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 MAX 1000005
#define ll long long
#define upperlimit 1000100
#define INF 1e18
#define eps 1e-8
#define endl '\n'
#define pcc pair<char,char>
#define pii pair<int,int>
#define pll pair<ll,ll>
#define tr(container,it) for(typeof(container.begin()) it=container.begin();it!=container.end();it++)
#define MOD 1000000007
#define slld(t) scanf("%lld",&t)
#define sd(t) scanf("%d",&t)
#define pd(t) printf("%d\n",t)
#define plld(t) printf("%lld\n",t)
#define mp(a,b) make_pair(a,b)
#define FF first
#define SS second
#define pb(x) push_back(x)
#define vi vector<int>
#define vll vector<ll>
#define clr(a) memset(a,0,sizeof(a))
#define debug(a) printf("check%d\n",a)
#define csl ios::sync_with_stdio(false);cin.tie(0);cout.tie(0);
using namespace std;
 
ll gcd(ll n1,ll n2){
	if(n2==0)
		return n1;
	if(n1%n2==0)return n2;
	return gcd(n2,n1%n2);
}
ll powmod(ll base,ll exponent)
{
	ll ans=1;
	while(exponent){
		if(exponent&1)ans=(ans*base)%MOD;
		base=(base*base)%MOD;
		exponent/=2;
	}
	return ans;
}
int arr[MAX];
int main()
{
	int n;
	cin>>n;
	bool flag=true;
	for(int i=0;i<n;i++)
		cin>>arr[i];
	sort(arr,arr+n);
	if(arr[n-1]-arr[0]>1)
		flag=false;
	else if(arr[n-1]==arr[0]&&arr[0]!=n-1)
	{
		int x=arr[0]*2;
		if(n<x)
			flag=false;
	}
	//assert(arr[1]==arr[0]);
	else
	{
		int cnt=0;
		for(int i=0;i<n;i++)
		if(arr[i]==arr[0])
		{
			cnt++;
		}
		//cout<<arr[n-1]<<endl;
		if(arr[n-1]!=cnt+1)
			flag=false;
	}

	if(flag)
		cout<<"Yes"<<endl;
	else
		cout<<"No"<<endl;
}