In the recently proposed Visual Python++ programming
language, a block of statements is represented as
a rectangle of characters with topleft corner in row
$r_1$ and column
$c_1$, and bottomright
corner in row $r_2$ and
column $c_2$. All
characters at locations $(r,
c)$ with $r_1 \leq r \leq
r_2$ and $c_1 \leq c \leq
c_2$ 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 syntactically 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 ‘$\ulcorner $’
in the topleft corner of the rectangle and one character
‘$\lrcorner $’ in the
bottomright 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 fivehour contract to
develop this part of the parser.
Input
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 topleft corner in row $r$ and column $c$ of the program you are parsing.
Following that are $n$
lines specifying the bottomright corners in the same way. All
corner locations are distinct.
Output
Display $n$ lines, each
containing one integer. A number $j$ in line $i$ means that the $i^{\text {th}}$ topleft corner and
the $j^{\text {th}}$
bottomright corner form one rectangle. Topleft and
bottomright 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 1 
Sample Output 1 
2
4 7
9 8
14 17
19 18

2
1

Sample Input 2 
Sample Output 2 
2
4 7
14 17
9 8
19 18

1
2

Sample Input 3 
Sample Output 3 
2
4 8
9 7
14 18
19 17

syntax error

Sample Input 4 
Sample Output 4 
3
1 1
4 8
8 4
10 6
6 10
10 10

syntax error
