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>
#define reg register
using namespace std;
int n, a[1000001], sum;
int main()
{ 
    cin >> n;
    for(int i = 1; i <= n; i++) scanf("%d", &a[i]);
    sort(a + 1, a + n + 1);
    if(a[n] - a[1] > 1) cout << "No\n";
    else if(a[n] - a[1] == 0){
        if(a[1] * 2 > n&&a[1]!=n-1) cout << "No\n";
        else cout << "Yes\n"; 
    }
    else if(a[n] - a[1] == 1){
        for(int i = 1; i <= n; i++)  if(a[i] == a[1]) sum++;
        if(sum >= a[n]) cout << "No\n";
        else if((a[n]-sum) * 2 > n - sum) cout <<"No\n";
        else cout << "Yes\n";
    }
}