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>
using namespace std;
const int N=1e5+10;
int cnt,mx,mn=1e9,n,t[N];
int main(){
    scanf("%d",&n);
    for(int i=1;i<=n;i++)
        scanf("%d",&t[i]),mx=max(mx,t[i]),mn=min(mn,t[i]);
    if(mx-mn>1){puts("No");return 0;}
    if(mx==mn){
        if(mx==n-1){puts("Yes");return 0;}
        if(mx*2<=n)puts("Yes");
        else puts("No");
        return 0;
    }
    for(int i=1;i<=n;i++)
        if(t[i]==mn)++cnt;
    if(cnt<mx&&cnt+(mx-cnt)*2<=n)puts("Yes");
    else puts("No");
}
