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
#!/usr/bin/env python
from __future__ import division, print_function

import io
import os
import sys

if sys.version_info[0] < 3:
    from __builtin__ import xrange as range
    from cStringIO import StringIO
    from future_builtins import ascii, filter, hex, map, oct, zip
else:
    from io import BytesIO as StringIO

sys.stdout, stream = io.IOBase(), StringIO()
sys.stdout.flush = lambda: os.write(1, stream.getvalue()) and not stream.truncate(0) and stream.seek(0)
sys.stdout.write = stream.write if sys.version_info[0] < 3 else lambda s: stream.write(s.encode())

input, flush = sys.stdin.readline, sys.stdout.flush
input = StringIO(os.read(0, os.fstat(0).st_size)).readline


def main():
    n = int(input())
    a = list(map(int, input().split()))
    p = [0, 0]

    e = []
    o = []

    for i in a:
        p[i & 1] += 1
        if i & 1:
            o.append(i)
        else:
            e.append(i)

    e.sort(reverse=True)
    o.sort(reverse=True)

    if abs(p[0] - p[1]) < 2:
        print(0)
    else:
        if p[0] < p[1]:
            d = sum(e) + sum(o[:p[0] + 1])
        else:
            d = sum(o) + sum(e[:p[1] + 1])

        print(sum(a) - d)


if __name__ == '__main__':
    main()
