#include <bits/stdc++.h>
using namespace std;
int n, c[25], coin[25];
int ans = 0;
bool can;
int p_b;
bool good() {
  int cnt = 0;
  for (int i = 0; i < 25; i++) cnt += coin[i];
  return cnt == 1;
}
void rec(int s, int r, int p) {
  if (r == 1) {
    if (c[p] > 1) coin[c[p]]++;
    p++;
    if (p < n) r = c[p];
    s = 1;
  }
  if (p == n && good()) can = true;
  for (int i = s; i < c[p] - 1; i++) {
    for (int j = 0; j <= coin[i]; j++) {
      if (r - i * j >= 1) {
        coin[i] -= j;
        rec(i + 1, r - i * j, p);
        coin[i] += j;
      }
      if (can) return;
    }
  }
  if (r == 1) {
    p--;
    if (c[p] > 1) coin[c[p]]--;
  }
}
int main() {
  scanf("%d", &n);
  for (int i = 0; i < n; i++) {
    scanf("%d", &c[i]);
    if (c[i] == 1) coin[1]++;
  }
  sort(c, c + n);
  int start_pos = 0;
  for (int i = 0; i < n; i++)
    if (c[i] != 1) {
      start_pos = i;
      break;
    }
  rec(1, c[start_pos], start_pos);
  if (can) {
    cout << "YES";
  } else
    cout << "NO";
  return 0;
}

### Prompt

Generate 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>
using namespace std;
int n, c[25], coin[25];
int ans = 0;
bool can;
int p_b;
bool good() {
  int cnt = 0;
  for (int i = 0; i < 25; i++) cnt += coin[i];
  return cnt == 1;
}
void rec(int s, int r, int p) {
  if (r == 1) {
    if (c[p] > 1) coin[c[p]]++;
    p++;
    if (p < n) r = c[p];
    s = 1;
  }
  if (p == n && good()) can = true;
  for (int i = s; i < c[p] - 1; i++) {
    for (int j = 0; j <= coin[i]; j++) {
      if (r - i * j >= 1) {
        coin[i] -= j;
        rec(i + 1, r - i * j, p);
        coin[i] += j;
      }
      if (can) return;
    }
  }
  if (r == 1) {
    p--;
    if (c[p] > 1) coin[c[p]]--;
  }
}
int main() {
  scanf("%d", &n);
  for (int i = 0; i < n; i++) {
    scanf("%d", &c[i]);
    if (c[i] == 1) coin[1]++;
  }
  sort(c, c + n);
  int start_pos = 0;
  for (int i = 0; i < n; i++)
    if (c[i] != 1) {
      start_pos = i;
      break;
    }
  rec(1, c[start_pos], start_pos);
  if (can) {
    cout << "YES";
  } else
    cout << "NO";
  return 0;
}

```