#include <bits/stdc++.h>
using namespace std;
int lf;
int a[24];
int n;
vector<int> A[24];
int dfs(int v = 0) {
  int cnt = 1;
  int ans = 0;
  for (int u : A[v]) {
    int x = dfs(u);
    if (x == -1) return -1;
    ans += x;
    cnt += a[u];
  }
  if (cnt > a[v]) return -1;
  if (a[v] == 2) return -1;
  if (cnt == a[v] && A[v].size() == 1) return -1;
  return ans + a[v] - cnt;
}
bool solve(int i = 1) {
  if (i == n) return dfs() == lf;
  for (int j = (0); j < (i); ++j) {
    A[j].push_back(i);
    if (solve(i + 1)) return 1;
    A[j].pop_back();
  }
  return 0;
}
int main() {
  ios::sync_with_stdio(false), cin.tie(0);
  ;
  cin >> n;
  for (int i = (0); i < (n); ++i) cin >> a[i], lf += a[i] == 1;
  if (lf * 2 < n + 1) exit((cout << ("NO") << '\n', 0));
  sort(a, a + n);
  reverse(a, a + n);
  while (n && a[n - 1] == 1) --n;
  if (n == 0) exit((cout << (((lf == 1) ? "YES" : "NO")) << '\n', 0));
  cout << ((solve()) ? "YES" : "NO") << '\n';
}

### Prompt

Your task is to create 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>
using namespace std;
int lf;
int a[24];
int n;
vector<int> A[24];
int dfs(int v = 0) {
  int cnt = 1;
  int ans = 0;
  for (int u : A[v]) {
    int x = dfs(u);
    if (x == -1) return -1;
    ans += x;
    cnt += a[u];
  }
  if (cnt > a[v]) return -1;
  if (a[v] == 2) return -1;
  if (cnt == a[v] && A[v].size() == 1) return -1;
  return ans + a[v] - cnt;
}
bool solve(int i = 1) {
  if (i == n) return dfs() == lf;
  for (int j = (0); j < (i); ++j) {
    A[j].push_back(i);
    if (solve(i + 1)) return 1;
    A[j].pop_back();
  }
  return 0;
}
int main() {
  ios::sync_with_stdio(false), cin.tie(0);
  ;
  cin >> n;
  for (int i = (0); i < (n); ++i) cin >> a[i], lf += a[i] == 1;
  if (lf * 2 < n + 1) exit((cout << ("NO") << '\n', 0));
  sort(a, a + n);
  reverse(a, a + n);
  while (n && a[n - 1] == 1) --n;
  if (n == 0) exit((cout << (((lf == 1) ? "YES" : "NO")) << '\n', 0));
  cout << ((solve()) ? "YES" : "NO") << '\n';
}

```