#include <bits/stdc++.h>
using namespace std;
const int MAXN = 25;
int n;
int a[MAXN];
int l[MAXN];
int pos = 0;
int s[MAXN];
int u[MAXN];
void rek(int cnt) {
  if (cnt == n) {
    while (s[pos] == 1) ++pos;
    if (pos == n) {
      printf("YES\n");
      exit(0);
    }
    return;
  }
  for (int i = 0; i < s[pos]; ++i) {
    if (l[i] == 0) continue;
    --l[i];
    s[cnt] = i;
    int opos = pos;
    s[pos] -= i;
    ++u[pos];
    if (u[pos] == 1 && s[pos] == 1)
      ;
    else {
      while (s[pos] == 1) ++pos;
      rek(cnt + 1);
    }
    pos = opos;
    --u[pos];
    s[pos] += i;
    ++l[i];
  }
}
void solve() {
  sort(a, a + n);
  reverse(a, a + n);
  for (int i = 0; i < n; ++i) l[a[i]]++;
  l[a[0]]--;
  s[0] = a[0];
  rek(1);
}
int main(void) {
  scanf("%d", &n);
  for (int i = 0; i < n; ++i) scanf("%d", &a[i]);
  int cnt = 0;
  for (int i = 0; i < n; ++i) cnt += a[i] == 1;
  if ((cnt + 1) * 2 < n) {
    printf("NO\n");
    return 0;
  }
  solve();
  printf("NO\n");
  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;
const int MAXN = 25;
int n;
int a[MAXN];
int l[MAXN];
int pos = 0;
int s[MAXN];
int u[MAXN];
void rek(int cnt) {
  if (cnt == n) {
    while (s[pos] == 1) ++pos;
    if (pos == n) {
      printf("YES\n");
      exit(0);
    }
    return;
  }
  for (int i = 0; i < s[pos]; ++i) {
    if (l[i] == 0) continue;
    --l[i];
    s[cnt] = i;
    int opos = pos;
    s[pos] -= i;
    ++u[pos];
    if (u[pos] == 1 && s[pos] == 1)
      ;
    else {
      while (s[pos] == 1) ++pos;
      rek(cnt + 1);
    }
    pos = opos;
    --u[pos];
    s[pos] += i;
    ++l[i];
  }
}
void solve() {
  sort(a, a + n);
  reverse(a, a + n);
  for (int i = 0; i < n; ++i) l[a[i]]++;
  l[a[0]]--;
  s[0] = a[0];
  rek(1);
}
int main(void) {
  scanf("%d", &n);
  for (int i = 0; i < n; ++i) scanf("%d", &a[i]);
  int cnt = 0;
  for (int i = 0; i < n; ++i) cnt += a[i] == 1;
  if ((cnt + 1) * 2 < n) {
    printf("NO\n");
    return 0;
  }
  solve();
  printf("NO\n");
  return 0;
}

```