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 <algorithm>
#include <iostream>
using namespace std;
int main() {
    int n; cin >> n;
    int a[n]; for (int i = 0; i < n; i++) cin >> a[i];
    int k = *max_element(a, a+n), l = *min_element(a, a+n);
    if (k - l >= 2) { cout << "No\n"; return  0; }
    if (k == l) {
        cout << (k == n-1 || n/2 >= k ? "Yes\n" : "No\n");
        return 0;
    }
    int x = 0;
    for (int b : a) if (b == k-1) x++;
    cout << (x <= k-1 && n-x >= 2 * (k-x) ? "Yes\n" : "No\n");
}
