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 <bits/stdc++.h>

#define rep(i, n) for (int i = 0; i < (int)(n); i++)
#define all(v) v.begin(), v.end()
#define SP << " " 
#define LLi long long int

using namespace std;

//vector<LLi>を出力
void PV(vector<int> pvv) {
	rep(i, (int)pvv.size()-1) cout << pvv[i] SP;
	cout<< pvv[(int)pvv.size()-1] <<endl;
}

int main(){

	int n, l=0, lm=0, sm=0;
	vector<int> a;
	cin>> n;
  
  	a.resize(n);
  	rep(i, n){
      	cin>> a[i];
      if(a[i]!=2) cout<< a[i] <<endl;
      	l=max(l, a[i]);
    }
  
  //cout<< "l=" << l <<endl;
  
  	rep(i, n){
      	if(a[i]==l) lm++;
      	if(a[i]==l-1) sm++;
    }
  
  //cout<< "lm=" << lm << " sm=" << sm <<endl;
  
  	if(n!=lm+sm){
      	cout<< "No" <<endl;
      	return 0;
    }
  
  	if(sm==0){
      	if(l==1){
      		cout<< "Yes" <<endl;
      		return 0;
    	}
  		if(l==n-1){
      		cout<< "Yes" <<endl;
      		return 0;
    	}
  		if(l*2<=n) cout<< "Yes" <<endl;
      	else cout<< "No" <<endl;
      	return 0;
    }
  
  	if(l==1 && 1<sm){
      	cout<< "No" <<endl;
      	return 0;
    }
  
  	if(l<=lm && lm<=2*n-l) cout<< "Yes" <<endl;
    else cout<< "No" <<endl;
  
     return 0;
}