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>
using namespace std;
using ll = long long;
using ull = unsigned long long;
constexpr long double EPS = 1e-15;
const long double PI = acos(-1);
constexpr int inf = 1e9;
constexpr ll INF = 2e18;
constexpr ll MOD = 1e9+7;
constexpr ll MOD1 = 998244353;
typedef pair<ll,ll> P;
//#define all(v) (v).begin(), (v).end()
#define rep(i,a,b) for (int i = (a); i < (b); i++)
#define REP(i,n) rep(i,0,n)
#define sz(s) (s).size()
#define pb push_back
#define fi first
#define se second
//#define mp make_pair

int n;
map<int,int> mp;

void input() {
    cin >> n;
    REP(i,n) {
        int k;
        cin >> k;
        mp[k]++;
    }
}

void solve() {
    if (sz(mp) > 2) {
        cout << "No" << endl;
        return;
    }
    if (sz(mp) == 1) {
        int num = (*mp.begin()).fi;
        cout << (num * 2 <= n || num == n - 1? "Yes":"No") << endl;
        return;
    }
    auto it = mp.begin();
    int k1 = (*it).fi;
    int num1 = (*it).se;
    it++;
    int k2 = (*it).fi;
    int num2 = (*it).se;
    int different_nums = k1 - num1 + 1;
    if (different_nums < 1 || different_nums * 2 > num2) {
        cout << "No" << endl;
        return;
    }
    cout << "Yes" << endl;
}

int main(int argc, char *argv[]){
    input();
    solve();
    return 0;
}