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, = map(int,input().split())
B = {}
for a in A: B[a] = B.get(a,0)+1
m = min(B)
M = max(B)
if m+1<M:
    print("No")
    exit()
def check(n):
    b0 = B.setdefault(n-1,0)
    b1 = B.setdefault(n,0)
    if b1==0:
        return b0==n
    else:
        return 1<= n-b0 <= b1//2
if m+1==M:
    ans = check(M)
else:
    ans = check(m) or check(m+1)
print("Yes" if ans else "No")