In the great Unovan sea, there are $$$n$$$ ($$$2 \leq n \leq 2600$$$) villages labeled $$$1$$$ through $$$n$$$, each of which is located on an island. At the moment, there is no way to travel between any pair of villages. As a result, you have been contracted to build $$$m$$$ ($$$0 \leq m \leq \min(n(n - 1), 2600)$$$) bidirectional magic bridges, each of which connects exactly two distinct villages.

Magic bridges come in two types — day bridges and night bridges. As their name implies, day bridges can only be crossed during the daytime, and night bridges can only be crossed at night. Crossing any bridge takes the entire duration of its active period (for example, crossing a night bridge takes the entire night). After your construction, two villages are said to be connected if it is possible to continuously travel from one village to the other without stopping for a day or night to pass.

Please find $$$m$$$ bridges to build such that afterwards, every single pair of villages is connected, or report that it is impossible.

In the great Unovan sea, there are $$$n$$$ ($$$2 \leq n \leq 2600$$$) villages labeled $$$1$$$ through $$$n$$$, each of which is located on an island. There are currently $$$m$$$ ($$$0 \leq m \leq \min(n(n - 1), 2600)$$$) bidirectional magic bridges, each of which connects two distinct villages.

Magic bridges come in two types — day bridges and night bridges. As their name implies, day bridges can only be crossed during the daytime, and night bridges can only be crossed at night. Crossing any bridge takes the entire duration of its active period (for example, crossing a night bridge takes the entire night). Two villages are said to be connected if it is possible to continuously travel from one village to the other without stopping for a day or night to pass.

Please determine whether every single pair of villages is connected or not.

This is an interactive problem. You have to use a flush operation right after printing each line. For example, in C++ you should use the function fflush(stdout), in Java — System.out.flush(), in Pascal — flush(output) and in Python — sys.stdout.flush().

Definitions

A permutation of length $$$n$$$ is a sequence of $$$n$$$ integers between $$$1$$$ and $$$n$$$ inclusive, such that each number appears exactly once.

When a string $$$s$$$ gets shifted, all characters except the last move to the right by one position. The last character moves to the beginning. For example, the string "End Time" can be shifted to read "eEnd Tim".

Let $$$\Sigma = \{a, b, ..., z, A, B, ..., Z\}$$$, in other words the set of lowercase and uppercase characters from the English alphabet. When a character $$$c$$$ in $$$\Sigma - \{z, Z\}$$$ gets shifted, it becomes the alphabetically next character of the same case. In particular, $$$z$$$ gets shifted to $$$A$$$, and $$$Z$$$ gets shifted to $$$a$$$.

Problem Statement

It is a sunny, but humid day as your time comes to an end. You are given a single integer $$$n$$$ $$$(1 \leq n \leq 100)$$$. Your last words are a sequence of $$$26n$$$ messages $$$m_1, m_2, ..., m_{26n}$$$, each of which is a string of length $$$26n$$$ consisting only of characters from $$$\Sigma$$$.

However, your last words have been misinterpreted, and the following transformation has occurred! A permutation $$$p$$$ of length $$$26n$$$ is picked. The $$$i$$$th message becomes the $$$p_i$$$th message. Afterwards, for each message $$$m_i$$$, two integers $$$a_i$$$ and $$$b_i$$$ are chosen from the range $$$[0, 52n - 1]$$$, inclusive. $$$m_i$$$ first gets shifted $$$a_i$$$ times. Then, for all $$$j$$$, the $$$j$$$th character of $$$m_i$$$ gets shifted $$$b_i(j - 1)$$$ times.

You see what your last words have been misinterpreted as. With your consciousness slowly fading, you are determined to figure out the permutation $$$p$$$.

Your program is given a single integer $$$n$$$ ($$$1 \leq n \leq 100$$$).

After reading in the integer, your program should output $$$26n$$$ lines, the $$$i$$$th line consisting of the message $$$m_i$$$. It must be true that each $$$m_i$$$ contains exactly $$$26n$$$ characters, and each character is a lowercase or uppercase letter.

The judge program will then respond with the $$$26n$$$ transformed strings, each of which is on a separate line.

Finally, your program should output $$$26n$$$ space-separated integers on a single line. The $$$i$$$th integer is what your program thinks $$$p_i$$$ is.

In order to pass a test case, the guessed permutation must be exactly correct, even if multiple permutations are possible.