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.Scanner;

public class Main{

	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int n[] = new int[sc.nextInt()];
		int even = 0;
		int odd = 0;
		for (int i = 0; i < n.length; i++) {
			n[i] = sc.nextInt();
			if (n[i] % 2 == 0) even++;
			else odd++;	
		}
		Arrays.sort(n);
		int times = 0;
		int ans = 0 ;
		if(Math.abs(even-odd)>=2) {
			if(even==0||odd==0) {
				for(int i=0;i<n.length-1;i++)ans+=n[i];
				System.out.println(ans);
			}
			else if(even>odd) { 
				times = even-odd-1;
				int x = 0;
				while(true) {
					for(int i=0;i<n.length;i++) {
						if(n[i]%2==0) {
							ans+=n[i];
							x++;
							if(times==x)break;
						}
					}
					break;
				}
				System.out.println(ans);
			}
			else if(even<odd) {
				times = odd-even-1;
				int x = 0;
				while(true) {
					for(int i=0;i<n.length;i++) {
						if(n[i]%2!=0) {
							ans+=n[i];
							x++;
							if(times==x)break;
						}
					}
					break;
				}
				System.out.println(ans);
			}
			
		}
		else if(n.length==1) System.out.println(n[0]);
		else System.out.println(0);
	}
}
	  	  							    		 		     			