Sum of Vectors

There are $N$ two-dimensional vectors. You can apply an operation that multiplies each coordinate by $-1$. For example, if $v = (x, y)$, you can transform it into one of the following four forms.

• 1: $(x, y)$
• 2: $(-x, y)$
• 3: $(x, -y)$
• 4: $(-x, -y)$

Among the $N$ vectors, choose two vectors $v_i$ and $v_j$ and write a program that finds the minimum value of $|v_i + v_j|$. Each of the two vectors may be transformed into one of the four forms above by applying the operation.

The first line gives the number of vectors $N$ ($2 \le N \le 100{,}000$). Each of the next $N$ lines gives the coordinates $x_i$, $y_i$ of the $i$-th vector $v_i$ ($-10{,}000 \le x, y \le 10{,}000$), one vector per line.

On the first line, print four integers $i$, $k_1$, $j$, $k_2$ separated by spaces. $i$ and $j$ are the indices of the chosen vectors, and $k_1$, $k_2$ are the numbers of the operations applied. If several answers attain the minimum, print any one of them.

The sum of two vectors $v = (x_v, y_v)$ and $u = (x_u, y_u)$ is $s = v + u = (x_v + x_u, y_v + y_u)$.

For a vector $v = (x, y)$, $|v|$ is $\sqrt{x^2 + y^2}$.