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 ParityAlternatedDeletions {

	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		int arr[] = new int[n];
		List<Integer> l = new ArrayList<>();
		List<Integer> l1 = new ArrayList<>();
		for(int i=0;i<n;i++) {
			arr[i] = sc.nextInt();
		}
		Arrays.sort(arr);
		for(int i=0;i<n;i++) {
			if(arr[i]%2==0) {
				l1.add(arr[i]);
			}
			else {
				l.add(arr[i]);
			}
		}
		boolean x = true;
		if(l.size()>=l1.size()) {
			for(int i=0;i<n;i++) {
				if(x) {
					if(l.size()==0) {
						break;
					}
					l.remove(l.size()-1);
					x = false;
				}
				else {
					if(l1.size()==0) {
						break;
					}
					l1.remove(l1.size()-1);
					x = true;
				}
			}
		}
		else {
			for(int i=0;i<n;i++) {
				if(x) {
					if(l1.size()==0) {
						break;
					}
					l1.remove(l1.size()-1);
					x = false;
				}
				else {
					if(l.size()==0) {
						break;
					}
					l.remove(l.size()-1);
					x = true;
				}
			}
		}
		int sum = 0;
		boolean f = false;
		if(l.size()==0 && l1.size()==0) {
			f = true;
		}
		else {
			if(l.size()>l1.size()) {
				for(int i=0;i<l.size();i++) {
					sum+=l.get(i);
				}
			}
			else {
				for(int i=0;i<l1.size();i++) {
					sum+=l1.get(i);
				}
			}
		}
		if(f) {
			System.out.println(0);
		}
		else {
			System.out.println(sum);
		}
	}

}