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
// https://codeforces.com/problemset/problem/1144/B

// https://codeforces.com/blog/entry/66307

import java.util.ArrayList;
import java.util.Collections;
import java.util.List;
import java.util.Scanner;

public class Solution {
	
	public static void main(String[] args) {
		Scanner read = new Scanner(System.in);
		
		int n = read.nextInt();
		
		List<Integer> oddNumbers = new ArrayList<>();
		List<Integer> evenNumbers = new ArrayList<>();
		int sum = 0;
		
		for (int i = 0; i < n; ++i) {
			int a = read.nextInt();
			if (a % 2 != 0) { oddNumbers.add(a); }
			else { evenNumbers.add(a); }
			sum += a;
		}
		
		Collections.sort( oddNumbers, Collections.reverseOrder() );
		Collections.sort( evenNumbers, Collections.reverseOrder() );
		
		int k = Math.min(oddNumbers.size(), evenNumbers.size());
		for (int i = 0; i < k; ++i) {
			sum -= oddNumbers.get(i);
			sum -= evenNumbers.get(i);
		}
		
		if (oddNumbers.size() != evenNumbers.size()) {
			sum -= 
				(oddNumbers.size() > evenNumbers.size()) 
				? oddNumbers.get(k) 
				: evenNumbers.get(k);
		}
		
		System.out.println(sum);
		
		// Close scanner
		read.close();
	}

}