#include <bits/stdc++.h>
using namespace std;
int n;
int d[30];
bool vis[2][30][1 << 12];
bool res[2][30][1 << 12];
vector<int> v;
bool forest(int ones, int s);
bool oneTree(int ones, int s) {
  if (s >= (1 << 12)) return false;
  if (s == 0) return ones == 1;
  if (vis[0][ones][s]) return res[0][ones][s];
  vis[0][ones][s] = true;
  int ct = 0;
  int mx = 0;
  int index = -1;
  for (int i = 0; i < 30; ++i) {
    if ((s >> i) & 1) {
      if (mx < v[i]) {
        mx = v[i];
        index = i;
      }
      ++ct;
    }
  }
  if (mx != ones + ct || ct >= ones) {
    res[0][ones][s] = false;
    return false;
  }
  s ^= 1 << index;
  for (int i = 1; i < ones; ++i) {
    int j = s;
    while (true) {
      j = s & (j - 1);
      if (oneTree(i, j) && forest(ones - i, s ^ j)) {
        res[0][ones][s | (1 << index)] = true;
        return true;
      }
      if (j == 0) break;
    }
  }
  res[0][ones][s | (1 << index)] = false;
  return false;
}
bool forest(int ones, int s) {
  if (s == 0) return ones != 0;
  if (vis[1][ones][s]) return res[1][ones][s];
  vis[1][ones][s] = true;
  if (oneTree(ones, s)) {
    res[1][ones][s] = true;
    return true;
  }
  for (int i = 1; i < ones; ++i) {
    int j = s;
    while (true) {
      j = s & (j - 1);
      if (oneTree(i, j) && forest(ones - i, s ^ j)) {
        res[1][ones][s] = true;
        return true;
      }
      if (j == 0) break;
    }
  }
  res[1][ones][s] = false;
  return false;
}
int main() {
  cin >> n;
  for (int i = 0; i < n; ++i) cin >> d[i];
  sort(d, d + n);
  reverse(d, d + n);
  for (int i = 0; i < n; ++i)
    if (d[i] != 1) v.push_back(d[i]);
  if (oneTree(n - v.size(), (1 << v.size()) - 1))
    puts("YES");
  else
    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;
int n;
int d[30];
bool vis[2][30][1 << 12];
bool res[2][30][1 << 12];
vector<int> v;
bool forest(int ones, int s);
bool oneTree(int ones, int s) {
  if (s >= (1 << 12)) return false;
  if (s == 0) return ones == 1;
  if (vis[0][ones][s]) return res[0][ones][s];
  vis[0][ones][s] = true;
  int ct = 0;
  int mx = 0;
  int index = -1;
  for (int i = 0; i < 30; ++i) {
    if ((s >> i) & 1) {
      if (mx < v[i]) {
        mx = v[i];
        index = i;
      }
      ++ct;
    }
  }
  if (mx != ones + ct || ct >= ones) {
    res[0][ones][s] = false;
    return false;
  }
  s ^= 1 << index;
  for (int i = 1; i < ones; ++i) {
    int j = s;
    while (true) {
      j = s & (j - 1);
      if (oneTree(i, j) && forest(ones - i, s ^ j)) {
        res[0][ones][s | (1 << index)] = true;
        return true;
      }
      if (j == 0) break;
    }
  }
  res[0][ones][s | (1 << index)] = false;
  return false;
}
bool forest(int ones, int s) {
  if (s == 0) return ones != 0;
  if (vis[1][ones][s]) return res[1][ones][s];
  vis[1][ones][s] = true;
  if (oneTree(ones, s)) {
    res[1][ones][s] = true;
    return true;
  }
  for (int i = 1; i < ones; ++i) {
    int j = s;
    while (true) {
      j = s & (j - 1);
      if (oneTree(i, j) && forest(ones - i, s ^ j)) {
        res[1][ones][s] = true;
        return true;
      }
      if (j == 0) break;
    }
  }
  res[1][ones][s] = false;
  return false;
}
int main() {
  cin >> n;
  for (int i = 0; i < n; ++i) cin >> d[i];
  sort(d, d + n);
  reverse(d, d + n);
  for (int i = 0; i < n; ++i)
    if (d[i] != 1) v.push_back(d[i]);
  if (oneTree(n - v.size(), (1 << v.size()) - 1))
    puts("YES");
  else
    puts("NO");
  return 0;
}

```