#include <bits/stdc++.h>
using namespace std;
const int N = 30;
bool comp(int first, int second) { return (first > second); }
int f, first, second, n, i, a[N], b[N];
void dfs(int v) {
  f++;
  if (f > 10000000) {
    cout << "NO";
    exit(0);
  }
  if (n - v < max(first, second))
    return;
  else if (v == n) {
    cout << "YES" << endl;
    exit(0);
  }
  for (int i = 0; i < v; i++)
    if (a[v] < a[i]) {
      if (b[i] == 1) second--;
      b[i]++;
      if (b[i] == 1) second++;
      a[i] -= a[v];
      if (a[i] == 1) first--;
      dfs(v + 1);
      if (a[i] == 1) first++;
      if (b[i] == 1) second--;
      b[i]--;
      if (b[i] == 1) second++;
      a[i] += a[v];
    }
}
int main() {
  cin.tie(0);
  ios_base::sync_with_stdio(0);
  cin >> n;
  for (i = 0; i < n; i++) {
    cin >> a[i];
    first += (a[i] != 1);
  }
  sort(a, a + n, comp);
  dfs(1);
  cout << "NO";
}

### 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;
const int N = 30;
bool comp(int first, int second) { return (first > second); }
int f, first, second, n, i, a[N], b[N];
void dfs(int v) {
  f++;
  if (f > 10000000) {
    cout << "NO";
    exit(0);
  }
  if (n - v < max(first, second))
    return;
  else if (v == n) {
    cout << "YES" << endl;
    exit(0);
  }
  for (int i = 0; i < v; i++)
    if (a[v] < a[i]) {
      if (b[i] == 1) second--;
      b[i]++;
      if (b[i] == 1) second++;
      a[i] -= a[v];
      if (a[i] == 1) first--;
      dfs(v + 1);
      if (a[i] == 1) first++;
      if (b[i] == 1) second--;
      b[i]--;
      if (b[i] == 1) second++;
      a[i] += a[v];
    }
}
int main() {
  cin.tie(0);
  ios_base::sync_with_stdio(0);
  cin >> n;
  for (i = 0; i < n; i++) {
    cin >> a[i];
    first += (a[i] != 1);
  }
  sort(a, a + n, comp);
  dfs(1);
  cout << "NO";
}

```