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)

// In the name of God

#include <bits/stdc++.h>

#define ll long long
#define pb push_back
#define mp make_pair
#define F first
#define S second
#define an size()

using namespace std;
const ll maxn=1e5+500;;
ll a[maxn];
bool f(ll n,ll x)
{
    if(x>n-1)
    {
        return 1;
    }
    if(n%(n-x)!=0)return 1;
    return 0;
}
int main()
{
    ll n,maxx=0,minn=1e9;
    cin>>n;
    for(ll i=0; i<n; i++)
    {
        cin>>a[i];
        minn=min(minn,a[i]);
        maxx=max(maxx,a[i]);
    }
    if(maxx-minn>1)
    {
        cout<<"No";
        return 0;
    }
    ll x=0,y=0;
    for(ll i=0; i<n; i++)
    {
        if(a[i]==minn)
        {
            x++;
        }
        else
        {
            y++;
        }
    }
    //cout<<x<<endl;
    if(minn!=maxx)
    {
        ll z=minn-(x-1);
        if(z==0)
        {
            cout<<"No";
            return 0;
        }
        maxx-=x;
        if(z==y&&maxx==y-1)
        {
            cout<<"Yes";
            return 0;
        }
        if(maxx>y/2)
        {
            cout<<"No";
            return 0;
        }
        if(z!=maxx)
        {
            cout<<"NO";
            return 0;
        }
        if(z==maxx&&2*maxx<y)
        {
            cout<<"Yes";
            return 0;
        }
        cout<<"No";
        return 0;
    }
    else
    {
        if(minn>n/2&&minn!=n-1)
        {
            cout<<"No";
            return 0;
        }
        cout<<"Yes";
        return 0;
    }
}