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)

// In the name of God

#include <iostream>
#include <algorithm>
#include <fstream>
#include <vector>
#include <deque>
#include <assert.h>
#include <queue>
#include <stack>
#include <set>
#include <map>
#include <stdio.h>
#include <string.h>
#include <utility>
#include <math.h>
#include <bitset>
#include <iomanip>
#include <complex>

using namespace std;

#define rep(i, a, b) for (int i = (a), i##_end_ = (b); i < i##_end_; ++i)
#define debug(...) fprintf(stderr, __VA_ARGS__)
#define mp make_pair
#define x first
#define y second
#define pb push_back
#define SZ(x) (int((x).size()))
#define ALL(x) (x).begin(), (x).end()

template<typename T> inline bool chkmin(T &a, const T &b) { return a > b ? a = b, 1 : 0; }
template<typename T> inline bool chkmax(T &a, const T &b) { return a < b ? a = b, 1 : 0; }
template<typename T> inline bool smin(T &a, const T &b)   { return a > b ? a = b : a;    }
template<typename T> inline bool smax(T &a, const T &b)   { return a < b ? a = b : a;    }

typedef long long LL;

const int N = (int) 1e6 + 6, mod = (int) 0;
int a[N];
int main() {
	int n;
	cin >> n;
	int mx = -1e9, mn = 1e9, cnt = 0;
	for (int j = 0; j < n; ++j) {
		cin >> a[j];
		mx = max(mx, a[j]);
		mn = min(mn, a[j]);
	}
	if (mx - mn > 1) {
		cout << "No\n";
		return 0;
	}
	for (int j = 0; j < n; ++j)
		cnt += (a[j] == mx);
	if (mx == mn) {
		if (mx == n - 1) {
			cout << "Yes\n";
			return 0;
		}
		if (mx <= n / 2) {
			cout << "Yes\n";
			return 0;
		}
		cout << "No\n";
		return 0;
	}
	int less = (n - cnt) + (cnt >= 1), most = (n - cnt) + (cnt / 2);
	for (int j = 0; j < n; ++j) {
		if (a[j] + 1 < less) {
			cout << "No\n";
			return 0;
		}
		if (a[j] > most) {
			cout << "No\n";
			return 0;
		}
	}
	cout << "Yes\n";
}