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.
def main():
    possible = True
    limit = -1
    a = {}
    count = {}
    for i in range(1, 1001):
        count[i] = 0
    n = int(raw_input())
    if n % 2 == 1:
        limit = ((n / 2) + 1) + 1
    else:
        limit = (n / 2) + 1
    input = raw_input()
    line = input.split(" ")
    for i in xrange(len(line)):
        a[i] = int(line[i])
        count[a[i]] += 1
        if count[a[i]] >= limit:
            possible = False
    if possible:
        print "YES"
    else:
        print "NO"
    
main()
