#include <bits/stdc++.h>
using namespace std;
int n;
int c[24];
bool used[24];
int clk;
void go(int here) {
  if (clock() - clk > 980) {
    printf("NO");
    exit(0);
  }
  if (here == n) {
    for (int i = 0; i < n - 1; i++) {
      if (!used[i]) return;
    }
    printf("YES");
    exit(0);
  }
  if (c[here] == 1) go(here + 1);
  int i, s, cnt;
  int p[24];
  memset(p, 0, sizeof(p));
  while (p[here] == 0) {
    s = cnt = 0;
    for (i = 0; i < here; i++) {
      if (p[i]) {
        s += c[i];
        if (s >= c[here]) break;
        cnt++;
      }
    }
    if (s + 1 == c[here] && cnt > 1) {
      for (i = 0; i < here; i++) {
        if (p[i]) {
          used[i] = true;
        }
      }
      go(here + 1);
      for (i = 0; i < here; i++) {
        if (p[i]) {
          used[i] = false;
        }
      }
    }
    p[0]++;
    for (i = 0; i < here; i++) {
      if (used[i]) {
        p[i + 1] += p[i];
        p[i] = 0;
      } else {
        if (p[i] < 2) break;
        p[i + 1] += 1;
        p[i] = 0;
      }
    }
  }
}
int main() {
  clk = clock();
  int i;
  scanf("%d", &n);
  for (i = 0; i < n; i++) {
    scanf("%d", &c[i]);
  }
  sort(c, c + n);
  go(0);
  printf("NO");
  return 0;
}

### 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;
int n;
int c[24];
bool used[24];
int clk;
void go(int here) {
  if (clock() - clk > 980) {
    printf("NO");
    exit(0);
  }
  if (here == n) {
    for (int i = 0; i < n - 1; i++) {
      if (!used[i]) return;
    }
    printf("YES");
    exit(0);
  }
  if (c[here] == 1) go(here + 1);
  int i, s, cnt;
  int p[24];
  memset(p, 0, sizeof(p));
  while (p[here] == 0) {
    s = cnt = 0;
    for (i = 0; i < here; i++) {
      if (p[i]) {
        s += c[i];
        if (s >= c[here]) break;
        cnt++;
      }
    }
    if (s + 1 == c[here] && cnt > 1) {
      for (i = 0; i < here; i++) {
        if (p[i]) {
          used[i] = true;
        }
      }
      go(here + 1);
      for (i = 0; i < here; i++) {
        if (p[i]) {
          used[i] = false;
        }
      }
    }
    p[0]++;
    for (i = 0; i < here; i++) {
      if (used[i]) {
        p[i + 1] += p[i];
        p[i] = 0;
      } else {
        if (p[i] < 2) break;
        p[i + 1] += 1;
        p[i] = 0;
      }
    }
  }
}
int main() {
  clk = clock();
  int i;
  scanf("%d", &n);
  for (i = 0; i < n; i++) {
    scanf("%d", &c[i]);
  }
  sort(c, c + n);
  go(0);
  printf("NO");
  return 0;
}

```