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;

#ifdef SG
	#include <debug.h>
#else
	template<typename T> struct outputer;
	struct outputable {};
	#define PRINT(...)
	#define OUTPUT(...)
	#define show(...)
	#define debug(...)
	#define deepen(...)
	#define timer(...)
	#define fbegin(...)
	#define fend
	#define pbegin(...)
	#define pend
#endif

#define ARG4(_1,_2,_3,_4,...) _4

#define forn3(i,l,r) for (int i = int(l); i < int(r); ++i)
#define forn2(i,n) forn3 (i, 0, n)
#define forn(...) ARG4(__VA_ARGS__, forn3, forn2) (__VA_ARGS__)

#define ford3(i,l,r) for (int i = int(r) - 1; i >= int(l); --i)
#define ford2(i,n) ford3 (i, 0, n)
#define ford(...) ARG4(__VA_ARGS__, ford3, ford2) (__VA_ARGS__)

#define ve vector
#define pa pair
#define tu tuple
#define mp make_pair
#define mt make_tuple
#define pb emplace_back
#define fs first
#define sc second
#define all(a) (a).begin(), (a).end()
#define sz(a) ((int)(a).size())

typedef long double ld;
typedef int64_t ll;
typedef uint64_t ull;
typedef uint32_t ui;
typedef uint16_t us;
typedef uint8_t uc;
typedef pa<int, int> pii;
typedef pa<int, ll> pil;
typedef pa<ll, int> pli;
typedef pa<ll, ll> pll;
typedef ve<int> vi;

template<typename T> inline auto sqr (T x) -> decltype(x * x) {return x * x;}
template<typename T1, typename T2> inline bool umx (T1& a, T2 b) {if (a < b) {a = b; return 1;} return 0;}
template<typename T1, typename T2> inline bool umn (T1& a, T2 b) {if (b < a) {a = b; return 1;} return 0;}

const int N = 100000;

struct Input {
	int n;
	int a[N];
	
	bool read () {
		if (!(cin >> n)) {
			return 0;
		}
		forn (i, n) {
			scanf("%d", &a[i]);
		}
		return 1;
	}

	void init (const Input &input) {
		*this = input;
	}
};

struct Data: Input {
	bool ans;
	
	void write () {
		puts(ans ? "Yes" : "No");
	}
};


namespace Main {
	
	struct Solution: Data {
		
		bool check (int k) {
			int cnt0 = 0, cnt1 = 0;
			forn (i, n) {
				if (a[i] == k) {
					cnt0++;
				} else if (a[i] == k - 1) {
					cnt1++;
				} else {
					return 0;
				}
			}
			debug(mt(n, k, cnt0, cnt1));
			if (cnt1 > k) {
				return 0;
			}
			int l = k - cnt1;
			debug(l);
			if (cnt0 && !l) {
				return 0;
			}
			if (2 * l > cnt0) {
				return 0;
			}
			debug(1);
			return 1;
		}
		
		void solve () {
			ans = check(a[0]) || check(a[0] + 1);
		}
		
		void clear () {
			*this = Solution();
		}
	};
}


Main::Solution sol;

int main () {
	cout.setf(ios::showpoint | ios::fixed);
	cout.precision(20);

	#ifdef SG
		freopen((problemname + ".in").c_str(), "r", stdin);
//		freopen((problemname + ".out").c_str(), "w", stdout);
		while (sol.read()) {
			sol.solve();
			sol.write();
			sol.clear();
		}
	#else
		sol.read();
		sol.solve();
		sol.write();
	#endif
	
	/*
	int t;
	cin >> t;
	forn (i, t) {
		sol.read();
		sol.solve();
		sol.write();
		sol.clear();
	}
	*/
	
	return 0;
}