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 sun.reflect.generics.tree.Tree;

import java.util.Arrays;
import java.util.Scanner;
import java.util.TreeMap;

public class AlternateDeletions {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int[] a = new int[n];
        int e=0, o=0;
        for(int i=0; i<n; i++)
        {
            a[i] = sc.nextInt();
            if(a[i]%2 == 0)
                e++;
            else
                o++;
        }

        int[] even = new int[e];
        int[] odd = new int[o];
        int k=0,l=0;
        for(int i=0; i<n; i++)
        {
            if(a[i]%2 == 0)
                even[k++] = a[i];
            else
                odd[l++] = a[i];
        }

        Arrays.sort(even);
        Arrays.sort(odd);
/*
        for(int i=0; i<e; i++)
            System.out.println(even[i]);
        for(int i=0; i<o; i++)
            System.out.println(odd[i]);
*/

    int min = Math.min(o,e);
    int max = Math.max(o,e);

    long sumo = 0l;
    long sume = 0l;
    if(max == o)
    {
        for(int i=0; i<= max-min-2; i++)
            sumo+=odd[i];
    }
    else
        {
            for(int i=0; i<= max-min-2; i++)
                sume+=even[i];
        }
    //    System.out.println("odd sum : "+sumo);

    //        System.out.println("even sum : "+sume);

        if(sume !=0)
            System.out.println(sume);
        else
            System.out.println(sumo);

     /*   TreeMap<Integer, Integer> evenTree = new TreeMap<>();
        TreeMap<Integer, Integer> oddTree = new TreeMap<>();

        for(int i=0; i<n; i++)
        {
            if(a[i] % 2 == 0)
            {
                if(evenTree.containsKey(a[i]))
                    evenTree.put(a[i], evenTree.get(a[i])+1);
                else
                    evenTree.put(a[i], 1);
            }
            else
            {
                if(oddTree.containsKey(a[i]))
                    oddTree.put(a[i], oddTree.get(a[i])+1);
                else
                    oddTree.put(a[i],1);
            }
        }

        System.out.println("even : "+evenTree+ evenTree.size());
        System.out.println("odd : "+oddTree+ oddTree.size());

        while(oddTree.size()>=0 || evenTree.size()>=0)
        {
            if (oddTree.size() >= evenTree.size())
            {
                System.out.println("Last : "+oddTree.lastKey());
                if(oddTree.get(oddTree.lastKey()) > 0)
                oddTree.put(oddTree.lastKey(),oddTree.get(oddTree.lastKey()) -1);
                System.out.println("last key value : "+oddTree.get(oddTree.lastKey()));
                if(oddTree.get(oddTree.lastKey()) == 0)
                    oddTree.remove(oddTree.lastKey());
                System.out.println("After del "+evenTree);

            }
            else
            {
                oddTree.put(evenTree.lastKey(), evenTree.get(evenTree.lastKey()) -1);
                if(evenTree.get(evenTree.lastKey())== 0)
                    evenTree.remove(evenTree.lastKey());
            }
        }
        System.out.println("e "+evenTree);
        System.out.println("o :"+oddTree);

        */

    }
}
