#include <bits/stdc++.h>
using namespace std;
int a[55];
time_t st;
int n;
int d[55];
int e[55];
bool cmp(int a, int b) { return (a > b); }
void rec(int x) {
  if ((clock() - st) / (double)CLOCKS_PER_SEC > 0.9) {
    puts("NO");
    exit(0);
  }
  if (d[x] != 1) return;
  if (e[x] == 1) return;
  if (x == 0) {
    puts("YES");
    exit(0);
  }
  for (int i = x - 1; i >= 0; --i) {
    if (d[i] > a[x]) {
      d[i] -= a[x];
      e[i]--;
      if (d[i] == 0 && e[i] > 0) {
        d[i] += a[x];
        e[i]++;
        continue;
      }
      rec(x - 1);
      d[i] += a[x];
      e[i]++;
    } else
      continue;
  }
}
int main() {
  st = clock();
  scanf("%d", &n);
  for (int i = 0; i < n; ++i) scanf("%d", &a[i]);
  sort(a, a + n, cmp);
  for (int i = 0; i < n; ++i) {
    d[i] = a[i];
    e[i] = 2;
  }
  if (a[0] != n) {
    cout << "NO" << endl;
    return 0;
  }
  rec(n - 1);
  cout << "NO" << endl;
  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>
using namespace std;
int a[55];
time_t st;
int n;
int d[55];
int e[55];
bool cmp(int a, int b) { return (a > b); }
void rec(int x) {
  if ((clock() - st) / (double)CLOCKS_PER_SEC > 0.9) {
    puts("NO");
    exit(0);
  }
  if (d[x] != 1) return;
  if (e[x] == 1) return;
  if (x == 0) {
    puts("YES");
    exit(0);
  }
  for (int i = x - 1; i >= 0; --i) {
    if (d[i] > a[x]) {
      d[i] -= a[x];
      e[i]--;
      if (d[i] == 0 && e[i] > 0) {
        d[i] += a[x];
        e[i]++;
        continue;
      }
      rec(x - 1);
      d[i] += a[x];
      e[i]++;
    } else
      continue;
  }
}
int main() {
  st = clock();
  scanf("%d", &n);
  for (int i = 0; i < n; ++i) scanf("%d", &a[i]);
  sort(a, a + n, cmp);
  for (int i = 0; i < n; ++i) {
    d[i] = a[i];
    e[i] = 2;
  }
  if (a[0] != n) {
    cout << "NO" << endl;
    return 0;
  }
  rec(n - 1);
  cout << "NO" << endl;
  return 0;
}

```