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
from sys import stdin,stdout
from itertools import combinations
from collections import defaultdict
import math
import heapq

def listIn():
    return list((map(int,stdin.readline().strip().split())))

def stringListIn():
    return([x for x in stdin.readline().split()])
    
def intIn():
    return (int(stdin.readline()))

def stringIn():
    return (stdin.readline().strip())


if __name__=="__main__":
    n=intIn()
    a=listIn()
    e,o=[],[]
    for i in range(n):
        if a[i]%2==0:
            e.append(a[i])
        else:
            o.append(a[i])
    #print(e,o)
    if len(e)==n:
        e.sort()
        print(sum(e[:-1]))
        exit(0)
    if len(o)==n:
        o.sort()
        print(sum(o[:-1]))
        exit(0)
    e1,o1=len(e),len(o)
    e.sort()
    o.sort()
    if e1==o1:
        print(0)
    else:
        if e1>o1:
            d=e1-o1
            print(sum(e[:d-1]))
        else:
            d=o1-e1
            print(sum(o[:d-1]))
                
    
        
    
    
    
    
    
    
    
    
