#include <bits/stdc++.h>
using namespace std;
int n, a[24];
int p[24], sz[24], c[24], ch[255];
bool check(int sum, int pos) { return ch[sum] >= pos; }
void check_init() {
  for (int i = n - 1; i > 0; --i) {
    for (int j = n; j >= 0; --j) {
      if (ch[j] != 0 && ch[j + a[i]] == 0) ch[j + a[i]] = i;
    }
    if (ch[a[i]] == 0) ch[a[i]] = i;
  }
  ch[0] = n;
}
void rec(int x) {
  if (x == n) {
    for (int i = 0; i < n; ++i) {
      if (sz[i] != 1 || c[i] == 1) return;
    }
    cout << "YES";
    exit(0);
  }
  for (int i = 0; i < x; ++i) {
    if (sz[i] <= a[x]) continue;
    if (!check(sz[i] - a[x] - 1, x + 1)) continue;
    if (a[i] - a[x] == 1) continue;
    p[x] = i;
    sz[i] -= a[x];
    ++c[i];
    rec(x + 1);
    p[x] = 0;
    sz[i] += a[x];
    --c[i];
  }
}
int main() {
  cin >> n;
  for (int i = 0; i < n; ++i) {
    cin >> a[i];
    if (a[i] == 2) {
      cout << "NO";
      exit(0);
    }
  }
  sort(a, a + n, greater<int>());
  for (int i = 0; i < n; ++i) sz[i] = a[i];
  check_init();
  rec(1);
  cout << "NO";
  return 0;
}

### Prompt

Your task is to create 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, a[24];
int p[24], sz[24], c[24], ch[255];
bool check(int sum, int pos) { return ch[sum] >= pos; }
void check_init() {
  for (int i = n - 1; i > 0; --i) {
    for (int j = n; j >= 0; --j) {
      if (ch[j] != 0 && ch[j + a[i]] == 0) ch[j + a[i]] = i;
    }
    if (ch[a[i]] == 0) ch[a[i]] = i;
  }
  ch[0] = n;
}
void rec(int x) {
  if (x == n) {
    for (int i = 0; i < n; ++i) {
      if (sz[i] != 1 || c[i] == 1) return;
    }
    cout << "YES";
    exit(0);
  }
  for (int i = 0; i < x; ++i) {
    if (sz[i] <= a[x]) continue;
    if (!check(sz[i] - a[x] - 1, x + 1)) continue;
    if (a[i] - a[x] == 1) continue;
    p[x] = i;
    sz[i] -= a[x];
    ++c[i];
    rec(x + 1);
    p[x] = 0;
    sz[i] += a[x];
    --c[i];
  }
}
int main() {
  cin >> n;
  for (int i = 0; i < n; ++i) {
    cin >> a[i];
    if (a[i] == 2) {
      cout << "NO";
      exit(0);
    }
  }
  sort(a, a + n, greater<int>());
  for (int i = 0; i < n; ++i) sz[i] = a[i];
  check_init();
  rec(1);
  cout << "NO";
  return 0;
}

```