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++ (GCC 5.4.1) (judge verdict: Wrong Answer)

#include<stdio.h>
#include<string.h>
#include<algorithm>
#define LL long long 
using namespace std;
const int inf=1<<30;
const int maxn=1e5+5;
int A[maxn];

bool solve(int n)
{
int max_=-inf,min_=inf;		
for(int i=1;i<=n;i++)
{
  scanf("%d",&A[i]);	
  max_=max(max_,A[i]);
  min_=min(min_,A[i]);	
}	
	
	
if(max_-min_>1) return 0;
if(max_==min_)
{
if(max_==n-1||max_<=n/2 ) return 1;
else return 0;
}



if(max_>n-1) return 0;

int unique=0;

for(int i=1;i<=n;i++)
if(A[i]==min_) unique++;

max_-=unique;
n-=unique;

//printf("max=%d n=%d\n",max_,n);

if(max_>0&&(max_==n-1||max_<=n/2 ) ) return 1;
else return 0;

}








int main(){
//freopen("C:\\Users\\deii\\Desktop\\test.txt","r",stdin);		

int n;
while(scanf("%d",&n)==1){

if(solve(n)) printf("Yes\n");
else printf("No\n");
}

}