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>
#define neko 100010
#define qwq return printf("Yes\n"),0
#define orz return printf("No\n"),0
#define f(i,a,b) for(register int i=(a);i<=(b);i=-(~i))
int n,minx=1e9,maxn,a[neko],cnt;
int cmin(int a,int b){return a<b?a:b;}
int cmax(int a,int b){return a>b?a:b;}
int main()
{
	scanf("%d",&n);
	f(i,1,n)scanf("%d",&a[i]),minx=cmin(minx,a[i]),maxn=cmax(maxn,a[i]);
	if(minx==maxn)
	{
		if(minx==n-1)qwq;
		else if(2*minx>n)orz;
		else qwq;
	}
	else if(minx<maxn-1)orz;
	else
	{
		f(i,1,n)if(minx==a[i])++cnt;
		if(maxn-cnt<=0)orz;
		else if(2*(maxn-cnt)>(n-cnt))orz;
		else qwq;
	}
}