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 maxn = 100005;

int n, mx = -1, mn = maxn;
int a[maxn], cnt[maxn];

signed main () {
	scanf("%d", &n);
	for (int i = 1; i <= n; ++i) {
		scanf("%d", &a[i]);
		++cnt[a[i]];
		mn = min(mn, a[i]), mx = max(mx, a[i]);
	}
	if (mx - mn > 1)
		printf("No\n");
	else if (mx == mn) {
		if (mx == n - 1 || 2 * mx <= n)
			printf("Yes\n");
		else
			printf("No\n");
	}
	else {
		if (cnt[mn] + 1 <= mx && mx <= cnt[mn] + cnt[mx] / 2)
			printf("Yes\n");
		else
			printf("No\n");
	}
}
