Yaroslav has an array that consists of n integers. In one second Yaroslav can swap two neighboring array elements. Now Yaroslav is wondering if he can obtain an array where any two neighboring elements would be distinct in a finite time.

Help Yaroslav.

Input

The first line contains integer n (1 ≤ n ≤ 100) — the number of elements in the array. The second line contains n integers a1, a2, ..., an (1 ≤ ai ≤ 1000) — the array elements.

Output

In the single line print "YES" (without the quotes) if Yaroslav can obtain the array he needs, and "NO" (without the quotes) otherwise.

Examples

Input

1
1


Output

YES


Input

3
1 1 2


Output

YES


Input

4
7 7 7 7


Output

NO

Note

In the first sample the initial array fits well.

In the second sample Yaroslav can get array: 1, 2, 1. He can swap the last and the second last elements to obtain it.

In the third sample Yarosav can't get the array he needs.
n = int(input())
arr = list(map(int,input().split()))
arr.sort()
lst = []
i = 0
j = n-1
turn = 0
while i<=j:
    if turn%2==0:
        lst.append(arr[i])
        i += 1
    else:
        lst.append(arr[j])
        j -= 1
    turn += 1
lst = [-1]+lst
count = cnt = 0
for i in range(-1,-n-1,-1):
    if lst[i]!=lst[i-1]:
        break
    else:
        count += 1
if count:
    cnt = 0
    num = lst[-1]
    for i in range(1,n+1):
        if num!=lst[i]:
            cnt += 1
        else:
            break
    if count<=cnt:
        print("YES")
    else:
        print("NO")
else:
    print("YES")

