Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

No tag edit access

C. Division and Union

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputThere are $$$n$$$ segments $$$[l_i, r_i]$$$ for $$$1 \le i \le n$$$. You should divide all segments into two non-empty groups in such way that there is no pair of segments from different groups which have at least one common point, or say that it's impossible to do it. Each segment should belong to exactly one group.

To optimize testing process you will be given multitest.

Input

The first line contains one integer $$$T$$$ ($$$1 \le T \le 50000$$$) — the number of queries. Each query contains description of the set of segments. Queries are independent.

First line of each query contains single integer $$$n$$$ ($$$2 \le n \le 10^5$$$) — number of segments. It is guaranteed that $$$\sum{n}$$$ over all queries does not exceed $$$10^5$$$.

The next $$$n$$$ lines contains two integers $$$l_i$$$, $$$r_i$$$ per line ($$$1 \le l_i \le r_i \le 2 \cdot 10^5$$$) — the $$$i$$$-th segment.

Output

For each query print $$$n$$$ integers $$$t_1, t_2, \dots, t_n$$$ ($$$t_i \in \{1, 2\}$$$) — for each segment (in the same order as in the input) $$$t_i$$$ equals $$$1$$$ if the $$$i$$$-th segment will belongs to the first group and $$$2$$$ otherwise.

If there are multiple answers, you can print any of them. If there is no answer, print $$$-1$$$.

Example

Input

3 2 5 5 2 3 3 3 5 2 3 2 3 3 3 3 4 4 5 5

Output

2 1 -1 1 1 2

Note

In the first query the first and the second segments should be in different groups, but exact numbers don't matter.

In the second query the third segment intersects with the first and the second segments, so they should be in the same group, but then the other group becomes empty, so answer is $$$-1$$$.

In the third query we can distribute segments in any way that makes groups non-empty, so any answer of $$$6$$$ possible is correct.

Codeforces (c) Copyright 2010-2019 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Dec/13/2019 09:29:42 (f1).

Desktop version, switch to mobile version.

Supported by

User lists

Name |
---|