#include <bits/stdc++.h>
using namespace std;
int n;
int a[233];
int ta[233];
int sons[233];
bool dfs(int one, int i) {
  if (i == n) {
    if (a[i] - 1 - one == 0)
      return 1;
    else
      return 0;
  }
  one -= a[i] - 1;
  if (one < 0) return 0;
  int s = sons[i];
  s += a[i] - 1;
  if (s < 2) return 0;
  for (int j = i + 1; j <= n; j++)
    if (a[j] > ta[i]) {
      a[j] -= ta[i];
      sons[j]++;
      if (dfs(one, i + 1)) return 1;
      sons[j]--;
      a[j] += ta[i];
    }
  return 0;
}
int main() {
  scanf("%d", &n);
  int one = 0;
  for (int i = 1; i <= n; i++) {
    scanf("%d", &a[i]);
    one += a[i] == 1;
  }
  sort(a + 1, a + 1 + n);
  for (int i = 1; i <= n; i++) ta[i] = a[i];
  if (one <= n / 2) {
    puts("NO");
    return 0;
  }
  if (n == 1) {
    if (a[1] == 1)
      puts("YES");
    else
      puts("NO");
    return 0;
  }
  if (n == 2) {
    puts("NO");
    return 0;
  }
  if (dfs(one, one + 1)) {
    puts("YES");
  } else {
    puts("NO");
  }
  return 0;
}

### Prompt

Please create a solution in Cpp 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;
int a[233];
int ta[233];
int sons[233];
bool dfs(int one, int i) {
  if (i == n) {
    if (a[i] - 1 - one == 0)
      return 1;
    else
      return 0;
  }
  one -= a[i] - 1;
  if (one < 0) return 0;
  int s = sons[i];
  s += a[i] - 1;
  if (s < 2) return 0;
  for (int j = i + 1; j <= n; j++)
    if (a[j] > ta[i]) {
      a[j] -= ta[i];
      sons[j]++;
      if (dfs(one, i + 1)) return 1;
      sons[j]--;
      a[j] += ta[i];
    }
  return 0;
}
int main() {
  scanf("%d", &n);
  int one = 0;
  for (int i = 1; i <= n; i++) {
    scanf("%d", &a[i]);
    one += a[i] == 1;
  }
  sort(a + 1, a + 1 + n);
  for (int i = 1; i <= n; i++) ta[i] = a[i];
  if (one <= n / 2) {
    puts("NO");
    return 0;
  }
  if (n == 1) {
    if (a[1] == 1)
      puts("YES");
    else
      puts("NO");
    return 0;
  }
  if (n == 2) {
    puts("NO");
    return 0;
  }
  if (dfs(one, one + 1)) {
    puts("YES");
  } else {
    puts("NO");
  }
  return 0;
}

```