A8347. Minimum Sum

You are given a set of $n$ vectors on a plane. For each vector you are allowed to multiply any of its coordinates by -1. Thus, each vector $v_{i}=(x_{i},y_{i})$ can be transformed into one of the following four vectors:

- $v_{i}^{1}=(x_{i},y_{i})$ ,
- $v_{i}^{2}=(-x_{i},y_{i})$ ,
- $v_{i}^{3}=(x_{i},-y_{i})$ ,
- $v_{i}^{4}=(-x_{i},-y_{i})$ .

You should find two vectors from the set and determine which of their coordinates should be multiplied by -1 so that the absolute value of the sum of the resulting vectors was minimally possible. More formally, you should choose two vectors $v_{i}$ , $v_{j}$ ( $1<=i,j<=n,i≠j$ ) and two numbers $k_{1}$ , $k_{2}$ ( $1<=k_{1},k_{2}<=4$ ), so that the value of the expression $|v_{i}^{k_{1}}+v_{j}^{k_{2}}|$ were minimum.

The first line contains a single integer $n$ ( $2<=n<=10^{5}$ ). Then $n$ lines contain vectors as pairs of integers " $x_{i}$ $y_{i}$ " ( $-10000<=x_{i},y_{i}<=10000$ ), one pair per line.

Print on the first line four space-separated numbers " $i$ $k_{1}$ $j$ $k_{2}$ " — the answer to the problem. If there are several variants the absolute value of whose sums is minimum, you can print any of them.

A sum of two vectors $v=(x_{v},y_{v})$ and $u=(x_{u},y_{u})$ is vector $s=v+u=(x_{v}+x_{u},y_{v}+y_{u})$ .

An absolute value of vector $v=(x,y)$ is number .

In the second sample there are several valid answers, such as:

(3 1 4 2), (3 1 4 4), (3 4 4 1), (3 4 4 3), (4 1 3 2), (4 1 3 4), (4 2 3 1).