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;
typedef long long ll;
#define rep(i, N) for (int i = 0; i < (int)N; i++)

bool isConsistent(vector<int> &a, int N) {
  sort(a.begin(), a.end());
  if(a[N-1] - a[0] > 1) return false;
  if(a[0] == a[N-1]) {
    return a[0] == N - 1 || (1 <= a[0] && a[0] <= N/2);
  } else {
    int i = 0;
    while(a[i] == a[0]) i++;
    return i <= a[0] && a[0] <= i - 1 + (N-i)/2;
  }
}

int main () {
  int N;
  scanf("%d", &N);
  vector<int> a(N, 0);
  rep(i,N) scanf("%d", &a[i]);

  printf(isConsistent(a, N) ? "Yes\n" : "No\n");
  return 0;
}
