ACQUIRE - Land Acquisition
题意翻译
## 题目大意
约翰准备扩大他的农场，眼下必须购买 N 块长方形的土地。如果约翰单买一块土地，价格就是土地的面积。他也可以选择并购一组土地，并购的价格为这些土地中最大的长乘以最大的宽。
比如约翰并购一块 3 × 5 和一块 5 × 3 的土地，他只需要支付 5 × 5 = 25 元，比分开买合算。
约翰发现，将这些土地分成不同的小组来并购可以节省经费。给定每份土地的尺寸，请你帮助他计算购买所有土地所需的最小费用。
### 输入格式
- 第一行：单个整数 N， 1 ≤ N ≤ 50000
- 第二行到第 N + 1 行：第 i + 1 行有两个整数 Hi 和 Wi， 1 ≤ Hi; Wi ≤ 106
### 输出格式
- 单个整数：购买所有土地的最小费用
#### 样例输入
4
100 1
15 15
20 5
1 100
#### 样例输出
500
### 解释：
>分三组：第一组 100 × 1，第二组 1 × 100，
第三组是 20 × 5 和 15 × 15，价格分别为 100、100 和 300
题目描述
```
<pre style="font-family: 'Andale Mono', 'Courier New', Courier, monospace;">```
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GOLD PROBLEMS
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Three problems numbered 1 through 3
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Problem 1: Land Acquisition [Paul Christiano, 2007]
Farmer John is considering buying more land for the farm and has
his eye on N (1 <= N <= 50,000) additional rectangular plots, each
with integer dimensions (1 <= width_i <= 1,000,000; 1 <= length_i
<= 1,000,000).
If FJ wants to buy a single piece of land, the cost is $1/square
unit, but savings are available for large purchases. He can buy
any number of plots of land for a price in dollars that is the width
of the widest plot times the length of the longest plot. Of course,
land plots cannot be rotated, i.e., if Farmer John buys a 3x5 plot
and a 5x3 plot in a group, he will pay 5x5=25.
FJ wants to grow his farm as much as possible and desires all the
plots of land. Being both clever and frugal, it dawns on him that
he can purchase the land in successive groups, cleverly minimizing
the total cost by grouping various plots that have advantageous
width or length values.
Given the number of plots for sale and the dimensions of each,
determine the minimum amount for which Farmer John can purchase all
PROBLEM NAME: acquire
INPUT FORMAT:
* Line 1: A single integer: N
* Lines 2..N+1: Line i+1 describes plot i with two space-separated
integers: width_i and length_i
SAMPLE INPUT:
4
100 1
15 15
20 5
1 100
INPUT DETAILS:
There are four plots for sale with dimensions as shown.
OUTPUT FORMAT:
* Line 1: The minimum amount necessary to buy all the plots.
SAMPLE OUTPUT:
500
OUTPUT DETAILS:
The first group contains a 100x1 plot and costs 100. The next group
contains a 1x100 plot and costs 100. The last group contains both the 20x5
plot and the 15x15 plot and costs 300. The total cost is 500, which is
minimal.
```
```