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;
#define IOS ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0);
#define ll long long
map<int, int> mp;
int main(){
	IOS
	int n,mn=1e6,mx=-1;
	cin>>n;
	for(int i=1;i<=n;i++){
		int a;
		cin>>a;
		mp[a]++;
		if(mp[a]==n){
			if(a==n-1||a*2<=n){
				cout<<"Yes";
			}
			else{
				cout<<"No";
			}
			return 0;
		}
		if(a<mn){
			mn=a;
		}
		if(a>mx){
			mx=a;
		}
	}
	if(mp.size()!=2){
		cout<<"No";
		return 0;
	}
	if((mx-mp[mn])*2<=mp[mx]&&mp[mn]<=mn){
		cout<<"Yes";
	}
	else{
		cout<<"No";
	}
	return 0;
}
/*

*/