F. Phoenix and Memory
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

Phoenix 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