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>

#define MAXN (100010)

int n;
int a[MAXN];

int main(){
	scanf("%d", &n);
	int t = 0;
	for(int i = 1; i <= n; ++ i){
		scanf("%d", a + i);
		t = std::max(t, a[i]);
	}
	int x = 0, y;
	for(int i = 1; i <= n; ++ i){
		if(a[i] != t && a[i] != t - 1) return printf("No\n"), 0;
		x += a[i] == t - 1;
	}
	y = n - x;
	if(y == n){
		return printf(1 <= t && t <= n / 2 || t == n - 1 ? "Yes\n" : "No\n"), 0;
	}
	printf(x + 1 <= t && t <= x + y / 2 ? "Yes\n" : "No\n");
	return 0;
}