#include <bits/stdc++.h>
using namespace std;
const int maxn = 30;
int n, c[maxn];
bool mark[maxn], flag1, flag2;
int main() {
  ios_base::sync_with_stdio(false), cin.tie(0), cout.tie(0);
  cin >> n;
  for (int i = 0; i < n; i++) cin >> c[i];
  sort(c, c + n);
  for (int i = 0; i < n; i++) {
    int sum = 1;
    for (int j = 0; j < i && sum < c[i]; j++)
      if (c[j] < c[i] - 1 && sum + c[j] <= c[i] && !mark[j])
        mark[j]++, sum += c[j];
    if (sum != c[i]) flag1++;
  }
  for (int i = 0; i < n - 1; i++)
    if (!mark[i]) flag1++;
  memset(mark, 0, sizeof mark);
  for (int i = 0; i < n; i++) {
    int sum = 1;
    for (int j = i - 1; j >= 0 && sum < c[i]; j--)
      if (c[j] < c[i] - 1 && sum + c[j] <= c[i] && !mark[j])
        mark[j]++, sum += c[j];
    if (sum != c[i]) flag2++;
  }
  for (int i = 0; i < n - 1; i++)
    if (!mark[i]) flag2++;
  if (flag1 && flag2)
    cout << "NO";
  else
    cout << "YES";
  cerr << endl;
}

### Prompt

Please provide a cpp coded solution to the problem described below:

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;
const int maxn = 30;
int n, c[maxn];
bool mark[maxn], flag1, flag2;
int main() {
  ios_base::sync_with_stdio(false), cin.tie(0), cout.tie(0);
  cin >> n;
  for (int i = 0; i < n; i++) cin >> c[i];
  sort(c, c + n);
  for (int i = 0; i < n; i++) {
    int sum = 1;
    for (int j = 0; j < i && sum < c[i]; j++)
      if (c[j] < c[i] - 1 && sum + c[j] <= c[i] && !mark[j])
        mark[j]++, sum += c[j];
    if (sum != c[i]) flag1++;
  }
  for (int i = 0; i < n - 1; i++)
    if (!mark[i]) flag1++;
  memset(mark, 0, sizeof mark);
  for (int i = 0; i < n; i++) {
    int sum = 1;
    for (int j = i - 1; j >= 0 && sum < c[i]; j--)
      if (c[j] < c[i] - 1 && sum + c[j] <= c[i] && !mark[j])
        mark[j]++, sum += c[j];
    if (sum != c[i]) flag2++;
  }
  for (int i = 0; i < n - 1; i++)
    if (!mark[i]) flag2++;
  if (flag1 && flag2)
    cout << "NO";
  else
    cout << "YES";
  cerr << endl;
}

```