#include <bits/stdc++.h>
using namespace std;
const int MAX = 30;
int a[MAX], be[MAX], n;
bool f1 = 1, f2 = 1;
int main() {
  cin >> n;
  for (int i = 0; i < n; i++) cin >> a[i];
  sort(a, a + n);
  for (int i = 0; i < n; i++) {
    int sz = 1;
    for (int j = 0; j < i && sz < a[i]; j++)
      if (a[j] <= a[i] - 2 && sz + a[j] <= a[i] && !be[j])
        be[j] = 1, sz += a[j];
    if (sz != a[i]) f1 = 0;
  }
  for (int i = 0; i < n; i++)
    if (i != n - 1 && !be[i]) f1 = 0;
  memset(be, 0, sizeof be);
  for (int i = 0; i < n; i++) {
    int sz = 1;
    for (int j = i - 1; j >= 0 && sz < a[i]; j--)
      if (a[j] <= a[i] - 2 && sz + a[j] <= a[i] && !be[j])
        be[j] = 1, sz += a[j];
    if (sz != a[i]) f2 = 0;
  }
  for (int i = 0; i < n; i++)
    if (i != n - 1 && !be[i]) f2 = 0;
  if (f1 || f2)
    cout << "YES";
  else
    cout << "NO";
}

### Prompt

Develop a solution in cpp 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 MAX = 30;
int a[MAX], be[MAX], n;
bool f1 = 1, f2 = 1;
int main() {
  cin >> n;
  for (int i = 0; i < n; i++) cin >> a[i];
  sort(a, a + n);
  for (int i = 0; i < n; i++) {
    int sz = 1;
    for (int j = 0; j < i && sz < a[i]; j++)
      if (a[j] <= a[i] - 2 && sz + a[j] <= a[i] && !be[j])
        be[j] = 1, sz += a[j];
    if (sz != a[i]) f1 = 0;
  }
  for (int i = 0; i < n; i++)
    if (i != n - 1 && !be[i]) f1 = 0;
  memset(be, 0, sizeof be);
  for (int i = 0; i < n; i++) {
    int sz = 1;
    for (int j = i - 1; j >= 0 && sz < a[i]; j--)
      if (a[j] <= a[i] - 2 && sz + a[j] <= a[i] && !be[j])
        be[j] = 1, sz += a[j];
    if (sz != a[i]) f2 = 0;
  }
  for (int i = 0; i < n; i++)
    if (i != n - 1 && !be[i]) f2 = 0;
  if (f1 || f2)
    cout << "YES";
  else
    cout << "NO";
}

```