#include <bits/stdc++.h>
const int N = 24;
int n, c[N], size[N], cnt[N];
bool Solve(int cur, int rem) {
  if (cur == n - 1) return cnt[cur] + rem > 1 && size[cur] + rem + 1 == c[cur];
  int temp = c[cur] - 1 - size[cur];
  if ((rem -= temp) < 0 || temp + cnt[cur] < 2) return false;
  for (int fa = cur + 1; fa < n; ++fa) {
    if (size[fa] + c[cur] < c[fa]) {
      size[fa] += c[cur];
      ++cnt[fa];
      if (Solve(cur + 1, rem)) return true;
      --cnt[fa];
      size[fa] -= c[cur];
    }
  }
  return false;
}
int main() {
  scanf("%d", &n);
  for (int i = 0; i < n; ++i) scanf("%d", c + i);
  std::sort(c, c + n);
  int cnt = std::count_if(c, c + n, std::bind1st(std::equal_to<int>(), 1));
  if (cnt == 1 && n == 1) {
    puts("YES");
  } else if (cnt < (n + 1) / 2) {
    puts("NO");
  } else {
    n = std::remove_if(c, c + n, std::bind1st(std::equal_to<int>(), 1)) - c;
    puts(Solve(0, cnt) ? "YES" : "NO");
  }
  return 0;
}

### Prompt

Please formulate 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>
const int N = 24;
int n, c[N], size[N], cnt[N];
bool Solve(int cur, int rem) {
  if (cur == n - 1) return cnt[cur] + rem > 1 && size[cur] + rem + 1 == c[cur];
  int temp = c[cur] - 1 - size[cur];
  if ((rem -= temp) < 0 || temp + cnt[cur] < 2) return false;
  for (int fa = cur + 1; fa < n; ++fa) {
    if (size[fa] + c[cur] < c[fa]) {
      size[fa] += c[cur];
      ++cnt[fa];
      if (Solve(cur + 1, rem)) return true;
      --cnt[fa];
      size[fa] -= c[cur];
    }
  }
  return false;
}
int main() {
  scanf("%d", &n);
  for (int i = 0; i < n; ++i) scanf("%d", c + i);
  std::sort(c, c + n);
  int cnt = std::count_if(c, c + n, std::bind1st(std::equal_to<int>(), 1));
  if (cnt == 1 && n == 1) {
    puts("YES");
  } else if (cnt < (n + 1) / 2) {
    puts("NO");
  } else {
    n = std::remove_if(c, c + n, std::bind1st(std::equal_to<int>(), 1)) - c;
    puts(Solve(0, cnt) ? "YES" : "NO");
  }
  return 0;
}

```