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;

long long int N, a[114514], m, c, i;

int main(){
    scanf("%lld", &N);
    for(; i < N; ++i){
        scanf("%lld", a + i);
        m = max(m, a[i]);
    }
    for(i = 0; i < N; ++i){
        if(a[i] < m)++c;
        if(a[i] < m - 1)return puts("No") & 0;
    }
    if((c == 0) && (m == N - 1))return puts("Yes") & 0;
    puts(((c > m - 1) || (c < m * 2 - N)) ? "No" : "Yes");
    return 0;
}
