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<iostream>
#include<stdio.h>
#include<string.h>
#define N 1200000
using namespace std;
int a[N],p[N],x;
int n,ans;
int solve(){
	if(x==n-1&&p[x]==n)return true;
	x--;
	// x 是 单独一个帽子 x+1是多个帽子
	if(p[x]+p[x+1]!=n)return false;
	ans=x+1;
	ans-=p[x];//还需要的颜色
	if(ans>p[x+1]/2)return false;
	if(ans<=0)return false;
	return true;
}
int main(){
	scanf("%d",&n);
	for(int i=1;i<=n;i++)scanf("%d",&a[i]),p[a[i]]++,x=max(x,a[i]);
	if(solve())printf("Yes\n");
	else printf("No\n");
}