#include <bits/stdc++.h>
using namespace std;
const int N_ = 25;
int N, C[N_], T[N_];
void QUIT(bool r) {
  puts(r ? "YES" : "NO");
  exit(0);
}
bool solve(int);
bool solve2(int s1, int s2, vector<int>& a, int c) {
  if (s1 == 0) {
    if (c < 2) return false;
    for (int i = 0; i < c; i++)
      if (!solve(a[i])) return false;
    return true;
  }
  if (s1 < s2) s2 = s1;
  for (int x = s2; x >= 1; x--)
    if (T[x] > 0) {
      --T[x];
      a[c] = x;
      if (solve2(s1 - x, x, a, c + 1)) return true;
      ++T[x];
      a[c] = 0;
    }
  return false;
}
bool solve(int sz) {
  if (sz == 1) return true;
  if (sz == 2) return false;
  vector<int> a(N + 2);
  return solve2(sz - 1, sz - 2, a, 0);
}
int main() {
  scanf("%d", &N);
  for (int i = 0; i < N; i++) scanf("%d", C + i), ++T[C[i]];
  if (T[N] != 1) QUIT(0);
  --T[N];
  QUIT(solve(N));
  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;
const int N_ = 25;
int N, C[N_], T[N_];
void QUIT(bool r) {
  puts(r ? "YES" : "NO");
  exit(0);
}
bool solve(int);
bool solve2(int s1, int s2, vector<int>& a, int c) {
  if (s1 == 0) {
    if (c < 2) return false;
    for (int i = 0; i < c; i++)
      if (!solve(a[i])) return false;
    return true;
  }
  if (s1 < s2) s2 = s1;
  for (int x = s2; x >= 1; x--)
    if (T[x] > 0) {
      --T[x];
      a[c] = x;
      if (solve2(s1 - x, x, a, c + 1)) return true;
      ++T[x];
      a[c] = 0;
    }
  return false;
}
bool solve(int sz) {
  if (sz == 1) return true;
  if (sz == 2) return false;
  vector<int> a(N + 2);
  return solve2(sz - 1, sz - 2, a, 0);
}
int main() {
  scanf("%d", &N);
  for (int i = 0; i < N; i++) scanf("%d", C + i), ++T[C[i]];
  if (T[N] != 1) QUIT(0);
  --T[N];
  QUIT(solve(N));
  return 0;
}

```