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 <cstdio>
#include <algorithm>
#include <cstring>
#include <iostream>
#include <utility>
#include <string>

#define loop(n) for(ll i=0;i<n;i++)

using namespace std;

typedef long long int ll;

int main() {
    ll b[100000],n,t,x = 0,y = 100000;
    memset(b,0,sizeof(ll[100000]));
    cin >> n;
    loop(n) {
        cin >> t;
        x = max(x,t);
        y = min(y,t);
        b[t]++;
    }
    
    if((x==y && (x+1 == n || x*2 <= n)) || (x==y+1 && b[y] + 1 <= x && x <= b[y] + b[x] / 2)) cout << "Yes" << endl;
    else cout << "No" << endl;
}