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 <algorithm>
#include <iostream>
#include <iomanip>
#include <cstring>
#include <string>
#include <vector>
#include <queue>
#include <cmath>
#include <stack>
#include <set>
#include <map>
typedef long long ll;
using namespace std;

int main(){
    int N;
    cin >> N;
    map<int, int> cnt;
    for(int i = 0; i < N; i++){
        int a;
        cin >> a;
        cnt[a]++;
    }

    int sz = cnt.size();
    string ans;

    if(sz == 1){
        auto it = cnt.begin();
        int num = it -> first;

        if(num * 2 <= N || num + 1 == N) ans = "Yes";
        else ans = "No";
    }

    else if(sz == 2){
        auto it = cnt.begin();
        int n1 = it -> first;
        it++;
        int n2 = it -> first;

        int mn = min(n1, n2);
        int mx = max(n1, n2);

        int rest = mx - cnt[mn];
        int restcnt = N - cnt[mn];
        if(mn + 1 == mx && rest > 0){
            if(restcnt >= rest * 2){
                ans = "Yes";
            }
            else {
                ans = "No";
            }
        }
        else {
            ans = "No";
        }
    }

    else {
        ans = "No";
    }

    cout << ans << endl;
    return 0;
}