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 java.util.*;
public class Main {

	public static void main(String[] args) {
		Scanner reader=new Scanner(System.in);
		int n=reader.nextInt();
		int t;
		int j=0,o=0;
		int js[]=new int[n];
		int os[]=new int[n];
		for(int i=0;i<n;i++) {
			t=reader.nextInt();
			if(t%2==1) {
				js[j]=t;
				j++;
			}else {
				os[o]=t;
				o++;
			}
		}
		Arrays.sort(js, 0, j);
		Arrays.sort(os, 0, o);
		int sum=0;
		if(o==0) {
			for(int i=0;i<j-1;i++)
				sum+=js[i];
		}else if(j==0) {
			for(int i=0;i<o-1;i++)
				sum+=os[i];
		}else if(o==j||o==j+1||j==o+1) {
			sum=0;
		}else if(o>j+1) {
			for(int i=0;i<o-j-1;i++) {
				sum+=os[i];
			}
		}else if(j>o+1) {
			for(int i=0;i<j-o-1;i++)
				sum+=js[i];
		}
		System.out.println(sum);
	}

}
		    	 					  	  	 				 	  	 	