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)

#ifdef _MSC_VER
#  define _CRT_SECURE_NO_WARNINGS
#  define _USE_MATH_DEFINES
#  include <intrin.h>
#  define __builtin_popcount __popcnt
#endif

#include <bits/stdc++.h>
using namespace std;
using i32 = int; using i64 = long long int; using f64 = double;
using u32 = unsigned int; using u64 = unsigned long long int; using str = string;
template <typename T> using vec = vector<T>; void in() { }
template <typename T, typename...TS> void in(T &&x, TS &&...xs) { cin >> x; in(move(xs)...); }
template <typename T> void out(T &&x) { cout << x << "\n"; }
template <typename T, typename...TS> void out(T &&x, TS &&...xs) { cout << x << " "; out(move(xs)...); }
#define indef(t, ...) t __VA_ARGS__; in(__VA_ARGS__)
#define get(t) []{ t x; cin >> x; return x; }()
#define times(n, i) for (i32 i = 0; i < (n); ++i)
#define range(a, b, i) for (i32 i = (a); i < (b); ++i)
#define upto(a, b, i) for (i32 i = (a); i <= (b); ++i)
#define downto(a, b, i) for (i32 i = (a); i >= (b); --i)
#define all(xs) (xs).begin(), (xs).end()
#define sortall(xs) sort(all(xs))
#define reverseall(xs) reverse(all(xs))
#define even(x) ((abs(x) & 1) == 0)
#define odd(x) ((abs(x) & 1) == 1)
#define bit(x, i) (((x) >> i) & 1)
#define append emplace_back
#define bisect_left lower_bound
#define bisect_right upper_bound
#define bound(a, x, b) (a <= x && x <= b)
const i64 MOD = 1000000007ll;
const f64 EPS = 1e-10;

i32 a[100000];

 bool solve() {
    indef(i32, n);
    i32 maxa = 0, mina = INT_MAX;
    times(n, ai) {
        in(a[ai]);
        maxa = max(maxa, a[ai]);
        mina = min(mina, a[ai]);
    }
    i32 mincnt = 0;
    times(n, ai) {
        mincnt += a[ai] == mina;
    }
    if (maxa - mina > 1) return false;
    if (maxa - mina == 1) {
        return maxa - mincnt > 0 && 2 * maxa <= n + mincnt;
    }
    return maxa == n-1 || maxa * 2 <= n;
}

i32 main()
{
    ios::sync_with_stdio(false);

#ifdef _MSC_VER
    /**
    ifstream fin("input.txt"); cin.rdbuf(fin.rdbuf()); assert(fin);
    ofstream fout("output.txt"); cout.rdbuf(fout.rdbuf()); assert(fout);
    /**/
#endif

    cout << fixed << setprecision(9);
    out(solve() ? "Yes" : "No");

    return 0;
}