#include <bits/stdc++.h>
int a[30], b[30], son[30], n;
int cmp(const void *a, const void *b) { return *(int *)a > *(int *)b ? 1 : -1; }
int dfs(int w) {
  int i;
  if (!w) {
    for (i = 1; i <= n; i++)
      if (a[i] != 1) return 0;
    return 1;
  }
  for (i = w + 1; i <= n; i++)
    if (a[w] < a[i] - (!son[i])) {
      a[i] -= a[w];
      son[i]++;
      if (dfs(w - 1)) return 1;
      a[i] += a[w];
      son[i]--;
    }
  return 0;
}
int main() {
  int i;
  while (scanf("%d", &n) != EOF) {
    memset(son, 0, sizeof(son));
    for (i = 1; i <= n; i++) scanf("%d", &a[i]);
    qsort(a + 1, n, sizeof(int), cmp);
    for (i = 1; i <= n; i++) {
      if (a[i] == 2) break;
      b[i] = a[i];
    }
    if (i <= n || !dfs(n - 1))
      printf("NO\n");
    else
      printf("YES\n");
  }
  return 0;
}

### Prompt

Your challenge is to write 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>
int a[30], b[30], son[30], n;
int cmp(const void *a, const void *b) { return *(int *)a > *(int *)b ? 1 : -1; }
int dfs(int w) {
  int i;
  if (!w) {
    for (i = 1; i <= n; i++)
      if (a[i] != 1) return 0;
    return 1;
  }
  for (i = w + 1; i <= n; i++)
    if (a[w] < a[i] - (!son[i])) {
      a[i] -= a[w];
      son[i]++;
      if (dfs(w - 1)) return 1;
      a[i] += a[w];
      son[i]--;
    }
  return 0;
}
int main() {
  int i;
  while (scanf("%d", &n) != EOF) {
    memset(son, 0, sizeof(son));
    for (i = 1; i <= n; i++) scanf("%d", &a[i]);
    qsort(a + 1, n, sizeof(int), cmp);
    for (i = 1; i <= n; i++) {
      if (a[i] == 2) break;
      b[i] = a[i];
    }
    if (i <= n || !dfs(n - 1))
      printf("NO\n");
    else
      printf("YES\n");
  }
  return 0;
}

```