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
def fun(array,n):
	odd,even=[],[]
	l_odd,l_even=0,0
	for v in array:
		if v%2==0:
			even.append(v)
			l_even+=1
		else:
			odd.append(v)
			l_odd+=1
	if l_odd==0:
		even.sort()
		return sum(even[:l_even-1])
	if l_even==0:
		odd.sort()
		return sum(odd[:l_odd-1])
	odd.sort()
	even.sort()
	if (l_odd==l_even) or (l_odd==l_even+1 or l_even==l_odd+1):
		return 0
	elif l_odd>l_even:
		return sum(odd[:l_odd-l_even-1])
	else:
		return sum(even[:l_even-l_odd-1])

n=int(input())
array=list(map(int,input().split( )))
print(fun(array,n))