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>
using namespace std;

int main()
{
    int n;
    cin >> n;
    int a[100005];
    int b[100005]{0};
    int l = n, r = 0;
    for(int i = 0; i < n; i++){
        cin >> a[i];
        b[a[i]]++;
        l = min(l, a[i]);
        r = max(r, a[i]);
    }
    if(r - l > 1){
        cout << "No" << endl;
    }
    else if(l == r){
        if(l <= n / 2 || l == n - 1) cout << "Yes" << endl;
        else cout << "No" << endl;
    }
    else{
        if(r >= b[l] + 1 && r <= b[l] + b[r] / 2) cout << "Yes" << endl;
        else cout << "No" << endl;
    }
}
