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 <cstdio>
#include <algorithm>

const int MN = 100005;

int N, A[MN];

int main() {
	scanf("%d", &N);
	for (int i = 1; i <= N; ++i) scanf("%d", &A[i]);
	int mx = *std::max_element(A + 1, A + N + 1);
	int mn = *std::min_element(A + 1, A + N + 1);
	if (mx == mn) {
		if (mx == N - 1) puts("Yes");
		else if (mx > N / 2) puts("No");
		else puts("Yes");
		return 0;
	}
	if (mx - mn >= 2) return puts("No"), 0;
	int cnt = 0;
	for (int i = 1; i <= N; ++i) if (A[i] == mn) ++cnt;
	puts(mx <= cnt || mx > cnt + (N - cnt) / 2 ? "No" : "Yes");
	return 0;
}