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;
int n;
vector<int> c;
vector<int> sum;
vector<vector<int> > g;
bool success;
bool brute_force(int v) {
  if (v == n) {
    bool f = true;
    for (int i = 0; i < n; ++i)
      if (sum[i] || (c[i] > 1 && g[i].size() < 2)) {
        f = false;
        break;
      }
    if (f)
      return true;
    else
      return false;
  }
  map<int, int> values;
  for (int i = 0; i < v; ++i)
    if (sum[i] > 0 && sum[i] > c[v] || (sum[i] == c[v] && g[i].size() > 0)) {
      if (values.find(sum[i]) == values.end())
        values.insert(make_pair(sum[i], i));
      else if (g[values[sum[i]]].size() > g[i].size())
        values[sum[i]] = i;
    }
  for (map<int, int>::iterator it = values.begin(); it != values.end(); ++it) {
    if (c[v] <= it->first) {
      int i = it->second;
      g[i].push_back(v);
      sum[i] -= c[v];
      if (brute_force(v + 1)) {
        return true;
      } else {
        g[i].pop_back();
        sum[i] += c[v];
      }
    }
  }
  return false;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin >> n;
  c.resize(n);
  for (int i = 0; i < n; ++i) cin >> c[i];
  sort(c.rbegin(), c.rend());
  if (n == 1) {
    cout << "YES";
    return 0;
  }
  if (n == 2) {
    cout << "NO";
    return 0;
  }
  if (c[0] != n) {
    cout << "NO";
    return 0;
  }
  if (c[0] == c[1]) {
    cout << "NO";
    return 0;
  }
  sum.resize(n);
  copy(c.begin(), c.end(), sum.begin());
  sum[0] -= c[1];
  for (int i = 0; i < n; ++i) --sum[i];
  g.resize(n);
  g[0].push_back(1);
  cout << (brute_force(2) ? "YES" : "NO");
  return 0;
}
