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.*;
import java.util.Arrays;
 import java.util.ArrayList;
 
public class siri{
	public static void main(String[] args){
		Scanner sc = new Scanner(System.in);
		 
		int pasuxi = 0; 
		 
		int zoma = sc.nextInt();
		ArrayList<Integer> knt = new ArrayList<Integer>();
		ArrayList<Integer> luw = new ArrayList<Integer>();
		
		for(int j = 0; j < zoma; j++){
		    int wevri = sc.nextInt();
		    if(wevri % 2 == 0){
		        luw.add(wevri);
		    }
		    else{
		        knt.add(wevri);
		    }
		}
		
		
		Collections.sort(knt);
		Collections.sort(luw);
		
		if(luw.size() >= knt.size() ){
		    for(int i = 0; i<luw.size()-1-knt.size();i++){
		        pasuxi += luw.get(i);
		    }
		}
		else{
		    for(int i = 0; i<knt.size()-1-luw.size();i++){
		        pasuxi += knt.get(i);
		    }
		}
		System.out.println(pasuxi);
		
	}
}