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
// No sorceries shall prevail. //           
import java.util.Scanner; 
import java.io.PrintWriter;
import java.util.Arrays;

public class InVoker {	
	
	public static void main(String args[]) {
		
		Scanner inp=new Scanner(System.in);
		PrintWriter out=new PrintWriter(System.out);
		
		int n=inp.nextInt();
		long a[]=new long[n];
		int odd=0;
		long sum=0;
		for(int i=0;i<n;i++) {
			a[i]=inp.nextLong();
			sum+=a[i];
			if(a[i]%2==1)
				odd++;
		}
		int even=n-odd;
		Arrays.sort(a);
		long s1=0,s2=0;
		int z=Math.min(odd, even);
		for(int i=n-1,c=0;i>=0 && c<z+1;i--) {
			if(a[i]%2==1) {
				s1+=a[i];
				c++;
			}
		}
		for(int i=n-1,c=0;i>=0 && c<z;i--) {
			if(a[i]%2==0) {
				s1+=a[i];
				c++;
			}
		}
		for(int i=n-1,c=0;i>=0 && c<z+1;i--) {
			if(a[i]%2==0) {
				s2+=a[i];
				c++;
			}
		}
		for(int i=n-1,c=0;i>=0 && c<z;i--) {
			if(a[i]%2==1) {
				s2+=a[i];
				c++;
			}
		}
		out.println(sum-Math.max(s1, s2));
		out.close();
		inp.close();
	}

}