#include <bits/stdc++.h>
const int N = 30;
int m, n, a[N], k, d[N], s[N];
bool dfs(int v) {
  if (v == n) {
    int g = 0;
    for (int i = 1; i <= n; i++) {
      if (s[i] + 1 > a[i]) return false;
      if (d[i] + a[i] - 1 - s[i] < 2) return false;
      g += a[i] - 1 - s[i];
    }
    return g == k;
  }
  for (int i = v + 1; i <= n; i++) {
    d[i] += 1;
    s[i] += a[v];
    if (dfs(v + 1)) return true;
    d[i] -= 1;
    s[i] -= a[v];
  }
  return false;
}
bool work() {
  scanf("%d", &m);
  for (int i = 1; i <= m; i++) {
    int x;
    scanf("%d", &x);
    if (x == 1)
      k++;
    else if (x == 2)
      return false;
    else
      a[++n] = x;
  }
  if (n == 0 && k == 1) return true;
  if (k < n) return false;
  std::sort(a + 1, a + 1 + n);
  return dfs(1);
}
int main() {
  if (work())
    printf("YES\n");
  else
    printf("NO\n");
}

### 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>
const int N = 30;
int m, n, a[N], k, d[N], s[N];
bool dfs(int v) {
  if (v == n) {
    int g = 0;
    for (int i = 1; i <= n; i++) {
      if (s[i] + 1 > a[i]) return false;
      if (d[i] + a[i] - 1 - s[i] < 2) return false;
      g += a[i] - 1 - s[i];
    }
    return g == k;
  }
  for (int i = v + 1; i <= n; i++) {
    d[i] += 1;
    s[i] += a[v];
    if (dfs(v + 1)) return true;
    d[i] -= 1;
    s[i] -= a[v];
  }
  return false;
}
bool work() {
  scanf("%d", &m);
  for (int i = 1; i <= m; i++) {
    int x;
    scanf("%d", &x);
    if (x == 1)
      k++;
    else if (x == 2)
      return false;
    else
      a[++n] = x;
  }
  if (n == 0 && k == 1) return true;
  if (k < n) return false;
  std::sort(a + 1, a + 1 + n);
  return dfs(1);
}
int main() {
  if (work())
    printf("YES\n");
  else
    printf("NO\n");
}

```