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
#include <bits/stdc++.h>
using namespace std;
template <class T>
inline int size(const T& c) {
  return c.size();
}
using namespace std;
int fastMax(int x, int y) { return (((y - x) >> (32 - 1)) & (x ^ y)) ^ y; }
int fastMin(int x, int y) { return (((y - x) >> (32 - 1)) & (x ^ y)) ^ x; }
const int maxn = 30;
int a[maxn];
vector<int> c;
deque<int> q;
bool used[maxn];
int schild[maxn];
int n;
int cnt1;
bool ok;
void dfs(int vt) {
  if (vt == c.size()) {
    int sum = 0;
    for (int i = 0; i < vt; i++) {
      if (schild[c[i]] + a[c[i]] - 1 == 1) return;
      sum += (a[c[i]] - 1);
    }
    if (sum == cnt1) ok = true;
    return;
  }
  for (int i = 0; i < vt; i++) {
    int u = c[i];
    if (a[u] > a[c[vt]]) {
      a[u] -= a[c[vt]];
      schild[u]++;
      dfs(vt + 1);
      schild[u]--;
      if (ok) return;
      a[u] += a[c[vt]];
    }
  }
}
bool mycmp(int u, int v) { return a[u] > a[v]; }
int main() {
  scanf("%d", &n);
  cnt1 = 0;
  for (int i = 1; i <= n; i++) {
    scanf("%d", &a[i]);
    if (a[i] != 1)
      c.push_back(i);
    else
      cnt1++;
  }
  sort(c.begin(), c.end(), mycmp);
  if (n == 1) {
    if (a[1] == 1)
      cout << "YES";
    else
      cout << "NO";
  } else if (c.size() * 2 > n - 1) {
    cout << "NO";
    return 0;
  } else {
    ok = false;
    dfs(1);
    if (ok)
      cout << "YES";
    else
      cout << "NO";
  }
  fclose(stdin);
  fclose(stdout);
  return 0;
}
