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;
const int N=1e5+5;

int n,a[N];

int coba(int x){
	int ct=0;
	for (int i=1;i<=n;i++){
		if (a[i]<x){
			ct++;
		}
	}
	if (x-ct){
		return (n-ct)/(x-ct)>1;
	}else{
		return !(n-ct);
	}
}

int main(){
	ios::sync_with_stdio(0);
	cin.tie(0);
	cin >> n;
	int mn=INT_MAX;
	int mx=INT_MIN;
	for (int i=1;i<=n;i++){
		cin >> a[i];
		mn=min(mn,a[i]);
		mx=max(mx,a[i]);
	}
	if (mx-mn<=1){
		int ans=0;
		if (mx==mn){
			ans=coba(mn);
		}
		ans|=coba(mn+1);
		cout << (ans?"Yes":
		"No") << "\n";
	}else{
		cout << "No\n";
	}
}