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.Arrays;
import java.util.Random;
import java.util.Scanner;

public class B {
	static Random random;
	private static void mySort(long[] s) {
        for (int i = 0; i < s.length; ++i) {
            int j = random.nextInt(i + 1);
            long t = s[i];
            s[i] = s[j];
            s[j] = t;
        }
        Arrays.sort(s);
    }
	
	public static void main(String[] args) {
		random = new Random(543534151132L + System.currentTimeMillis());
		Scanner scan=new Scanner(System.in);
		int nb=scan.nextInt();
		int nodd=0;
		int neven=0;
		long tmp;
		long[] oddTmp=new long[nb];
		long[] evenTmp=new long[nb];
		for(int i=0;i<nb;i++) {
			tmp=scan.nextLong();
			if(tmp%2==0)evenTmp[neven++]=tmp;
			else oddTmp[nodd++]=tmp;
		}
		long[] odd=new long[nodd];
		long[] even=new long[neven];
		for(int i=0;i<nodd;i++)odd[i]=oddTmp[i];
		for(int i=0;i<neven;i++)even[i]=evenTmp[i];
		mySort(odd);
		mySort(even);
		long sum=0;
		if(even.length>=odd.length) {
			for(int i=0;i<nb;i++) {
				if(i%2==0) {
					if(neven>0)neven--;
					else break;
				}
				else {
					if(nodd>0)nodd--;
					else break;
				}
			}			
			for(int i=0;i<neven;i++)sum+=even[i];
			for(int i=0;i<nodd;i++)sum+=odd[i];
		}else {
			for(int i=0;i<nb;i++) {
				if(i%2!=0) {
					if(neven>0)neven--;
					else break;
				}
				else {
					if(nodd>0)nodd--;
					else break;
				}
			}
			for(int i=0;i<neven;i++)sum+=even[i];
			for(int i=0;i<nodd;i++)sum+=odd[i];
		}
		
		
		System.out.println(sum);
		scan.close();
	}
}	