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
def ri(): return int(input())
def rli(): return list(map(int, input().split()))
def ris(): return list(input())
def pli(): return "".join(list(map(str, ans)))
 
 
N = ri()
a = rli()
ma = max(a)
mi = min(a)
if(ma - mi > 1):
    print("No")
elif(ma - mi == 1):
    l_ma = a.count(ma)
    l_mi = a.count(mi)
    if(ma <= l_mi):
        print("No")
    elif(l_mi + l_ma/2 >= ma):
        print("Yes")
    else:
        print("No")
else:
    if(a[0] == N-1):
        print("Yes")
    elif(N/a[0] >= 2):
        print("Yes")
    else:
        print("No")