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 write1 { puts("Yes"); return 0;}
# define write2 { puts("No"); return 0;}
# define INF 100000000
using namespace std;
int n, sum, minn = INF, maxn = -INF;
int a[110000];
int main()
{
	cin >> n;
	for (int i = 1; i <= n; ++i)
	{
		cin >> a[i];
		maxn = max(maxn, a[i]);
		minn = min(minn, a[i]);
	}
	if (maxn - minn >= 2) write2
	if (maxn == minn)
	{
		if (maxn == n - 1) write1
		if (maxn * 2 <= n) write1
		else write2
	}
	for (int i = 1; i <= n; i++) if (a[i] == minn) ++sum;
	if (minn < sum) write2
	if (n - sum < 2 * (maxn - sum)) write2
	else write1
	return 0;
}
