Polycarp has an array a consisting of n integers.

He wants to play a game with this array. The game consists of several moves. On the first move he chooses any element and deletes it (after the first move the array contains n-1 elements). For each of the next moves he chooses any element with the only restriction: its parity should differ from the parity of the element deleted on the previous move. In other words, he alternates parities (even-odd-even-odd-... or odd-even-odd-even-...) of the removed elements. Polycarp stops if he can't make a move.

Formally: 

  * If it is the first move, he chooses any element and deletes it; 
  * If it is the second or any next move: 
    * if the last deleted element was odd, Polycarp chooses any even element and deletes it; 
    * if the last deleted element was even, Polycarp chooses any odd element and deletes it. 
  * If after some move Polycarp cannot make a move, the game ends. 



Polycarp's goal is to minimize the sum of non-deleted elements of the array after end of the game. If Polycarp can delete the whole array, then the sum of non-deleted elements is zero.

Help Polycarp find this value.

Input

The first line of the input contains one integer n (1 ≤ n ≤ 2000) — the number of elements of a.

The second line of the input contains n integers a_1, a_2, ..., a_n (0 ≤ a_i ≤ 10^6), where a_i is the i-th element of a.

Output

Print one integer — the minimum possible sum of non-deleted elements of the array after end of the game.

Examples

Input


5
1 5 7 8 2


Output


0


Input


6
5 1 2 4 6 3


Output


0


Input


2
1000000 1000000


Output


1000000
import math
from collections import defaultdict, Counter, deque


def primeFactor(n):
	if n % 2 == 0:
		return 2
	i = 3
	while (i ** 2) <= n:
		if n % i == 0:
			return i 
		i += 1
	return n


def main():
	n = int(input())
	arr = list(map(int, input().split()))

	even = []
	odd = []
	for i in range(n):
		if arr[i] % 2 == 0:
			even.append(arr[i])
		else:
			odd.append(arr[i])

	even.sort(reverse=True)
	odd.sort(reverse=True)

	if len(even) > len(odd):
		f = even
		s = odd
	else:
		f = odd
		s = even

	diff = len(f) - len(s) - 1
	# print(diff)
	if diff <= 0:
		print(0)
		return 
	else:
		print(sum(f[-diff::1])) 

	 

if __name__ == "__main__":
	# t = int(input())
	t = 1
	for _ in range(t):
		main()







