#include <bits/stdc++.h>
using namespace std;
const int N = 30;
int n;
int cnt[N];
int old_cnt[N];
int old_deg[N];
int deg[N];
void rec(int ind) {
  if (ind == n || cnt[ind] == 1) {
    for (int i = 0; i < ind; i++) {
      old_cnt[i] = cnt[i];
      old_deg[i] = deg[i];
    }
    int ones = n - ind;
    bool xuy = false;
    for (int i = 0; i < ind; i++) {
      while (ones > 0 && cnt[i] > 1) {
        ones--;
        cnt[i]--;
        deg[i]++;
      }
      if (deg[i] < 2 || cnt[i] != 1) xuy = true;
    }
    if (ones != 0) xuy = true;
    for (int i = 0; i < ind; i++) {
      cnt[i] = old_cnt[i];
      deg[i] = old_deg[i];
    }
    if (!xuy) {
      puts("YES");
      exit(0);
    }
    return;
  }
  for (int i = 0; i < ind; i++) {
    cnt[i] -= cnt[ind];
    deg[i]++;
    if (cnt[i] >= 1) rec(ind + 1);
    deg[i]--;
    cnt[i] += cnt[ind];
  }
}
int main() {
  scanf("%d", &n);
  for (int i = 0; i < n; i++) scanf("%d", &cnt[i]);
  sort(cnt, cnt + n, greater<int>());
  if (n == 1) {
    puts("YES");
    return 0;
  }
  rec(1);
  puts("NO");
  return 0;
}

### Prompt

Create a solution in CPP for 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;
int n;
int cnt[N];
int old_cnt[N];
int old_deg[N];
int deg[N];
void rec(int ind) {
  if (ind == n || cnt[ind] == 1) {
    for (int i = 0; i < ind; i++) {
      old_cnt[i] = cnt[i];
      old_deg[i] = deg[i];
    }
    int ones = n - ind;
    bool xuy = false;
    for (int i = 0; i < ind; i++) {
      while (ones > 0 && cnt[i] > 1) {
        ones--;
        cnt[i]--;
        deg[i]++;
      }
      if (deg[i] < 2 || cnt[i] != 1) xuy = true;
    }
    if (ones != 0) xuy = true;
    for (int i = 0; i < ind; i++) {
      cnt[i] = old_cnt[i];
      deg[i] = old_deg[i];
    }
    if (!xuy) {
      puts("YES");
      exit(0);
    }
    return;
  }
  for (int i = 0; i < ind; i++) {
    cnt[i] -= cnt[ind];
    deg[i]++;
    if (cnt[i] >= 1) rec(ind + 1);
    deg[i]--;
    cnt[i] += cnt[ind];
  }
}
int main() {
  scanf("%d", &n);
  for (int i = 0; i < n; i++) scanf("%d", &cnt[i]);
  sort(cnt, cnt + n, greater<int>());
  if (n == 1) {
    puts("YES");
    return 0;
  }
  rec(1);
  puts("NO");
  return 0;
}

```