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 For(i, j, k) for(int i = j; i <= k; i++)

const int N = 1e5 + 10;

int cnt[N], n;

int main(){
	
	scanf("%d", &n);
	For(i, 1, n){
		int x;
		scanf("%d", &x);
		cnt[x]++;
	}

	int pos = 0;
	For(i, 1, n) if(cnt[i]){
		pos = i;
		if(cnt[i] + cnt[i + 1] != n){
			puts("No");
			return 0;
		}
		break;
	}

	if(!cnt[pos + 1]){
		puts(pos == n - 1 || pos <= n / 2 ? "Yes" : "No");
	}
	else{
		if(cnt[pos + 1] <= 1) puts("No");
		else{
			int x = cnt[pos];
			if(pos + 1 - x <= cnt[pos + 1] / 2 && pos + 1 - x >= 1) puts("Yes");
			else puts("No");
		}
	}

	return 0;
}