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 <iostream>
#include <cstdio>
#include <vector>
#include <string>
#include <algorithm>

bool solve() {
	int n;
	std::cin >> n;
	std::vector<int> a(n);
	int max = 0;
	int min = 1e9;
	for (int i = 0; i < n; i++) {
		scanf("%d", &a[i]);
		max = std::max(max, a[i]);
		min = std::min(min, a[i]);
	}

	if (max - min >= 2) {
		return false;
	}

	if (max == min) {
		return max <= n / 2 || max == n - 1;
	}

	int cnt = std::count(a.begin(), a.end(), min);
	
	return cnt + 1 <= max && max <= cnt + (n - cnt) / 2;
}

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