#include <bits/stdc++.h>
const int INF_INT = 0x3f3f3f3f;
const long long INF_LL = 0x7f7f7f7f;
const int MOD = 1e9 + 7;
const double eps = 1e-10;
const double pi = acos(-1);
using namespace std;
int n;
int a[30];
int vis[30];
bool dfs(int root, int cnt, int son) {
  if (root == n + 1) return true;
  if (cnt + 1 == a[root]) {
    if (son != 1 && dfs(root + 1, 0, 0)) return true;
    return false;
  }
  int same = 0;
  for (int i = 1; i <= n; i++) {
    if (!vis[i] && cnt + a[i] < a[root] && a[i] != same) {
      same = a[i];
      vis[i] = 1;
      if (dfs(root, cnt + a[i], son + 1)) return true;
      vis[i] = 0;
    }
  }
  return false;
}
int main(int argc, char const *argv[]) {
  scanf("%d", &n);
  for (int i = 1; i <= n; i++) scanf("%d", &a[i]);
  sort(a + 1, a + 1 + n);
  memset(vis, 0, sizeof(vis));
  if (a[n] != n)
    puts("NO");
  else {
    if (dfs(1, 0, 0))
      puts("YES");
    else
      puts("NO");
  }
  return 0;
}

### 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>
const int INF_INT = 0x3f3f3f3f;
const long long INF_LL = 0x7f7f7f7f;
const int MOD = 1e9 + 7;
const double eps = 1e-10;
const double pi = acos(-1);
using namespace std;
int n;
int a[30];
int vis[30];
bool dfs(int root, int cnt, int son) {
  if (root == n + 1) return true;
  if (cnt + 1 == a[root]) {
    if (son != 1 && dfs(root + 1, 0, 0)) return true;
    return false;
  }
  int same = 0;
  for (int i = 1; i <= n; i++) {
    if (!vis[i] && cnt + a[i] < a[root] && a[i] != same) {
      same = a[i];
      vis[i] = 1;
      if (dfs(root, cnt + a[i], son + 1)) return true;
      vis[i] = 0;
    }
  }
  return false;
}
int main(int argc, char const *argv[]) {
  scanf("%d", &n);
  for (int i = 1; i <= n; i++) scanf("%d", &a[i]);
  sort(a + 1, a + 1 + n);
  memset(vis, 0, sizeof(vis));
  if (a[n] != n)
    puts("NO");
  else {
    if (dfs(1, 0, 0))
      puts("YES");
    else
      puts("NO");
  }
  return 0;
}

```