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<pair<int, int> > c;
set<pair<int, int> > v;
int n;
pair<int, int> getEl(int k) {
  k = v.size() - k - 1;
  for (__typeof((v).begin()) it = (v).begin(); it != (v).end(); it++) {
    if (k == 0) return *it;
    k--;
  }
}
bool get(vector<pair<int, int> > &w, int tot, int i, int sum) {
  if (i == v.size()) return tot == 0;
  pair<int, int> p = getEl(i);
  if (p.first > tot || p.first == sum) return get(w, tot, i + 1, sum);
  if (get(w, tot - p.first, i + 1, sum)) {
    w.push_back(p);
    return true;
  }
  if (get(w, tot, i + 1, sum)) {
    return true;
  }
}
int main() {
  cin >> n;
  for (int i = 0; i < n; i++) {
    int k;
    scanf("%d", &k);
    if (k == 1)
      v.insert(make_pair(k, i + 1));
    else
      c.insert(make_pair(k, i + 1));
  }
  bool bad = 0;
  while (c.size() > 0) {
    pair<int, int> p = *c.begin();
    if (p.first <= 2) {
      bad = 1;
      break;
    }
    c.erase(c.begin());
    vector<pair<int, int> > w;
    if (get(w, p.first - 1, 0, p.first - 1) == 0) {
      bad = 1;
      break;
    }
    for (int i = 0; i < w.size(); i++) {
      v.erase(w[i]);
    }
    v.insert(p);
  }
  if (bad || c.size() > 0 || v.size() > 1)
    cout << "NO" << endl;
  else
    cout << "YES" << endl;
  return 0;
}
