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Problem 1094. -- Is Bigger Smarter?

## Is Bigger Smarter?

Time Limit: 1 Sec  Memory Limit: 64 MB  Special Judge
Submit: 701  Solved: 390
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## Description

Some people think that the bigger an elephant is, the smarter it is. To disprove this, you want to analyze a collection of elephants and place as large a subset of elephants as possible into a sequence whose weights are increasing but IQ's are decreasing.

## Input

The input will consist of data for a bunch of elephants, at one elephant per line terminated by the end-of-file. The data for each particular elephant will consist of a pair of integers: the first representing its size in kilograms and the second representing its IQ in hundredths of IQ points. Both integers are between 1 and 10,000. The data contains information on at most 1,000 elephants. Two elephants may have the same weight, the same IQ, or even the same weight and IQ.

## Output

The first output line should contain an integer n, the length of elephant sequence found. The remaining n lines should each contain a single positive integer representing an elephant. Denote the numbers on the ith data line as W[i] and S[i]. If these sequence of n elephants are a[1], a[2],..., a[n] then it must be the case that W[a[1]] < W[a[2]] < ... < W[a[n]] and S[a[1]] > S[a[2]] > ... > S[a[n]] In order for the answer to be correct, n must be as large as possible. All inequalities are strict: weights must be strictly increasing, and IQs must be strictly decreasing. Your program can report any correct answer for a given input.

## Sample Input

```6008 1300
6000 2100
500 2000
1000 4000
1100 3000
6000 2000
8000 1400
6000 1200
2000 1900

```

```4
4
5
9
7

```

## Source

Waterloo Local Contest Oct. 7, 1997

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