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
#include <bits/stdc++.h>
using namespace std;
set<vector<int> > sub[25], blob[25];
bool work() {
  int n;
  cin >> n;
  vector<int> cnt(n + 1);
  for (auto i = (0); i < n; i++) {
    int sz;
    cin >> sz;
    if (sz == 2)
      return false;
    else
      cnt[sz]++;
  }
  if (2 * cnt[1] < n) return false;
  vector<int> leaf(n + 1);
  leaf[1] = 1;
  sub[1].insert(leaf);
  for (auto i = (2); i < n + 1; i++) {
    for (auto j = (1); j < i / 2 + 1; j++) {
      int k = i - j;
      for (auto& s : sub[j]) {
        for (auto& t : blob[k]) {
          vector<int> u(n + 1);
          bool ok = true;
          for (auto l = (0); l < n + 1; l++) {
            u[l] = s[l] + t[l];
            if (u[l] > cnt[l]) {
              ok = false;
              break;
            }
          }
          if (ok) blob[i].insert(u);
        }
        for (auto& t : sub[k]) {
          vector<int> u(n + 1);
          bool ok = true;
          for (auto l = (0); l < n + 1; l++) {
            u[l] = s[l] + t[l];
            if (u[l] > cnt[l]) {
              ok = false;
              break;
            }
          }
          if (ok) blob[i].insert(u);
        }
      }
    }
    if (cnt[i]) {
      for (auto& s : blob[i - 1]) {
        vector<int> t = s;
        t[i] = 1;
        sub[i].insert(t);
      }
    }
  }
  return sub[n].count(cnt);
}
int main() {
  cout << (work() ? "YES" : "NO") << endl;
  return 0;
}
