#include <bits/stdc++.h>
using namespace std;
const int inf = 1000000000;
const int MOD = 1000000007;
const double pi = acos(-1.0);
bool can;
int a[33], deg[33];
int g[33];
int n;
void go(int pos) {
  if (a[pos] == 1) {
    bool ok = true;
    int leaf = 0;
    for (int i = (pos + 1); i <= (n); ++i) {
      if (deg[i] + 1 == a[i] && g[i] == 1) ok = false;
      if (deg[i] >= a[i]) ok = false;
      if (a[i] - deg[i] - 1 == 1 && deg[i] == 0) ok = false;
      leaf += a[i] - deg[i] - 1;
    }
    if (ok && leaf == pos) can = true;
    return;
  }
  for (int fath = (pos + 1); fath <= (n); ++fath) {
    g[fath]++;
    deg[fath] += a[pos];
    if (deg[fath] < a[fath]) go(pos - 1);
    deg[fath] -= a[pos];
    g[fath]--;
  }
}
int main() {
  cin >> n;
  for (int i = (1); i <= (n); ++i) cin >> a[i];
  if (n == 1 && a[1] == 1) {
    cout << "YES" << endl;
    return 0;
  }
  sort(a + 1, a + n + 1);
  if (a[1] != 1) {
    cout << "NO" << endl;
    return 0;
  }
  can = false;
  go(n - 1);
  if (can)
    cout << "YES" << endl;
  else
    cout << "NO" << endl;
}

### Prompt

Please provide a cpp coded solution to the problem described below:

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 inf = 1000000000;
const int MOD = 1000000007;
const double pi = acos(-1.0);
bool can;
int a[33], deg[33];
int g[33];
int n;
void go(int pos) {
  if (a[pos] == 1) {
    bool ok = true;
    int leaf = 0;
    for (int i = (pos + 1); i <= (n); ++i) {
      if (deg[i] + 1 == a[i] && g[i] == 1) ok = false;
      if (deg[i] >= a[i]) ok = false;
      if (a[i] - deg[i] - 1 == 1 && deg[i] == 0) ok = false;
      leaf += a[i] - deg[i] - 1;
    }
    if (ok && leaf == pos) can = true;
    return;
  }
  for (int fath = (pos + 1); fath <= (n); ++fath) {
    g[fath]++;
    deg[fath] += a[pos];
    if (deg[fath] < a[fath]) go(pos - 1);
    deg[fath] -= a[pos];
    g[fath]--;
  }
}
int main() {
  cin >> n;
  for (int i = (1); i <= (n); ++i) cin >> a[i];
  if (n == 1 && a[1] == 1) {
    cout << "YES" << endl;
    return 0;
  }
  sort(a + 1, a + n + 1);
  if (a[1] != 1) {
    cout << "NO" << endl;
    return 0;
  }
  can = false;
  go(n - 1);
  if (can)
    cout << "YES" << endl;
  else
    cout << "NO" << endl;
}

```