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.

Examples

Input

3
1 2 2


Output

Yes


Input

3
1 1 2


Output

No


Input

5
4 3 4 3 4


Output

No


Input

3
2 2 2


Output

Yes


Input

4
2 2 2 2


Output

Yes


Input

5
3 3 3 3 3


Output

No
import sys
from collections import defaultdict, Counter
from itertools import product, groupby, count, permutations, combinations
from math import pi, sqrt, ceil, floor
from collections import deque
from bisect import bisect, bisect_left, bisect_right
from string import ascii_lowercase
from functools import lru_cache, reduce
from operator import xor
INF = float("inf")
sys.setrecursionlimit(10**7)

# 4近傍（右, 下, 左, 上）
dy = [0, -1, 0, 1]
dx = [1, 0, -1, 0]


def inside(y: int, x: int, H: int, W: int) -> bool: return 0 <= y < H and 0 <= x < W


def solve(N, l):
    a, b = min(l), max(l)
    if b - a > 1:
        return False
    if a == b:
        if a == N - 1:
            return True
        return N >= (a * 2)

    num_a = l.count(a)

    return num_a < b and num_a + 2 * (b - num_a) <= N


def main():
    N = int(input())
    a_list = list(map(int, input().split()))
    print("Yes" if solve(N, a_list) else "No")

if __name__ == '__main__':
    main()
