Codeforces158E Dividing Kingdom 暴力枚举 + 可持久化线段树

E. Dividing Kingdom

time limit per test

2 seconds

memory limit per test

256 megabytes

input

standard input

output

standard output

A country called Flatland is an infinite two-dimensional plane. Flatland has n cities, each of them is a point on the plane.

Flatland is ruled by king Circle IV. Circle IV has 9 sons. He wants to give each of his sons part of Flatland to rule. For that, he wants to draw four distinct straight lines, such that two of them are parallel to the Ox axis, and two others are parallel to the Oy axis. At that, no straight line can go through any city. Thus, Flatland will be divided into 9 parts, and each son will be given exactly one of these parts. Circle IV thought a little, evaluated his sons' obedience and decided that the i-th son should get the part of Flatland that has exactly aicities.

Help Circle find such four straight lines that if we divide Flatland into 9 parts by these lines, the resulting parts can be given to the sons so that son number i got the part of Flatland which contains ai cities.

Input

The first line contains integer n (9 ≤ n ≤ 105) — the number of cities in Flatland. Next n lines each contain two space-separated integers: xi, yi ( - 109 ≤ xi, yi ≤ 109) — the coordinates of the i-th city. No two cities are located at the same point. The last line contains nine space-separated integers: .

Output

If there is no solution, print a single integer -1.

Otherwise, print in the first line two distinct real space-separated numbers: x1, x2 — the abscissas of the straight lines that are parallel to the Oy axis. And in the second line print two distinct real space-separated numbers: y1, y2 — the ordinates of the straight lines, parallel to the Ox. If there are multiple solutions, print any of them.

When the answer is being checked, a city is considered to lie on a straight line, if the distance between the city and the line doesn't exceed 10 - 6. Two straight lines are considered the same if the distance between them doesn't exceed 10 - 6.

Examples

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output

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output

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Note

The solution for the first sample test is shown below:

The solution for the second sample test is shown below:

There is no solution for the third sample test.

题意:

将平面用两条垂直于x轴的直线和两条垂直与y轴的直线划分成如图所示的九个区域,要求每个区域内的点为一定的数目(顺序随意),问这四条直线的坐标。如果不能输出-1。

思路:

先将点离散化,再插入按y值建树的可持久化线段树,每个x值一棵树。这样就可以快速的查一个矩形区域内的点的个数。然后暴力全排列枚举每个区域内点的个数。再用建好的可持久化线段树检查即可。具体方法是根据枚举的区域内的点的个数,可以知道垂直于x轴分出的三个区域内点的个数,这样就可以确定直线的x值,再这样确定两个y值。再分别检查划分出的区域内的点是否和枚举的相同。如果相同,就可以输出了。

 

 

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