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<cstring>
#include<iostream>
#include<algorithm>
using namespace std; 

const int N=100010, INF=1000000000;
int n, mina=INF, maxa=-1, cnt;
int a[N];

int main(){
	scanf("%d", &n);
	for(int i=1; i<=n; ++i){
		scanf("%d", &a[i]);
		mina = min(mina, a[i]);
		maxa = max(maxa, a[i]);
	}
	if(maxa-mina>1){ puts("No"); return 0; }
	if(maxa==mina){ printf("%s\n", (maxa<=n/2 || maxa==n-1) ? "Yes" : "No" ); return 0; }
	for(int i=1; i<=n; ++i) if(a[i]==mina) cnt++;
	maxa-=cnt; n-=cnt; if(maxa<=0){ puts("No"); return 0; }
	printf("%s\n", (maxa<=n/2) ? "Yes" : "No" );
}
