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)

/*
    Author:zeke
    
    pass System Test!
    GET AC!!
*/
#include <iostream>
#include <queue>
#include <vector>
#include <iostream>
#include <vector>
#include <string>
#include <cassert>
#include <algorithm>
#include <functional>
#include <cmath>
#include <queue>
#include <set>
#include <stack>
#include <deque>
#include <map>
#include <iomanip>
#include <utility>
#include <stack>
#include <bitset>
using ll = long long;
using ld = long double;
using namespace std;
#define rep(i, n) for (int i = 0; i < (int)(n); i++)
#define all(x) (x).begin(), (x).end()
#define rep3(var, min, max) for (ll(var) = (min); (var) < (max); ++(var))
#define repi3(var, min, max) for (ll(var) = (max)-1; (var) + 1 > (min); --(var))
#define Mp(a, b) make_pair((a), (b))
#define F first
#define S second
#define Icin(s) \
    ll(s);      \
    cin >> (s);
#define Scin(s) \
    ll(s);      \
    cin >> (s);
template <class T>
bool chmax(T &a, const T &b)
{
    if (a < b)
    {
        a = b;
        return 1;
    }
    return 0;
}
template <class T>
bool chmin(T &a, const T &b)
{
    if (b < a)
    {
        a = b;
        return 1;
    }
    return 0;
}
typedef pair<ll, ll> P;
typedef vector<ll> V;
typedef vector<V> VV;
typedef vector<P> VP;
ll mod = 1e9 + 7;
ll MOD = 1e9 + 7;
ll INF = 1e18;
int main()
{
    cin.tie(0);
    ios::sync_with_stdio(false);
    ll n;
    cin >> n;
    V vec(n);
    rep(i, n) cin >> vec[i];
    ll Max = 0;
    ll Min = 1e18;
    rep(i,n){
        chmax(Max, vec[i]);
        chmin(Min, vec[i]);
    }
    if(Max-Min>1){
        cout << "No" << endl;
        return 0;
    }
    ll MinCount = 0;
    rep(i,n){
        if(vec[i]==Min){
            MinCount++;
        }
    }
    if(Max==Min){
        if(n>=(Max*2)){
            cout << "Yes" << endl;
        }else{
            cout << "No" << endl;
        }
    }else{
        if(n>=Max+1&&MinCount<Max){
            cout << "Yes" << endl;
        }else{
            cout << "No" << endl;
        }
    }
}