#include <bits/stdc++.h>
using namespace std;
int n, nleaves, p, need, sated;
vector<int> nodes;
bool valid[4096];
int main() {
  cin >> n;
  for (int i = 0; i < n; i++) {
    cin >> p;
    if (p == 1)
      nleaves++;
    else
      nodes.push_back(p), need += p - 1;
  }
  sort(nodes.begin(), nodes.end());
  for (int i = 0; i + 1 < nodes.size(); i++) sated += nodes[i];
  if (n == 1 && nleaves == 1) {
    cout << "YES\n";
    return 0;
  }
  if (need - sated != nleaves || nodes.size() == 0 || nodes[0] == 2 ||
      nleaves < nodes.size()) {
    cout << "NO\n";
    return 0;
  }
  valid[0] = true;
  for (int cur = 0; cur < nodes.size(); cur++) {
    for (int base = (1 << cur) - 1; base >= 0; base--)
      for (int i = 0; i <= base; i++) {
        if ((i & base) != i) continue;
        int csum = 0, nch = 0;
        for (int j = 0; j < cur; j++)
          if ((i & (1 << j)) != 0) csum += nodes[j], nch++;
        if (csum <= nodes[cur] - 1 && (nodes[cur] - 1) - csum + nch > 1)
          if (valid[base - i] == true) valid[base] = true;
      }
  }
  if (valid[(1 << (nodes.size() - 1)) - 1])
    cout << "YES\n";
  else
    cout << "NO\n";
  return 0;
}

### Prompt

Generate a CPP solution 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;
int n, nleaves, p, need, sated;
vector<int> nodes;
bool valid[4096];
int main() {
  cin >> n;
  for (int i = 0; i < n; i++) {
    cin >> p;
    if (p == 1)
      nleaves++;
    else
      nodes.push_back(p), need += p - 1;
  }
  sort(nodes.begin(), nodes.end());
  for (int i = 0; i + 1 < nodes.size(); i++) sated += nodes[i];
  if (n == 1 && nleaves == 1) {
    cout << "YES\n";
    return 0;
  }
  if (need - sated != nleaves || nodes.size() == 0 || nodes[0] == 2 ||
      nleaves < nodes.size()) {
    cout << "NO\n";
    return 0;
  }
  valid[0] = true;
  for (int cur = 0; cur < nodes.size(); cur++) {
    for (int base = (1 << cur) - 1; base >= 0; base--)
      for (int i = 0; i <= base; i++) {
        if ((i & base) != i) continue;
        int csum = 0, nch = 0;
        for (int j = 0; j < cur; j++)
          if ((i & (1 << j)) != 0) csum += nodes[j], nch++;
        if (csum <= nodes[cur] - 1 && (nodes[cur] - 1) - csum + nch > 1)
          if (valid[base - i] == true) valid[base] = true;
      }
  }
  if (valid[(1 << (nodes.size() - 1)) - 1])
    cout << "YES\n";
  else
    cout << "NO\n";
  return 0;
}

```