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<bits/stdc++.h>

using namespace std;

typedef long long LL;

const int maxn=100005;
const int INF=0x3f3f3f3f;

int cnt[maxn];

int main()
{
	int n,x;
	int MAX=0,MIN=INF;
	scanf("%d",&n);
	for(int i=1;i<=n;i++){
		scanf("%d",&x);
		MAX=max(x,MAX);MIN=min(x,MIN);
		cnt[x]++;
	}
	if(MAX-MIN>1||(cnt[n-1]!=2&&cnt[n-1]!=n&&cnt[n-1])||(cnt[1]!=n&&cnt[1]>1)||(MAX==MIN&&MAX!=1&&MAX!=n-1&&n/MAX<2)||(MAX!=MIN&&((n-cnt[MIN])/(MAX-cnt[MIN])<2)))puts("No");
	else puts("Yes");
	return 0;
}