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>
#define ll long long
using namespace std;
int main(){
	int n;
	cin >> n;
	vector<int> a(n);
	int ans = 0;
	for(int i = 0; i < n; i ++) scanf("%d",&a[i]);
	sort(a.begin(),a.end());
	int minn = a[0];
	int maxn = a.back();
	if(minn == maxn){
		if(minn*2 <= n || minn == n-1) ans = 1;
	}
	if(maxn == minn +1 ){
		int cnt = 0;
		for(int i = 0; a[i] == minn; i++) cnt++;
		if(maxn > cnt && cnt + 2*(maxn-cnt) <= n) ans = 1;
	}
	printf("%s\n",ans?"Yes":"No");
	return 0;
}