#include <bits/stdc++.h>
using namespace std;
int n, c[25], m;
int sub[25], ch[25];
bool dfs(int cur, int n1) {
  if (cur == 0) {
    int rest = c[cur] - sub[cur];
    if (rest > n1 || ch[cur] + rest < 2) return 0;
    return 1;
  } else {
    int rest = c[cur] - sub[cur];
    if (rest > n1 || ch[cur] + rest < 2) return 0;
    n1 -= rest;
    for (int i = 0; i < (cur); i++)
      if (sub[i] + c[cur] <= c[i]) {
        sub[i] += c[cur];
        ch[i]++;
        if (dfs(cur - 1, n1) == 1) return 1;
        sub[i] -= c[cur];
        ch[i]--;
      }
    return 0;
  }
}
int main() {
  cin.tie(0);
  ios_base::sync_with_stdio(0);
  cin >> n;
  for (int i = 0; i < (n); i++) cin >> c[i];
  sort(c, c + n, greater<int>());
  m = 0;
  while (m < n && c[m] != 1) m++;
  if (c[0] != n || m + m + 1 > n) return cout << "NO" << endl, 0;
  if (n == 1) return cout << "YES" << endl, 0;
  for (int i = 0; i < (n); i++) sub[i] = 1;
  cout << (dfs(m - 1, n - m) ? "YES" : "NO") << endl;
}

### 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], m;
int sub[25], ch[25];
bool dfs(int cur, int n1) {
  if (cur == 0) {
    int rest = c[cur] - sub[cur];
    if (rest > n1 || ch[cur] + rest < 2) return 0;
    return 1;
  } else {
    int rest = c[cur] - sub[cur];
    if (rest > n1 || ch[cur] + rest < 2) return 0;
    n1 -= rest;
    for (int i = 0; i < (cur); i++)
      if (sub[i] + c[cur] <= c[i]) {
        sub[i] += c[cur];
        ch[i]++;
        if (dfs(cur - 1, n1) == 1) return 1;
        sub[i] -= c[cur];
        ch[i]--;
      }
    return 0;
  }
}
int main() {
  cin.tie(0);
  ios_base::sync_with_stdio(0);
  cin >> n;
  for (int i = 0; i < (n); i++) cin >> c[i];
  sort(c, c + n, greater<int>());
  m = 0;
  while (m < n && c[m] != 1) m++;
  if (c[0] != n || m + m + 1 > n) return cout << "NO" << endl, 0;
  if (n == 1) return cout << "YES" << endl, 0;
  for (int i = 0; i < (n); i++) sub[i] = 1;
  cout << (dfs(m - 1, n - m) ? "YES" : "NO") << endl;
}

```