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>
int solve()
{
	int n,i,a,A=0,AS=1,B=0,BS=1,C=0;
	scanf("%d",&n);
	for(i=1;i<=n;++i)scanf("%d",&a),A?A==a?++AS:B?B==a?++BS:C=1:B=a:A=a;
	if(C)return 0*puts("No");
	if(A<B)A^=B^=A^=B,AS^=BS^=AS^=BS;
	if(B)
	{
		if(B!=A-1)return 0*puts("No");
		if(BS>=A)return 0*puts("No");
		puts(2*(A-BS)>n-BS?"No":"Yes");
	}
	else puts(2*A>n&&A!=n-1?"No":"Yes");
}
int main()
{
	int T=1;
	for(;T--;)solve();
}