#include <bits/stdc++.h>
using namespace std;
int getint() {
  int x = 0, tmp = 1;
  char c = getchar();
  while ((c < '0' || c > '9') && c != '-') c = getchar();
  if (c == '-') c = getchar(), tmp = -1;
  while (c >= '0' && c <= '9') x *= 10, x += (c - '0'), c = getchar();
  return x * tmp;
}
int n, a[25];
void init() {
  n = getint();
  for (int i = 1; i <= n; i++) a[i] = getint();
  std::sort(a + 1, a + n + 1);
}
bool tk[25];
bool solve() {
  if (a[n] != n) return false;
  for (int i = n; i >= 1; i--)
    if (a[i] > 1) {
      int nd = a[i] - 1, got = 0;
      for (int j = i - 1; j >= 1 && nd > 0; j--)
        if (!tk[j] && a[j] <= nd) {
          nd -= a[j];
          tk[j] = true;
          got++;
        }
      if (got <= 1) return false;
    }
  return true;
}
int main() {
  init();
  puts(solve() ? "YES" : "NO");
}

### 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 getint() {
  int x = 0, tmp = 1;
  char c = getchar();
  while ((c < '0' || c > '9') && c != '-') c = getchar();
  if (c == '-') c = getchar(), tmp = -1;
  while (c >= '0' && c <= '9') x *= 10, x += (c - '0'), c = getchar();
  return x * tmp;
}
int n, a[25];
void init() {
  n = getint();
  for (int i = 1; i <= n; i++) a[i] = getint();
  std::sort(a + 1, a + n + 1);
}
bool tk[25];
bool solve() {
  if (a[n] != n) return false;
  for (int i = n; i >= 1; i--)
    if (a[i] > 1) {
      int nd = a[i] - 1, got = 0;
      for (int j = i - 1; j >= 1 && nd > 0; j--)
        if (!tk[j] && a[j] <= nd) {
          nd -= a[j];
          tk[j] = true;
          got++;
        }
      if (got <= 1) return false;
    }
  return true;
}
int main() {
  init();
  puts(solve() ? "YES" : "NO");
}

```