#include <bits/stdc++.h>
using namespace std;
int n, a[24];
bool ans;
void dfs(const vector<pair<int, int> >& s, int i);
int get_sum(const vector<pair<int, int> >& a) {
  int sum = 0;
  for (pair<int, int> i : a) {
    sum += i.second;
  }
  return sum;
}
void insert(vector<pair<int, int> >& a, int i, int j) {
  for (pair<int, int>& x : a) {
    if (x.first == i) {
      x.second += j;
      if (x.second == 0) {
        a.erase(find(a.begin(), a.end(), pair<int, int>(i, 0)));
      }
      return;
    }
  }
  a.push_back(pair<int, int>(i, j));
}
void dfs2(const vector<pair<int, int> >& s, vector<pair<int, int> >& t, int sum,
          int i, int i_out) {
  if (i == (int)s.size()) {
    if (sum == 0 && get_sum(s) > get_sum(t)) {
      dfs(t, i_out + 1);
    }
    return;
  }
  for (int rep = 0; rep <= s[i].second && rep * s[i].first <= sum; ++rep) {
    insert(t, s[i].first, s[i].second - rep);
    dfs2(s, t, sum - rep * s[i].first, i + 1, i_out);
    if (ans) {
      return;
    }
    insert(t, s[i].first, -(s[i].second - rep));
  }
}
void dfs(const vector<pair<int, int> >& s, int i) {
  if (i == n) {
    if (get_sum(s) == 1) {
      ans = true;
    }
    return;
  }
  vector<pair<int, int> > t(1, pair<int, int>(a[i], 1));
  dfs2(s, t, a[i] - 1, 0, i);
}
int main(void) {
  scanf("%d", &n);
  bool flag = false;
  for (int i = 0; i < n; ++i) {
    scanf("%d", a + i);
    if (a[i] == n) {
      if (flag == false) {
        flag = true;
      } else {
        puts("NO");
        return 0;
      }
    }
  }
  if (!flag) {
    puts("NO");
    return 0;
  }
  sort(a, a + n);
  int i;
  for (i = 0; i < n; ++i) {
    if (a[i] != 1) {
      break;
    }
  }
  vector<pair<int, int> > s(1, pair<int, int>(1, i));
  dfs(s, i);
  puts(ans ? "YES" : "NO");
  return 0;
}

### Prompt

Your task is to create a Cpp solution 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;
int n, a[24];
bool ans;
void dfs(const vector<pair<int, int> >& s, int i);
int get_sum(const vector<pair<int, int> >& a) {
  int sum = 0;
  for (pair<int, int> i : a) {
    sum += i.second;
  }
  return sum;
}
void insert(vector<pair<int, int> >& a, int i, int j) {
  for (pair<int, int>& x : a) {
    if (x.first == i) {
      x.second += j;
      if (x.second == 0) {
        a.erase(find(a.begin(), a.end(), pair<int, int>(i, 0)));
      }
      return;
    }
  }
  a.push_back(pair<int, int>(i, j));
}
void dfs2(const vector<pair<int, int> >& s, vector<pair<int, int> >& t, int sum,
          int i, int i_out) {
  if (i == (int)s.size()) {
    if (sum == 0 && get_sum(s) > get_sum(t)) {
      dfs(t, i_out + 1);
    }
    return;
  }
  for (int rep = 0; rep <= s[i].second && rep * s[i].first <= sum; ++rep) {
    insert(t, s[i].first, s[i].second - rep);
    dfs2(s, t, sum - rep * s[i].first, i + 1, i_out);
    if (ans) {
      return;
    }
    insert(t, s[i].first, -(s[i].second - rep));
  }
}
void dfs(const vector<pair<int, int> >& s, int i) {
  if (i == n) {
    if (get_sum(s) == 1) {
      ans = true;
    }
    return;
  }
  vector<pair<int, int> > t(1, pair<int, int>(a[i], 1));
  dfs2(s, t, a[i] - 1, 0, i);
}
int main(void) {
  scanf("%d", &n);
  bool flag = false;
  for (int i = 0; i < n; ++i) {
    scanf("%d", a + i);
    if (a[i] == n) {
      if (flag == false) {
        flag = true;
      } else {
        puts("NO");
        return 0;
      }
    }
  }
  if (!flag) {
    puts("NO");
    return 0;
  }
  sort(a, a + n);
  int i;
  for (i = 0; i < n; ++i) {
    if (a[i] != 1) {
      break;
    }
  }
  vector<pair<int, int> > s(1, pair<int, int>(1, i));
  dfs(s, i);
  puts(ans ? "YES" : "NO");
  return 0;
}

```