#include <bits/stdc++.h>
using namespace std;
int n;
int a[26];
int b[26];
bool ok;
inline void go(int v, int rem, int cur, int last) {
  if (v == n) {
    ok = 1;
    for (int i = 1; i <= n && ok; ++i)
      if (b[i]) ok = 0;
    if (ok) {
      puts("YES");
      exit(0);
    }
  }
  if (rem == 1) {
    if (cur == 1) return;
    if (v + 1 != n) ++b[a[v]];
    go(v + 1, a[v + 1], 0, n);
    if (v + 1 != n) --b[a[v]];
    return;
  }
  if (!cur) {
    for (int i = rem - 2; i >= 1; --i) {
      if (!b[i]) continue;
      --b[i];
      go(v, rem - i, cur + 1, i);
      ++b[i];
    }
  } else {
    for (int i = min(rem - 1, last); i >= 1; --i) {
      if (!b[i]) continue;
      --b[i];
      go(v, rem - i, cur + 1, i);
      ++b[i];
    }
  }
}
int main() {
  scanf("%d", &n);
  for (int i = 0; i < n; ++i) scanf("%d", &a[i]);
  sort(a, a + n);
  ok = 1;
  for (int i = 0; i < n; ++i)
    if (a[i] == 2) ok = 0;
  if (a[n - 1] != n || !ok) {
    puts("NO");
    return 0;
  }
  go(0, a[0], 0, n);
  puts("NO");
  return 0;
}

### Prompt

Construct a Cpp code solution to the problem outlined:

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;
int n;
int a[26];
int b[26];
bool ok;
inline void go(int v, int rem, int cur, int last) {
  if (v == n) {
    ok = 1;
    for (int i = 1; i <= n && ok; ++i)
      if (b[i]) ok = 0;
    if (ok) {
      puts("YES");
      exit(0);
    }
  }
  if (rem == 1) {
    if (cur == 1) return;
    if (v + 1 != n) ++b[a[v]];
    go(v + 1, a[v + 1], 0, n);
    if (v + 1 != n) --b[a[v]];
    return;
  }
  if (!cur) {
    for (int i = rem - 2; i >= 1; --i) {
      if (!b[i]) continue;
      --b[i];
      go(v, rem - i, cur + 1, i);
      ++b[i];
    }
  } else {
    for (int i = min(rem - 1, last); i >= 1; --i) {
      if (!b[i]) continue;
      --b[i];
      go(v, rem - i, cur + 1, i);
      ++b[i];
    }
  }
}
int main() {
  scanf("%d", &n);
  for (int i = 0; i < n; ++i) scanf("%d", &a[i]);
  sort(a, a + n);
  ok = 1;
  for (int i = 0; i < n; ++i)
    if (a[i] == 2) ok = 0;
  if (a[n - 1] != n || !ok) {
    puts("NO");
    return 0;
  }
  go(0, a[0], 0, n);
  puts("NO");
  return 0;
}

```