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, x;
int a, b, anum, bnum;

int main() {
  scanf("%d", &n);
  for (int i = 1; i <= n; ++i) {
    scanf("%d", &x);
    if (!a) a = x, anum = 1;
    else if (x == a) anum++;
    else if (!b) b = x, bnum = 1;
    else if (x == b) bnum++;
    else return !puts("No");
  }
  if (a < b) swap(a, b), swap(anum, bnum);
  if (b && b != a - 1) return !puts("No");
  if (bnum) a -= bnum, n -= bnum;
  else if (a == n - 1) return !puts("Yes");
  if (a <= 0 || a == n) return !puts("No");
  puts(a * 2 <= n ? "Yes" : "No");
  return 0;
}
