n]);
  }
  return F[n];
}
int main() {
  ios_base::sync_with_stdio(false);
  cin >> n;
  if (n == 1) {
    cout << "YES" << endl;
    return 0;
  }
  goal.resize(n);
  for (int i = 0; i < (n); ++i) {
    cin >> goal[i];
    used[goal[i]]++;
  }
  sort(goal.begin(), goal.end());
  f(n);
  cout << "NO" << endl;
  return 0;
}

```