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 _USE_MATH_DEFINES
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
using P   = pair<ll, ll>;
using mat = vector<vector<ll>>;

void IOS() { ios::sync_with_stdio(false), cin.tie(0); }

const ll INF = 1e16;
const ll MOD = 1e9 + 7;

ll mod(ll a) {
	if (a > 0) return a % MOD;
	if (a % MOD == 0) return 0;
	ll x = -a / MOD + 1;
	a += x * MOD;
	return a % MOD;
}

template <typename T> void dump(T x) { cout << x << endl; }
void dumpf(double x, ll t) { cout << setprecision(t) << fixed << x << endl; }
template <typename A, size_t N, typename T>
void Fill(A (&array)[N], const T &val) {
	fill((T *)array, (T *)(array + N), val);
}
// ll dx[4]    = {1, 0, -1, 0};
// int dy[4]    = {0, 1, 0, -1};
// ll pas[5001][5002];

int main() {
	IOS();
	ll n;
	cin >> n;
	vector<ll> a(n);
	map<ll, ll> mp;
	ll M = 0, m = n;
	for (int i = 0; i < n; ++i) {
		cin >> a[i];
		mp[a[i]]++;
		m = min(m, a[i]);
		M = max(M, a[i]);
	}
	if (M == m) {
		dump(M == n - 1 || m * 2 <= n ? "Yes" : "No");
	} else if (m + 1 == M) {
		dump(mp[m] == m && mp[M] >= M ? "Yes" : "No");
	} else {
		dump("No");
	}
}