Description

There is a strange language called the “Two Five” language. Each of its words consists of exactly one of each of the 25 letters from A to Y. However, not every permutation is a valid word in this language. A word is valid if, when its 25 letters are arranged into a $5\times 5$ matrix, every row and every column is strictly increasing. For example, the word ACEPTBDHQUFJMRWGKNSXILOVY forms the following matrix:

ACEPT
BDHQU
FJMRW
GKNSX
ILOVY

Since every row and column is strictly increasing, it is a valid word. The word YXWVUTSRQPONMLKJIHGFEDCBA is clearly invalid.

Because words are too long to store conveniently, we assign a code to each word. The coding method is as follows: read a matrix from left to right and then from top to bottom to obtain a word; then sort the words in lexicographic order. For example, the word ABCDEFGHIJKLMNOPQRSTUVWXY has code $1$, and the word ABCDEFGHIJKLMNOPQRSUTVWXY has code $2$.

Now you need to write a program to convert between words and their codes.

Input Format

The first line contains a letter N or W. N means converting a code to a word, and W means converting a word to a code.

If the first line is N, then the second line contains an integer representing the word’s code. If the first line is W, then the second line contains a valid word.

Output Format

Each line contains one integer or word.

N
2

ABCDEFGHIJKLMNOPQRSUTVWXY

W 
ABCDEFGHIJKLMNOPQRSUTVWXY

2

Hint

The statement is translated from NOCOW.

USACO Training Section 5.5.

Translated by ChatGPT 5