You are given $n$ chips on a number line. The $i$-th chip is placed at the integer coordinate $x_i$. Some chips can have equal coordinates.

You can perform each of the two following types of moves any (possibly, zero) number of times on any chip:

• Move the chip $i$ by $2$ to the left or $2$ to the right for free (i.e. replace the current coordinate $x_i$ with $x_i - 2$ or with $x_i + 2$);
• move the chip $i$ by $1$ to the left or $1$ to the right and pay one coin for this move (i.e. replace the current coordinate $x_i$ with $x_i - 1$ or with $x_i + 1$).

Note that it's allowed to move chips to any integer coordinate, including negative and zero.

Your task is to find the minimum total number of coins required to move all $n$ chips to the same coordinate (i.e. all $x_i$ should be equal after some sequence of moves).

Input

The first line of the input contains one integer $n$ ($1 \le n \le 100$) — the number of chips.

The second line of the input contains $n$ integers $x_1, x_2, \dots, x_n$ ($1 \le x_i \le 10^9$), where $x_i$ is the coordinate of the $i$-th chip.

Output

Print one integer — the minimum total number of coins required to move all $n$ chips to the same coordinate.

Note

In the first example you need to move the first chip by $2$ to the right and the second chip by $1$ to the right or move the third chip by $2$ to the left and the second chip by $1$ to the left so the answer is $1$.

In the second example you need to move two chips with coordinate $3$ by $1$ to the left so the answer is $2$.

Samples

3
1 2 3

1

5
2 2 2 3 3

2