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<bits/stdc++.h>
using namespace std;
const int maxn=1e5+10;
int n,a[maxn];
int m,s;
bool check()
{
	for (int i=1;i<=n;i++)
	    if (a[i]!=n-1) return 0;
	return 1;
}
int main()
{
	cin>>n;
	for (int i=1;i<=n;i++) scanf("%d",&a[i]),m=max(m,a[i]);
	if (check())
	{
		cout<<"Yes";return 0;
	}
	for (int i=1;i<=n;i++)
	    if (a[i]<m)
	    {
	    	if (a[i]==m-1) s++;
	    	else
	    	{
	    		cout<<"No";return 0;
			}
		}
	if (m<s||2*(m-s)>n-s||(n>s&&m-s<1)) cout<<"No";
	else cout<<"Yes";
	return 0;
}