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.

×
E. Tree Reconstruction

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputMonocarp has drawn a tree (an undirected connected acyclic graph) and then has given each vertex an index. All indices are distinct numbers from $$$1$$$ to $$$n$$$. For every edge $$$e$$$ of this tree, Monocarp has written two numbers: the maximum indices of the vertices of the two components formed if the edge $$$e$$$ (and only this edge) is erased from the tree.

Monocarp has given you a list of $$$n - 1$$$ pairs of numbers. He wants you to provide an example of a tree that will produce the said list if this tree exists. If such tree does not exist, say so.

Input

The first line contains one integer $$$n$$$ ($$$2 \le n \le 1\,000$$$) — the number of vertices in the tree.

Each of the next $$$n-1$$$ lines contains two integers $$$a_i$$$ and $$$b_i$$$ each ($$$1 \le a_i < b_i \le n$$$) — the maximal indices of vertices in the components formed if the $$$i$$$-th edge is removed.

Output

If there is no such tree that can produce the given list of pairs, print "NO" (without quotes).

Otherwise print "YES" (without quotes) in the first line and the edges of the tree in the next $$$n - 1$$$ lines. Each of the last $$$n - 1$$$ lines should contain two integers $$$x_i$$$ and $$$y_i$$$ ($$$1 \le x_i, y_i \le n$$$) — vertices connected by an edge.

Note: The numeration of edges doesn't matter for this task. Your solution will be considered correct if your tree produces the same pairs as given in the input file (possibly reordered). That means that you can print the edges of the tree you reconstructed in any order.

Examples

Input

4

3 4

1 4

3 4

Output

YES

1 3

3 2

2 4

Input

3

1 3

1 3

Output

NO

Input

3

1 2

2 3

Output

NO

Note

Possible tree from the first example. Dotted lines show edges you need to remove to get appropriate pairs.

Codeforces (c) Copyright 2010-2021 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Oct/25/2021 01:08:44 (h1).

Desktop version, switch to mobile version.

Supported by

User lists

Name |
---|