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;
typedef pair<int, int> pii;

const int MX = 400010;

int n,a[MX];;

map<int,int> freq;

int main() {
	//freopen("input.txt", "r", stdin);
	scanf("%d",&n);
	for (int i = 0; i < n; ++i){
		scanf("%d",&a[i]);
		freq[a[i]]++;
	}
	sort(a,a+n);
	if(freq.size() == 1){
		if(freq[a[0]] == a[0]+1 || freq[a[0]] >= 2 * a[0]){
			puts("Yes");
			return 0;
		}
	}
	if(freq.size() == 2 && (a[n-1]-freq[a[0]]) > 0 && freq[a[n-1]] >= 2 * (a[n-1]-freq[a[0]]) && a[n-1]-a[0] == 1){
		puts("Yes");
		return 0;
	}

	puts("No");
	return 0;
}