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 5.4.1) (judge verdict: Accepted)

//In The Name of Beauty
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef vector<ll> vll;
#define IB std::ios::sync_with_stdio(0);
#define pb(x) push_back(x);
#define mp(x,y) make_pair(x,y)
#define pll pair<ll,ll>
#define F first
#define S second
ll const MAXN = 1e5 + 8;
ll const INF  = 1e12 + 8;
ll const delta = 1000000007;

int main()
{
    IB;
    cin.tie(0);
    cout.tie(0);
    ll n;
    cin >> n;
    ll a[n];
    ll mmin = INF;
    set<ll> st;
    for(ll i = 0;i < n;i++){
        cin >> a[i];
        mmin = min(mmin,a[i]);
        st.insert(a[i]);
    }
    if(st.size() > 2)return cout << "No",0;
    if(st.size() == 1){
        if(mmin == n - 1)return cout << "Yes",0;
        if(mmin * 2 <= n)return cout << "Yes",0;
        return cout << "No",0;
    }
    ll cnt = 0;
    for(ll i = 0;i < n;i++){
        if(a[i] == mmin)cnt++;
        if(a[i] - mmin > 1)return cout << "No",0;
    }
    if(mmin < cnt  - 1 + ((n - cnt) > 0))return cout << "No",0;
    if(2 * (mmin - cnt + 1) + cnt > n)return cout << "No",0;
    cout << "Yes";
    return 0;
}
//Written by M_H_H_7