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.math.*;
public class Sol {
      public static void main(String[] args) {
    	  Scanner ip=new Scanner(System.in);
    	  int n=ip.nextInt();
    	  int arr[]=new int[n];
    	  int oddC=0;
    	  int evenC=0;
    	  for(int i=0;i<n;i++) {
    		  arr[i]=ip.nextInt();
    		  if(arr[i]%2==0) {
    			  evenC++;  
    		  }else {
    			  oddC++;
    		  }
    	  }
    	  int evenA[]=new int[evenC];
    	  int oddA[]=new int[oddC];
    	  int j=0;
    	  int k=0;
    	  for(int i=0;i<n;i++) {
    		  if(arr[i]%2==0) {
    			  evenA[j]=arr[i];
    			  j++;
    		  }else {
    			  oddA[k]=arr[i];
    			  k++;
    		  }
    	  }
    	  if(Math.abs(oddC-evenC)<=1) {
    		  System.out.println(0);
    	  }else {
    		  Arrays.sort(oddA);
    		  Arrays.sort(evenA);
    		  if(oddA.length>evenA.length) {
    			  int sum=0;
    			  for(int m=0;m<oddA.length-evenA.length-1;m++) {
    				  sum+=oddA[m];
    			  }
    			  System.out.println(sum);
    		  }else {
    			  int sum=0;
    			  for(int m=0;m<evenA.length-oddA.length-1;m++) {
    				  sum+=evenA[m];
    			  }
    			  System.out.println(sum);
    		  }
    		  
    	  }
      }
}