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>

int ri() {
	int n;
	scanf("%d", &n);
	return n;
}

bool solve(int n, int *a) {
	int min = *std::min_element(a, a + n);
	int max = *std::max_element(a, a + n);
	if (max - min > 1) return false;
	if (max == min) return min <= n / 2 || min == n - 1;
	int min_cnt = std::count(a, a + n, min);
	int max_cnt = n - min_cnt;
	if (max_cnt == 1) return false;
	return max >= min_cnt + 1 && max <= min_cnt + max_cnt / 2;
}

int main() {
	int n = ri();
	int a[n];
	for (int i = 0; i < n; i++) a[i] = ri();
	std::cout << (solve(n, a) ? "Yes" : "No") << std::endl;
	
	return 0;
}

