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;
typedef long long ll;
#define F first
#define S second
#define pii pair<int, int>
#define eb emplace_back
#define all(v) v.begin(), v.end()
#define rep(i, n) for (int i = 0; i < n; ++i)
#define rep3(i, l, n) for (int i = l; i < n; ++i)
#define max(a, b) (a > b ? a : b)
#define min(a, b) (a < b ? a : b)
#define chmax(a, b) a = (a >= b ? a : b)
#define chmin(a, b) a = (a <= b ? a : b)
#define out(a) cout << a << endl
#define outa(a, n) { rep(_, n) cout << a[_] << " "; cout << endl; }
#define outp(a, n) { cout << endl; rep(_, n) cout << a[_].F << " " << a[_].S << endl; }
#define SZ(v) (int)v.size()
#define inf (int)(1e9+7)
#define abs(x) (x >= 0 ? x : -(x))
#define ceil(a, b) a / b + !!(a % b)
#define FIX(a) fixed << setprecision(a)
#define LB(v, n) (int)(lower_bound(all(v), n) - v.begin())
#define UB(v, n) (int)(upper_bound(all(v), n) - v.begin())

bool solve() {
    int n;
    cin >> n;
    vector<int> a(n);
    int one = 0;
    int mmax = -inf, mmin = inf;
    rep(i, n) {
        cin >> a[i];
        if (a[i] == 1) one++;
        chmax(mmax, a[i]);
        chmin(mmin, a[i]);
    }
    
    if (one >= 2 && one != n) return 0;
    if (mmax - mmin > 1) return 0;
    
    if (mmax - mmin == 0)
    { // 差が0のケース
        // 全部帽子の色違う
        if (mmax == n - 1) return 1;
        if (n / mmax >= 2) return 1;
        return 0;
    }
    
    { // 差が1のケース
        // 低いのが1つだけ
        int cnt = 0;
        rep(i, n) if (a[i] == mmin) cnt++;
        if (cnt == 1 && mmax <= n - 1 && mmax >= 2) return 1;
        
        return 0;
    }
}
int main() {
    ios::sync_with_stdio(false);
    cin.tie(0);
    
    if (solve()) out("Yes");
    else out("No");
}