#include <bits/stdc++.h>
using namespace std;
inline void checkmin(int& a, int b) {
  if (a > b) a = b;
}
inline void checkmax(int& a, int b) {
  if (a < b) a = b;
}
const int inf = ~0U >> 1;
const int N = 30;
int n, c[N], child[N];
bool gao(int v, int p) {
  if (v == n) {
    for (int i = 0; i < n; ++i)
      if (c[i] > 1 || child[i] == 1) return 0;
    return 1;
  }
  if (p >= 0) {
    child[p]++;
    c[p] -= c[v];
  }
  for (int i = 0; i <= v; i++) {
    if (c[i] > c[v + 1] && gao(v + 1, i)) return 1;
  }
  if (p >= 0) {
    child[p]--;
    c[p] += c[v];
  }
  return 0;
}
int main() {
  if (0) freopen("c:\\data.txt", "r", stdin);
  cin >> n;
  for (int i = 0; i < n; ++i) cin >> c[i];
  sort(c, c + n, greater<int>());
  if (c[0] != n) {
    cout << "NO" << endl;
  } else {
    for (int i = 0; i < n; i++)
      if (c[i] == 2) {
        cout << "NO\n" << endl;
        return 0;
      }
    if (gao(0, -1))
      cout << "YES" << endl;
    else
      cout << "NO" << endl;
  }
}

### Prompt

In Cpp, your task is to solve 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;
inline void checkmin(int& a, int b) {
  if (a > b) a = b;
}
inline void checkmax(int& a, int b) {
  if (a < b) a = b;
}
const int inf = ~0U >> 1;
const int N = 30;
int n, c[N], child[N];
bool gao(int v, int p) {
  if (v == n) {
    for (int i = 0; i < n; ++i)
      if (c[i] > 1 || child[i] == 1) return 0;
    return 1;
  }
  if (p >= 0) {
    child[p]++;
    c[p] -= c[v];
  }
  for (int i = 0; i <= v; i++) {
    if (c[i] > c[v + 1] && gao(v + 1, i)) return 1;
  }
  if (p >= 0) {
    child[p]--;
    c[p] += c[v];
  }
  return 0;
}
int main() {
  if (0) freopen("c:\\data.txt", "r", stdin);
  cin >> n;
  for (int i = 0; i < n; ++i) cin >> c[i];
  sort(c, c + n, greater<int>());
  if (c[0] != n) {
    cout << "NO" << endl;
  } else {
    for (int i = 0; i < n; i++)
      if (c[i] == 2) {
        cout << "NO\n" << endl;
        return 0;
      }
    if (gao(0, -1))
      cout << "YES" << endl;
    else
      cout << "NO" << endl;
  }
}

```