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 <iostream>
#include <algorithm>
#define REP(i, a, n) for(int i = ((int) a); i < ((int) n); i++)
using namespace std;

int N, A[100000];

int main(void) {
  cin >> N;
  REP(i, 0, N) cin >> A[i];

  sort(A, A + N);

  if(A[N - 1] - A[0] > 1) {
    cout << "No" << endl;
    return 0;
  }

  int k;
  for(k = 0; k < N; k++) if(A[0] != A[k]) break;
  if(k < N) {
    cout << (1 <= A[N - 1] - k && A[N - 1] - k <= (N - k) / 2 ? "Yes" : "No") << endl;
  } else {
    cout << (A[0] * 2 <= N || A[0] + 1 == N ? "Yes" : "No") << endl;
  }

  return 0;
}
