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;

int N;
map<int, int> c;

int main() {
  scanf("%d", &N);
  for(int i = 0; i < N; ++i) {
    int a; scanf("%d", &a); ++c[a];
  }
  int a = c.begin()->first, n = c.begin()->second;
  if(c.size() == 1) {
    printf("%s\n",
      a == N - 1 || a <= N / 2 ? "Yes" : "No");
  } else {
    auto it = c.begin(); ++it;
    if(c.size() >= 3 || it->first != a + 1) {
      printf("No\n");
    } else {
      int k = (N - n) / 2;
      int b = a + 1 - n;
      printf("%s\n",
        k > 0 && b > 0 && b <= k ? "Yes" : "No");
    }
  }
  return 0;
}
