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
//package Codef;

import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.PriorityQueue;
import java.util.Scanner;

public class B_1144 {

	public static void main(String[] args) {
		// TODO Auto-generated method stub
		Scanner s = new Scanner(System.in);
		int n = s.nextInt();
		int[] a = new int[n];;
		//int[] l = new int[n];
		//int[] r = new int[n];
		PriorityQueue<Integer> l1 = new PriorityQueue<>();
		PriorityQueue<Integer> l2 = new PriorityQueue<>();

		int co=0,ce=0;
		for(int i=0;i<n;i++) {
			a[i] = s.nextInt();
			if(a[i]%2 == 0) {
			   //ce++;
				l1.add(a[i]);
				//k++;
			}
			else { 
				//co++;
				l2.add(a[i]);
			}
		}
		//System.out.println(l2.size());
		int dif = Math.abs(l1.size()-l2.size());
		if(dif <= 1) {
			System.out.println(0);
		}else {
			PriorityQueue<Integer> l3 ;
			if(l1.size() > l2.size()) {
				l3 = l1;
			}else {
				l3 = l2;
			}
			long sum=0;
			 for(int i=0;i<dif-1;i++) {
				 //System.out.println(l3.peek());
				 sum+= l3.poll();
			 }
			 System.out.println(sum);

		}
		
	}

}
