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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Collections;
import java.util.Comparator;
import java.util.StringTokenizer;

public class Answer {
	public static void main(String[] args) {
	      MyScanner in = new MyScanner();
	      int n = in.nextInt(); 
	      ArrayList<Integer> oddParity = new ArrayList<>();
	      ArrayList<Integer> evenParity = new ArrayList<>();
	      int sum = 0;
	      for (int i = 0; i < n; i++) {
	    	  int ele = in.nextInt(); 
	    	  sum += ele;
	    	  if ((ele & 1) == 1) evenParity.add(ele); 
	    	  else oddParity.add(ele);
	      }
	      ReverseSort reverseSort = new ReverseSort(); 
	      Collections.sort(oddParity, reverseSort);
	      Collections.sort(evenParity, reverseSort);
	      int sizeDifference = Math.abs(oddParity.size() - evenParity.size());
	      if (sizeDifference <= 1) {
	    	  System.out.println(0);
	      } else {
	    	  int k = Math.min(oddParity.size(), evenParity.size()); 
	    	  int overall = sum; 
	    	  overall -= getExcess(oddParity, k); 
	    	  overall -= getExcess(evenParity, k);
	    	  if (oddParity.size() > evenParity.size()) {
	    		  overall -= oddParity.get(k); 
	    	  } else {
	    		  overall -= evenParity.get(k); 
	    	  }
	    	  System.out.println(overall);
	      }
	}
	
	private static int getExcess(ArrayList<Integer> arrayList, int k) {
		int sum = 0; 
		for (int i = 0; i < k; i++) {
			sum += arrayList.get(i); 
		}
		return sum; 
	}

	public static PrintWriter out;
	   public static class MyScanner {
	      BufferedReader br;
	      StringTokenizer st;

	      public MyScanner() {
	         br = new BufferedReader(new InputStreamReader(System.in));
	      }

	      String next() {
	          while (st == null || !st.hasMoreElements()) {
	              try {
	                  st = new StringTokenizer(br.readLine());
	              } catch (IOException e) {
	                  e.printStackTrace();
	              }
	          }
	          return st.nextToken();
	      }

	      int nextInt() {
	          return Integer.parseInt(next());
	      }

	      long nextLong() {
	          return Long.parseLong(next());
	      }

	      double nextDouble() {
	          return Double.parseDouble(next());
	      }

	      String nextLine(){
	          String str = "";
		      try {
		         str = br.readLine();
		      } catch (IOException e) {
		         e.printStackTrace();
		      }
		      return str;
	      }
	   }
}

class ReverseSort implements Comparator<Integer> {
	@Override
	public int compare(Integer o1, Integer o2) {
		if (o1 == o2) return 0; 
		else if (o1 > o2) return -1; 
		return +1;
	}
}
