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.InputStreamReader;
import java.util.Arrays;
import java.util.Stack;
import java.util.StringTokenizer;

public class no2 {

	public static void main(String[] args) throws Exception {
		BufferedReader read = new BufferedReader(new InputStreamReader(System.in));
	
		int n = Integer.parseInt(read.readLine());
		
		StringTokenizer str = new StringTokenizer(read.readLine());
		int[] num = new int[n];
		Stack<Integer> odd = new Stack<>();
		Stack<Integer> even = new Stack<>();
		for ( int i = 0; i < n; i++ )
			num[i] = Integer.parseInt(str.nextToken());
		Arrays.sort(num);
		for ( int i = 0; i < n; i++ ) {
			if ( num[i] % 2 == 0 )
				even.add(num[i]);
			else
				odd.add(num[i]);
		}
		
		while ( !even.isEmpty() && !odd.isEmpty() ) {
			even.pop(); odd.pop();
		}
		
		if ( !even.isEmpty() ) {
			even.pop();
		} else if ( !odd.isEmpty() ) {
			odd.pop();
		}
		long sum = 0;
		while ( !even.isEmpty() ) {
			sum += even.pop();
		}
		while ( !odd.isEmpty() ) {
			sum += odd.pop();
		}
		System.out.println(sum);
	}

}
