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;

int n,a[100010],mx,cmx;

int main() {
    ios_base::sync_with_stdio(0); cin.tie(0);
    cin>>n;
    for (int i=1;i<=n;i++) {
        cin>>a[i];
        mx=max(mx,a[i]);
    }
    for (int i=1;i<=n;i++) {
        if (a[i]<mx-1) {
            cout<<"No"<<endl;
            return 0;
        }
        cmx+=(a[i]==mx);
    }
    if (cmx==1) {
        cout<<"No"<<endl;
        return 0;
    }
    if (cmx==n && mx==n-1) {
        cout<<"Yes"<<endl;
        return 0;
    }
    if (n-cmx+1<=mx && mx<=n-cmx+cmx/2) cout<<"Yes"<<endl;
    else cout<<"No"<<endl;
}