#include <bits/stdc++.h>
using namespace std;
const int maxn = 24;
const int inf = 2e9;
int main_c[maxn], c[maxn];
void solve(int ind) {
  if (c[ind] == 1) {
    cout << "YES\n";
    exit(0);
  }
  for (int i = 0; i < ind; i++) {
    if (c[i] > c[ind] and (c[i] != main_c[i] or c[ind] != c[i] - 1)) {
      c[i] -= c[ind];
      solve(ind + 1);
      c[i] += c[ind];
    }
  }
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0), cout.tie(0);
  int n;
  cin >> n;
  bool has2 = false;
  for (int i = 0; i < n; i++) {
    cin >> main_c[i];
    c[i] = main_c[i];
    if (c[i] == 2) has2 = true;
  }
  sort(c, c + n, greater<int>());
  if (c[0] != n or has2) return cout << "NO\n", 0;
  if (n == 1) return cout << "YES\n", 0;
  solve(1);
  cout << "NO\n";
}

### 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;
const int maxn = 24;
const int inf = 2e9;
int main_c[maxn], c[maxn];
void solve(int ind) {
  if (c[ind] == 1) {
    cout << "YES\n";
    exit(0);
  }
  for (int i = 0; i < ind; i++) {
    if (c[i] > c[ind] and (c[i] != main_c[i] or c[ind] != c[i] - 1)) {
      c[i] -= c[ind];
      solve(ind + 1);
      c[i] += c[ind];
    }
  }
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0), cout.tie(0);
  int n;
  cin >> n;
  bool has2 = false;
  for (int i = 0; i < n; i++) {
    cin >> main_c[i];
    c[i] = main_c[i];
    if (c[i] == 2) has2 = true;
  }
  sort(c, c + n, greater<int>());
  if (c[0] != n or has2) return cout << "NO\n", 0;
  if (n == 1) return cout << "YES\n", 0;
  solve(1);
  cout << "NO\n";
}

```