#include <bits/stdc++.h>
using namespace std;
int a[30], b[30], lf = 0, in = 0;
bool check(int now) {
  if (now == in) {
    int cnt = 0;
    for (int i = 0; i < in; i++) cnt += b[i];
    if (cnt == lf) return true;
    return false;
  }
  for (int i = 0; i < now; i++) {
    if (a[now] < a[i] - 1 && a[now] <= b[i]) {
      b[i] -= a[now];
      if (check(now + 1)) return true;
      b[i] += a[now];
    }
  }
  return false;
}
int main() {
  int n, i;
  bool flag = true;
  scanf("%d", &n);
  for (i = 0; i < n; i++) scanf("%d", &a[i]);
  sort(a, a + n, greater<int>());
  for (i = 0; i < n; i++) {
    b[i] = a[i] - 1;
    if (a[i] > 2)
      in++;
    else if (a[i] == 2)
      flag = false;
    else
      lf++;
  }
  if (lf <= in || a[0] != n) flag = false;
  if (flag && (n == 1 || check(1)))
    printf("YES\n");
  else
    printf("NO\n");
  return 0;
}

### Prompt

Create a solution in CPP for 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 a[30], b[30], lf = 0, in = 0;
bool check(int now) {
  if (now == in) {
    int cnt = 0;
    for (int i = 0; i < in; i++) cnt += b[i];
    if (cnt == lf) return true;
    return false;
  }
  for (int i = 0; i < now; i++) {
    if (a[now] < a[i] - 1 && a[now] <= b[i]) {
      b[i] -= a[now];
      if (check(now + 1)) return true;
      b[i] += a[now];
    }
  }
  return false;
}
int main() {
  int n, i;
  bool flag = true;
  scanf("%d", &n);
  for (i = 0; i < n; i++) scanf("%d", &a[i]);
  sort(a, a + n, greater<int>());
  for (i = 0; i < n; i++) {
    b[i] = a[i] - 1;
    if (a[i] > 2)
      in++;
    else if (a[i] == 2)
      flag = false;
    else
      lf++;
  }
  if (lf <= in || a[0] != n) flag = false;
  if (flag && (n == 1 || check(1)))
    printf("YES\n");
  else
    printf("NO\n");
  return 0;
}

```