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"
#ifndef err
#define err(...)(void)0
#endif
using namespace std;
using ll = long long;
using ull = decltype(1ull);
template<class T>int size(T&&a) { return a.size(); }
#define REP(t,a)for(typename make_signed<decltype(a.second)>::type t=a.first,_l##t=a.second;t<_l##t;t++)
#define RREP(t,a)for(typename make_signed<decltype(a.second)>::type t=a.second-1,_l##t=a.first;t>=_l##t;t--)
template<class B>pair<int, B>make_pair(B b) { return{ 0,b }; }
#define rep(t,...)REP(t,make_pair(__VA_ARGS__))
#define rrep(t,...)RREP(t,make_pair(__VA_ARGS__))
#define all(a)begin(a),end(a)
#define rall(a)a.rbegin(),a.rend()
#define var(t, ...) t __VA_ARGS__;in,__VA_ARGS__;

void Calc();
int main() {
  ios::sync_with_stdio(false); cin.tie(nullptr);
  cin.exceptions(istream::failbit | istream::badbit);
  cout << fixed << setprecision(15); Calc(); cout.flush(); return 0;
}
template<class A>void amax(A&a, A b) { a = max(a, b); }
template<class A>void amin(A&a, A b) { a = min(a, b); }
template<class A>int comp(A a, A b) { return a < b ? 1 : b < a ? -1 : 0; }
struct Scanner {
  template<class A = string>A Next() { A a; cin >> a; return a; }
  template<class A = int>vector<A>Array(int n) { vector<A>a(n); for (A&i : a) cin >> i; return a; }
  string Line() const { string s; getline(cin, s); return s; }
  template<class A>Scanner&operator,(A&a) { a = Next<A>(); return *this; }
  template<class A>operator A() { return Next<A>(); }
}in;

/*---------------------------------------------------------------------*/

bool solve(vector<int> a) {
  sort(all(a));
  int n = (int)a.size();
  auto mini = a.front();
  auto maxi = a.back();
  if (maxi - mini >= 2) {
    return false;
  }
  if (maxi == mini) {
    if (maxi + 1 == n || 2 * maxi <= n) {
      return true;
    }
    return false;
  }

  int cnt = 0;
  rep(i, n)if (a[0] == a[i])cnt++; else break;

  if (cnt == mini) {
    return (n - cnt >= 2);
  }
  if (cnt < mini) {
    return 2 * (maxi - cnt) <= (n - cnt);
  }
  if (cnt != 1) {
    return false;
  }

  if (2 * mini <= n - 1) {
    return true;
  }
  return false;
}


void Calc() {

  int n = in;
  auto a = in.Array(n);

  if (solve(a)) cout << ("Yes") << endl;
  else cout << ("No") << endl;
}