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B. Parity Alternated Deletions

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputPolycarp 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 $$$n$$$ ($$$1 \le n \le 2000$$$) — the number of elements of $$$a$$$.

The second line of the input contains $$$n$$$ integers $$$a_1, a_2, \dots, a_n$$$ ($$$0 \le a_i \le 10^6$$$), 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

Codeforces (c) Copyright 2010-2021 Mike Mirzayanov

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