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)

#define _CRT_SECURE_NO_WARNINGS
#include "bits/stdc++.h"
using namespace std;

#define int long long

#define rep(i, n) for (signed i = 0; i < signed(n); i++)
#define REP(i, s, n) for (signed i = signed(s); i < signed(n); i++)
#define rrep(i, n) for (signed i = signed(s) - 1; i >= 0; i--)

#define all(c) begin(c), end(c)
template<typename T>bool maxup(T& a, const T&& b) { if (a < b) { a = b; return true; }; }
template<typename T>bool maxup(T& a, const T& b) { if (a < b) { a = b; return true; }; }
template<typename T>bool minup(T& a, const T&& b) { if (a > b) { a = b; return true; }; }
template<typename T>bool minup(T& a, const T& b) { if (a > b) { a = b; return true; }; }

#define X first
#define Y second

using VV = vector<vector<int>>;
using V = vector<int>;
using P = pair<int, int>;
using IP = pair<int, P>;

template<typename T>
inline void input(vector<T>& v) { for (auto& x : v) cin >> x; }

void calc() {
	int n; cin >> n;
	V v(n); input(v);
	int minv = *min_element(all(v));
	int maxv = *max_element(all(v));
	bool ok = false;
	if (minv == maxv) {
		int a = minv;
		ok = (a == n - 1 || a * 2 <= n);
	} else if (minv + 1 == maxv) {
		int c = 0;
		rep(i, n) c += v[i] == minv;
		int cnt = 0;
		rep(i, n) cnt += v[i] == maxv;
		ok = maxv == c + (n - c) / 2;
	}

	cout << (ok ? "Yes" : "No") << endl;
}

signed main() {
	cin.tie(0);
	ios::sync_with_stdio(false);
	calc();
#ifdef _MSC_VER
	system("pause");
#endif
}