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>
#define rep(i,n) for(int i = 0; i < n; i++)
#define repp(i, m, n) for(int i = m; i < n; i++)
#define reps(i, n) for(int i = 1; i <= n; i++)
const int    INF = 100000000;
const double EPS = 1e-10;
const int    MOD = 1000000007;
using namespace std;
typedef long long ll;
typedef pair<int, int> pai;
typedef pair<ll,ll> pal;



int main()
{
	int n, x, y, z;
	cin >> n;
	cin >> x;
	int a=1, b=0, cnt=0, muri=0;
	rep(i, n-1)
	{
		cin >> y;
		if(cnt==0)
		{
			if(y==x) a++;
			else
			{	
				z=y-x;
				if(z==1) cnt=1, b++;
				else if(z==-1) cnt=-1, b++;
				else
				{
					muri=1;
					break;
				}
			}
		}
		else
		{
			if(y==x) a++;
			else
			{
				if(y!=x+cnt)
				{
					muri=1;
					break;
				}
				else b++;
			}
		}
	}
	if(muri==1) cout << "No" << endl;
	else
	{
		if(cnt==0)
		{
			if(x==n-1 || x<=n/2) cout << "Yes" << endl;
			else cout << "No" << endl;
		}
		else if(cnt==1)
		{
			z=x+1-a;
			if(z>=1 && z<=b/2) cout << "Yes" << endl;
			else cout << "No" << endl;
		}
		else
		{
			z=x-b;
			if(z>=1 && z<=a/2) cout << "Yes" << endl;
			else cout << "No" << endl;
		}
	}
	return 0;
}