Problem:
Score : 700 points

Problem Statement

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.

Sample Input 1

3
1 2 2

Sample Output 1

Yes

For example, if cat 1, 2 and 3 wears red, blue and blue hats, respectively, it is consistent with the remarks of the cats.

Sample Input 2

3
1 1 2

Sample Output 2

No

From the remark of cat 1, we can see that cat 2 and 3 wear hats of the same color.
Also, from the remark of cat 2, we can see that cat 1 and 3 wear hats of the same color.
Therefore, cat 1 and 2 wear hats of the same color, which contradicts the remark of cat 3.

Sample Input 3

5
4 3 4 3 4

Sample Output 3

No

Sample Input 4

3
2 2 2

Sample Output 4

Yes

Sample Input 5

4
2 2 2 2

Sample Output 5

Yes

Sample Input 6

5
3 3 3 3 3

Sample Output 6

No

Solution in C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <cstdio>
#include <algorithm>

int n;
int a[100010];

int main(void)
{
	int i;
	int w = -1;
	int p,q;

	//freopen("x.in","r",stdin);

	scanf("%d",&n);
	for(i = 1;i <= n;++i)
		scanf("%d",&a[i]);

	for(i = 1;i <= n;++i)
		w = std::max(w,a[i]);
	for(i = 1;i <= n;++i)
		if(a[i] != w && a[i] != w - 1)
			return puts("No"),0;
	p = q = 0;
	for(i = 1;i <= n;++i)
		if(a[i] == w)
			++p;
		else
			++q;
	if(!q){
		if(2 * w <= n)
			return puts("Yes"),0;
		if(w == n - 1)
			return puts("Yes"),0;
		puts("No");
		return 0;
	}
	if(w > q && 2 * (w - q) + q <= n)
		return puts("Yes"),0;
	puts("No");

	return 0;
}