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>
using namespace std;

const int MAXN = 100005;

int N;
int cnt[MAXN];
int mx, mn = MAXN;

void load() {
	scanf("%d", &N);
	for (int i = 0; i < N; i++) {
		int x;
		scanf("%d", &x);
		cnt[x]++;
		mx = max(mx, x);
		mn = min(mn, x);
	}
}

bool solve() {
	if (mx - mn > 1)
		return false;
	if (mx == mn) 
		return mx == N - 1 || mx <= N / 2;
	return mx > cnt[mn] && mx - cnt[mn] <= cnt[mx] / 2;
}

int main() {
	load();
	puts(solve() ? "Yes" : "No");
	return 0;
}	