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: Accepted)

#include <bits/stdc++.h>
using namespace std;

long long n;
map<long long, long long> mp;

bool solve();

int main() {
  cin >> n;
  for(int i = 0; i < n; ++i) {
    int a;
    cin >> a;
    ++mp[a];
  }
  if(solve())
    cout << "Yes" << endl;
  else
    cout << "No" << endl;
  return 0;
}

bool solve() {
  if(mp.size() != 2 && mp.size() != 1) return 0;
  long long x = 0, y = 0, xnum = 0, ynum = 0;
  for(auto m : mp) {
    x = y;
    xnum = ynum;
    y = m.first;
    ynum = m.second;
  }
  if(x == 0)
    return y * 2 <= n || y == n - 1;
  else {
    if(x > y) {
      swap(x, y);
      swap(xnum, ynum);
    }
    if(y - x != 1) return 0;
    n -= xnum;
    y -= xnum;
    assert(n == ynum);
    return y * 2 <= n && y > 0;
  }
}