#include <bits/stdc++.h>
using namespace std;
const int P = 1e9 + 7;
long long gcd(long long a, long long b) { return b ? gcd(b, a % b) : a; }
long long qpow(long long a, long long n) {
  long long r = 1 % P;
  for (a %= P; n; a = a * a % P, n >>= 1)
    if (n & 1) r = r * a % P;
  return r;
}
long long inv(long long x) { return x <= 1 ? 1 : inv(P % x) * (P - P / x) % P; }
const int N = 2e5 + 10;
int a[N], b[N], f[N], n, m, k;
bool dfs(int cur, int sum, int cnt) {
  if (cur > n) return 1;
  if (sum + 1 == a[cur]) {
    return cnt != 1 && dfs(cur + 1, 0, 0);
  }
  int lst = -1;
  for (int i = 1; i <= n; ++i) {
    if (!f[i] && a[i] != lst && sum + a[i] < a[cur]) {
      f[i] = 1, lst = a[i];
      if (dfs(cur, sum + a[i], cnt + 1)) return 1;
      f[i] = 0;
    }
  }
  return 0;
}
int main() {
  scanf("%d", &n);
  for (int i = 1; i <= n; ++i) scanf("%d", a + i);
  sort(a + 1, a + 1 + n);
  puts(a[n] == n && dfs(1, 0, 0) ? "YES" : "NO");
}

### Prompt

In CPP, your task is to solve 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 P = 1e9 + 7;
long long gcd(long long a, long long b) { return b ? gcd(b, a % b) : a; }
long long qpow(long long a, long long n) {
  long long r = 1 % P;
  for (a %= P; n; a = a * a % P, n >>= 1)
    if (n & 1) r = r * a % P;
  return r;
}
long long inv(long long x) { return x <= 1 ? 1 : inv(P % x) * (P - P / x) % P; }
const int N = 2e5 + 10;
int a[N], b[N], f[N], n, m, k;
bool dfs(int cur, int sum, int cnt) {
  if (cur > n) return 1;
  if (sum + 1 == a[cur]) {
    return cnt != 1 && dfs(cur + 1, 0, 0);
  }
  int lst = -1;
  for (int i = 1; i <= n; ++i) {
    if (!f[i] && a[i] != lst && sum + a[i] < a[cur]) {
      f[i] = 1, lst = a[i];
      if (dfs(cur, sum + a[i], cnt + 1)) return 1;
      f[i] = 0;
    }
  }
  return 0;
}
int main() {
  scanf("%d", &n);
  for (int i = 1; i <= n; ++i) scanf("%d", a + i);
  sort(a + 1, a + 1 + n);
  puts(a[n] == n && dfs(1, 0, 0) ? "YES" : "NO");
}

```