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
n = int(input())
a = list(map(int, input().split()))

def solve():
    if max(a)-min(a) > 1:
        return False
    if all(i==a[0] for i in a):
        if a[0] == n-1 or a[0] <= n//2:
            return True
        else:
            return False
    color = [0]*n
    unique = min(a)
    for i, ai in enumerate(a):
        if ai == unique:
            color[i] = 1
    s = sum(color)
    can = (n-s)//2

    for i, ai in enumerate(a):
        if ai == unique:
            if not (s <= ai <= s-1+can):
                return False
        else:
            if not (s+1 <= ai <= s+can):
                return False
    return True

if solve():
    print("Yes")
else:
    print("No")