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 countSetBits(n): 

	count = 0
	while (n): 
		n &= (n-1) 
		count+=1
	
	return count 

L1=[]
L2=[]
n=int(input())
L=[int(x) for x in input().split()]
for i in L:
    c=countSetBits(i)
    if i%2==0:
        L2.append(i)
    else:
        L1.append(i)
L1=sorted(L1)
L2=sorted(L2)

status=0
if len(L1)==len(L2):
    print(0)
    status=1
elif max(len(L1),len(L2))-min(len(L1),len(L2))==1:
    print(0)
    status=1
elif len(L1)>len(L2):
    c1=len(L1)-1
    c2=c1-len(L2)
    Add=0
    for x1 in range(0,c2):
        Add+=L1[x1]
elif  len(L2)>len(L1):
    c1=len(L2)-1
    c2=c1-len(L1)
    Add=0
    for x2 in range(0,c2):
        Add+=L2[x2]
if status==0:
    print(Add)
