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: Wrong Answer)

#include <iostream>
#include <cstring>
#include <cstdio>
#include <map>
using namespace std;
int n;
int a[1000000];
map<int, int>M;
int main()
{
    cin>>n;
    for(int i = 0; i < n; i++) cin>>a[i];
    int Max = 0, t = 0;
    for(int i = 0; i < n; i++){
        if(!M[a[i]]) { M[a[i]] = 1; t++; Max = max(Max, a[i]); }
    }
    if(t > 2) { cout<<"No"<<endl; }
    else {
        int m = 0;
        for(int i = 0; i < n; i++) if(a[i] == Max-1) m++;
        if(m < Max && (m + 2*(Max-m) <= n)) cout<<"Yes"<<endl;
        else cout<<"No"<<endl;
    }
}