K. Leapfrog
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

All Rabbit's friends-and-relations play a leapfrog. Today, $$$n$$$ of them have stood in a straight line and begun to play. How do they play a leapfrog? They do it as follows:

  1. One of friends-and-relations (let's call him $$$X$$$) chooses another one ($$$Y$$$) to jump over his back.
  2. $$$X$$$ jumps over $$$Y$$$'s back in such a way that he still stands on the same line as others do, and the distance between $$$X$$$ and $$$Y$$$ remains the same as before the jump.

Rabbit's friends-and-relations are quite small, so any of them can easily fit into pretty the same place.

Input

First line contains the only integer $$$n$$$ ($$$1 \leq n \leq 100$$$).

Second line contains $$$n$$$ numbers $$$a_i$$$ separated by spaces — initial positions of Rabbit's friends-and-relations on the line. So $$$i$$$-th person stands in position $$$a_i$$$.

Third line contains $$$n$$$ numbers separated by spaces — desired positions of Rabbit's friends-and-relations. Current positions are considered desired iff it is possible to permute numbers of current positions in such a way that the list of positions' numbers becomes equal to the list of desired positions' numbers.

All the numbers are integers ranging from $$$1$$$ to $$$100$$$ inclusive.

Output

Output "No" if Rabbit's friends-and-relations will never come into desired positions.

Otherwise, output "Yes" and then output the performed leapfrogs (you can output none, if it's the case). Each next line should contain a pair of numbers $$$X$$$ and $$$Y$$$ for each time when $$$X$$$ jumps over $$$Y$$$'s back (Rabbit's friends-and-relations' names are $$$1$$$, $$$2$$$, $$$\ldots$$$, $$$n$$$).

The number of jumps shouldn't exceed $$$5 \cdot 10^5$$$, and no one should ever stand in a position that is more than $$$10^8$$$ units far from position $$$0$$$.

Examples
Input
2
1 2
5 6
Output
Yes
1 2
2 1
1 2
2 1
Input
2
1 2
1 3
Output
No
Input
2
10 20
20 30
Output
Yes
1 2