#include <bits/stdc++.h>
using namespace std;
const int maxn = 30;
int nums[maxn];
int c[maxn];
int table[maxn][maxn * maxn];
int n;
bool cmp(const int& a, const int& b) { return a > b; }
bool dfs(int st, int i) {
  if (i == n) {
    for (int j = 0; j < n; ++j)
      if (nums[j]) return false;
    return true;
  }
  int begin = st;
  if (nums[i] != nums[i - 1]) begin = 0;
  for (int j = begin; j < i; ++j)
    if (nums[j] >= c[i] && c[i] < c[j] - 1 &&
        ((i + 1 >= n) || table[i + 1][nums[j] - c[i]])) {
      nums[j] -= c[i];
      if (dfs(j, i + 1)) return true;
      nums[j] += c[i];
    }
  return false;
}
int main() {
  scanf("%d", &n);
  for (int i = 0; i < n; ++i) scanf("%d", c + i);
  sort(c, c + n, cmp);
  memset(table, 0, sizeof(table));
  table[n - 1][0] = 1;
  table[n - 1][c[n - 1]] = 1;
  for (int i = n - 2; i >= 0; --i)
    for (int j = 0; j < maxn * maxn; ++j) {
      if (j + c[i] < maxn * maxn) table[i][j + c[i]] += table[i + 1][j];
      table[i][j] += table[i + 1][j];
    }
  for (int i = 0; i < n; ++i) nums[i] = c[i] - 1;
  if ((n == 1 || table[1][nums[0]]) && dfs(1, 1))
    puts("YES");
  else
    puts("NO");
  return 0;
}

### Prompt

Please create a solution in CPP 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;
const int maxn = 30;
int nums[maxn];
int c[maxn];
int table[maxn][maxn * maxn];
int n;
bool cmp(const int& a, const int& b) { return a > b; }
bool dfs(int st, int i) {
  if (i == n) {
    for (int j = 0; j < n; ++j)
      if (nums[j]) return false;
    return true;
  }
  int begin = st;
  if (nums[i] != nums[i - 1]) begin = 0;
  for (int j = begin; j < i; ++j)
    if (nums[j] >= c[i] && c[i] < c[j] - 1 &&
        ((i + 1 >= n) || table[i + 1][nums[j] - c[i]])) {
      nums[j] -= c[i];
      if (dfs(j, i + 1)) return true;
      nums[j] += c[i];
    }
  return false;
}
int main() {
  scanf("%d", &n);
  for (int i = 0; i < n; ++i) scanf("%d", c + i);
  sort(c, c + n, cmp);
  memset(table, 0, sizeof(table));
  table[n - 1][0] = 1;
  table[n - 1][c[n - 1]] = 1;
  for (int i = n - 2; i >= 0; --i)
    for (int j = 0; j < maxn * maxn; ++j) {
      if (j + c[i] < maxn * maxn) table[i][j + c[i]] += table[i + 1][j];
      table[i][j] += table[i + 1][j];
    }
  for (int i = 0; i < n; ++i) nums[i] = c[i] - 1;
  if ((n == 1 || table[1][nums[0]]) && dfs(1, 1))
    puts("YES");
  else
    puts("NO");
  return 0;
}

```