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 9.2.1) (judge verdict: Runtime Error)

#include <iostream>
//#include <iomanip>
//#include <string>
#include <vector>
#include <algorithm>
//#include <utility>
//#include <set>
#include <map>
//#include <queue>
//#include <deque>
//#include <bitset>
//#include <math.h>
using namespace std ;
using ll = long long ;
//using ld = long double ;
using vll = vector<ll> ;
using vvll = vector<vll> ;
//using vc = vector<char> ;
//using vvc = vector<vc> ;
//using vb = vector<bool> ;
//using vvb = vector<vb> ;
//using pll = pair<ll,ll> ;
#define all(v) v.begin(),v.end()
//ll mod = 1000000007 ;
//long double pie = acos(-1) ;
//ll INF = 1000000000000 ;

void yorn(bool a){if(a) cout << "Yes" << endl ; else cout << "No" << endl ;}
//void YorN(bool a){if(a) cout << "YES" << endl ; else cout << "NO" << endl ;}
//ll gcd(long long a,long long b){if(b==0) return a ; return gcd(b,a%b) ;}
//ll lcm(long long a,long long b){return a/gcd(a,b)*b ;}
//ll sa(long long a,long long b){if(a>b) return a-b ; return b-a ;}
//void fix_cout(){cout << fixed << setprecision(20) ;}

int main(){
	ll n ; cin >> n ;
	vll a(n) ;
	for(auto &i:a) cin >> i ;
	sort(all(a)) ;
	bool ok = true ;
	for(int i=0;i<n;i++) ok &= (a.at(0)==a.at(i)) ;
	if(ok){
		yorn(a.at(0)==n-1||a.at(0)<=n/2) ;
		cout << a.at(n) << endl ;
	}else{
		map<ll,ll> m ;
		for(int i=0;i<n;i++) m[a.at(i)]++ ;
		bool ok = true ;
		for(int i=0;i<n;i++) ok &= (a.at(i)==m.size()-(m[a.at(i)]==1)) ;
		yorn(ok) ;
	}
}