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)

#include <bits/stdc++.h>

using namespace std;

#define fi first
#define se second
#define mp make_pair
#define pb push_back
#define pf push_front
#define iter(v, i) for (__typeof__((v).begin()) i = (v).begin(); i != (v).end(); i++)
#define fast_io_without_cstdio ios_base::sync_with_stdio(false), cin.tie(NULL)
#define all(v) (v).begin(), (v).end()
#define rep(i, s, e) for (int i = s; i < e; i++)

#ifdef __linux__
#define gc getchar_unlocked
#define pc putchar_unlocked
#else
#define gc getchar
#define pc putchar
#endif

#if __cplusplus <= 199711L
template<class BidirIt>
BidirIt prev(BidirIt it, typename iterator_traits<BidirIt>::difference_type n = 1) {
    advance(it, -n);
    return it;
}

template<class ForwardIt>
ForwardIt next(ForwardIt it, typename iterator_traits<ForwardIt>::difference_type n = 1) {
    advance(it, n);
    return it;
}
#endif

typedef long long ll;
typedef pair<int, int> ii;
typedef vector<int> vi;
typedef vector<ii> vii;
typedef long double ldouble;

const double EPS = 1e-9;
const double PI = 3.141592653589793238462;

template<typename T>
inline T sq(T a) { return a * a; }

//#ifdef LOCAL_MACHINE
//#endif

const int MAXN = 1e5 + 5;

int cnt[MAXN];

int main() {
    //freopen("", "r", stdin);
    //freopen("", "w", stdout);
    int n;
    scanf("%d", &n);
    int diff = 0, mn = 1e9, mx = 0;
    for (int i = 0; i < n; i++) {
        int a; scanf("%d", &a);
        cnt[a]++;
        if (cnt[a] == 1) diff++;
        mn = min(mn, a);
        mx = max(mx, a);
    }
    if (mx == mn) {
        if (n == mx + 1)
            puts("Yes");
        else if (mx * 2 <= n)
            puts("Yes");
        else
            puts("No");
    } else if (mn + 1 == mx) {
        if (cnt[mn] + 1 == mx)
            puts("Yes");
        else
            puts("No");
    } else {
        puts("No");
    }
    return 0;
}