CF120J.Minimum Sum
普及/提高-
通过率:0%
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题目描述
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 vi=(xi,yi) can be transformed into one of the following four vectors:
- vi1=(xi,yi) ,
- vi2=(−xi,yi) ,
- vi3=(xi,−yi) ,
- vi4=(−xi,−yi) .
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 vi , vj ( 1<=i,j<=n,i=j ) and two numbers k1 , k2 ( 1<=k1,k2<=4 ), so that the value of the expression ∣vik1+vjk2∣ were minimum.
输入格式
The first line contains a single integer n ( 2<=n<=105 ). Then n lines contain vectors as pairs of integers " xi yi " ( −10000<=xi,yi<=10000 ), one pair per line.
输出格式
Print on the first line four space-separated numbers " i k1 j k2 " — the answer to the problem. If there are several variants the absolute value of whose sums is minimum, you can print any of them.
输入输出样例
输入#1
5 -7 -3 9 0 -8 6 7 -8 4 -5
输出#1
3 2 4 2
输入#2
5 3 2 -4 7 -6 0 -8 4 5 1
输出#2
3 4 5 4
说明/提示
A sum of two vectors v=(xv,yv) and u=(xu,yu) is vector s=v+u=(xv+xu,yv+yu) .
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).