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
m = int(input())
# for i in range(m):
# 	s=input()
# 	a=[]
# 	c=0
# 	i=0
# 	while(i<len(s)):
# 		a.append(ord(s[i]))
# 		i+=1
# 	a.sort()
# 	i=0
# 	while(i<len(a)-1):
# 		if(a[i+1]-a[i]!=1):
# 			print("no")
# 			c=1
# 			break
# 		i+=1
# 	if(c==0):
# 		print("yes")
a=list(map(int,input().split()))
a.sort()
i=0
s=0
o=0
e=0
while(i<len(a)):
	if(a[i]%2!=0):
		o+=1
	else:
		e+=1
	i+=1
if(e==o or e-o==1 or o-e==1):
	print(0)
elif(o==0 or e==0):
	print(sum(a)-a[len(a)-1])
else:
	if(o>e):
		t=o-e-1
		i=1
		j=0
		while(i<=t and j<len(a)):
			if(a[j]%2!=0):
				s+=a[j]
				i+=1
			j+=1
		print(s)
	else:
		t=e-o-1
		i=1
		j=0
		while(i<=t and j<len(a)):
			if(a[j]%2==0):
				s+=a[j]
				i+=1
			j+=1
		print(s)
