题目描述
Problem Description
In the recently proposed Visual Python++ programming language, a block of statements is represented as a rectangle of characters with the top-left corner at coordinates \((r_1, c_1)\) and the bottom-right corner at \((r_2, c_2)\). All characters at locations \((r, c)\) where \(r_1 \leq r \leq r_2\) and \(c_1 \leq c \leq c_2\) are considered to belong to that block. Among these locations, those with \(r = r_1\) or \(r = r_2\) or \(c = c_1\) or \(c = c_2\) are called borders.
Statement blocks can be nested (rectangles contained within other rectangles) to an arbitrary level. In a syntactically correct program, every two statement blocks are either nested (one contained within the other) or disjoint (not overlapping). In both cases, their borders may not overlap.
Programmers are not expected to draw the many rectangles contained in a typical program – this takes too long, and Visual Python++ would not have a chance to become the next ICPC programming language. So a programmer only has to place a character 'p' in the top-left corner of the rectangle and a character 'y' in the bottom-right corner. The parser will automatically match up the appropriate corners to obtain the nesting structure of the program.
Your team has just been awarded a five-hour contract to develop this part of the parser.
Input Format
The first line of the input contains an integer \(n (1 \leq n \leq 10^5)\), the number of corner pairs. Each of the next \(n\) lines contains two integers \(r\) and \(c (1 \leq r, c \leq 10^9)\), specifying that there is a top-left corner at row \(r\) and column \(c\) of the program you are parsing. Following that are \(n\) lines specifying the bottom-right corners in the same way. All corner locations are distinct.
Output Format
Display \(n\) lines, each containing one integer. A number \(j\) in line \(i\) means that the \(i^{th}\) top-left corner and the \(j^{th}\) bottom-right corner form one rectangle. Top-left and bottom-right corners are each numbered from 1 to \(n\) in the order they appear in the input. The output must be a permutation of the numbers from 1 to \(n\) such that the matching results in properly nested rectangles. If there is more than one valid matching, any one will be accepted. If no such matching exists, display syntax error.
Sample Input and Output
Input Sample #1
2
4 7
9 8
14 17
19 18
Output Sample #1
2
1
Input Sample #2
2
4 7
14 17
9 8
19 18
Output Sample #2
1
2
Input Sample #3
2
4 8
9 7
14 18
19 17
Output Sample #3
syntax error
Input Sample #4
3
1 1
4 8
8 4
10 6
6 10
10 10
Output Sample #4
syntax error
Notes/Hints
Time limit: 5 seconds, Memory limit: 512 MB.
输入格式
见题面 Input 部分
输出格式
见题面 Output 部分