In the recently proposed Visual Python++ programming language, a block of statements is represented as a rectangle of characters with t\(op-le\)ft corner in row \(r_{1}\) and column \(c_{1}\), and bott\(om-ri\)ght corner in row \(r_{2}\) and column \(c_{2}\). All characters at locations (r, c) with \(r_{1} \le r \le r_{2}\) and \(c_{1} \le c \le c_{2}\) are then considered to belong to that block. Among these locations, the ones with \(r = r_{1}\) or \(r = r_{2}\) or \(c = c_{1}\) or \(c = c_{2}\) are called a border. Statement blocks can be nested (rectangles contained in other rectangles) to an arbitrary level. In a synt\(ac- ti\)cally correct program, every two statement blocks are either nested (one contained in 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 put one character ‘⌜’ in the t\(op-le\)ft corner of the rectangle and one character ‘^{⌟}’ in the bott\(om-ri\)ght 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 fi\(ve-ho\)ur contract to develop this part of the parser.

The first line of the input contains an integer \(n\) (\(1 \le n \le 10^{5}\)), the number of corner pairs. Each of the next \(n\) lines contains two integers \(r\) and \(c\) (\(1 \le r\), \(c \le 10^{9}\)), specifying that there is a t\(op-le\)ft corner in row \(r\) and column \(c\) of the program you are parsing. Following that are \(n\) lines specifying the bott\(om-ri\)ght corners in the same way. All corner locations are distinct.

Display \(n\) lines, each containing one integer. A number \(j\) in line \(i\) means that the \(i^{th}\) t\(op-le\)ft corner and the \(j^{th}\) bott\(om-ri\)ght corner form one rectangle. T\(op-le\)ft and bott\(om-ri\)ght 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.

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출처 ICPC World Finals 2017