There are N cats. We number them from 1 through N.

Each of the cats wears a hat. Cat i says: "there are exactly a_i different colors among the N - 1 hats worn by the cats except me."

Determine whether there exists a sequence of colors of the hats that is consistent with the remarks of the cats.

Constraints

* 2 ≤ N ≤ 10^5
* 1 ≤ a_i ≤ N-1

Input

Input is given from Standard Input in the following format:


N
a_1 a_2 ... a_N


Output

Print `Yes` if there exists a sequence of colors of the hats that is consistent with the remarks of the cats; print `No` otherwise.

Examples

Input

3
1 2 2


Output

Yes


Input

3
1 1 2


Output

No


Input

5
4 3 4 3 4


Output

No


Input

3
2 2 2


Output

Yes


Input

4
2 2 2 2


Output

Yes


Input

5
3 3 3 3 3


Output

No
#include <bits/stdc++.h>
using namespace std;
void err() {
  cout << "No" << endl;
  exit(0);
}
void yes() {
  cout << "Yes" << endl;
  exit(0);
}
int main() {
  int n;
  cin >> n;
  map<int, int> mp;
  for (int i = 0; i < n; i++) {
    int t;
    cin >> t;
    mp[t]++;
  }
  int sz = mp.size();
  if (sz >= 3) err();
  int k = mp.rbegin()->first;
  if (k == n - 1 && sz == 1) yes();
  int one = 0;
  if (sz == 2) {
    if (next(mp.rbegin())->first != k - 1) err();
    one = next(mp.rbegin())->second;
  }
  int many = n - one;
  k -= one;
  if (k <= 0 || many / 2 < k) err();
  yes();
  return 0;
}