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>
int N, a[100001], Max, Min, CMax, CMin;
int main()
{
	scanf("%d", &N);
	for (int i = 1; i <= N; i++)
		scanf("%d", a + i);
	Max = *std::max_element(a + 1, a + N + 1);
	Min = *std::min_element(a + 1, a + N + 1);
	CMax = std::count(a + 1, a + N + 1, Max);
	CMin = std::count(a + 1, a + N + 1, Min);
	if (Max == Min)
		puts(Max <= N >> 1 || Max == N - 1 ? "Yes" : "No");
	else if (Max == Min + 1)
		puts(CMin + 1 <= Max && Max <= CMin + (CMax >> 1) ? "Yes" : "No");
	else
		puts("No");
	return 0;
}
