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

The problem statement has recently been changed. View the changes.

×
F. Phoenix and Memory

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputPhoenix is trying to take a photo of his $$$n$$$ friends with labels $$$1, 2, \dots, n$$$ who are lined up in a row in a special order. But before he can take the photo, his friends get distracted by a duck and mess up their order.

Now, Phoenix must restore the order but he doesn't remember completely! He only remembers that the $$$i$$$-th friend from the left had a label between $$$a_i$$$ and $$$b_i$$$ inclusive. Does there exist a unique way to order his friends based of his memory?

Input

The first line contains one integer $$$n$$$ ($$$1 \le n \le 2\cdot10^5$$$) — the number of friends.

The $$$i$$$-th of the next $$$n$$$ lines contain two integers $$$a_i$$$ and $$$b_i$$$ ($$$1 \le a_i \le b_i \le n$$$) — Phoenix's memory of the $$$i$$$-th position from the left.

It is guaranteed that Phoenix's memory is valid so there is at least one valid ordering.

Output

If Phoenix can reorder his friends in a unique order, print YES followed by $$$n$$$ integers — the $$$i$$$-th integer should be the label of the $$$i$$$-th friend from the left.

Otherwise, print NO. Then, print any two distinct valid orderings on the following two lines. If are multiple solutions, print any.

Examples

Input

4 4 4 1 3 2 4 3 4

Output

YES 4 1 2 3

Input

4 1 3 2 4 3 4 2 3

Output

NO 1 3 4 2 1 2 4 3

Codeforces (c) Copyright 2010-2021 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Jan/16/2021 15:25:26 (f2).

Desktop version, switch to mobile version.

Supported by

User lists

Name |
---|