[Hidden]

#### Description

A word search puzzle is a grid of letters where your challenge is to find selected words as formed by consecutive letters in a line along the rows, columns, or diagonals of the grid. Tougher word searches also allow words in the grid to be forwards or backwards in any of those directions. In the “loopy word search”, we will also allow words to go off the edge of the grid and continue (along the same line) on the other side, and potentially even reuse letters from that same word. However, in this problem, we won’t search for words along diagonal lines, i.e., we only search along the rows and columns. (The UCF programming coaches are sure nice!)

The Problem:

Given a grid of letters and a list of words, identify the location of the first letter of each word in the grid and the direction in which remaining letters of the word can be found in sequence.

#### Input

The first input line contains a positive integer, n, indicating the number of word search puzzles. This is followed by the data for these puzzles. The first input line for each puzzle contains two positive integers (separated by a space): r, the number of rows in the grid (between 3 and 12 inclusive), and c, the number of columns in the grid (between 3 and 20 inclusive). Each of the next r input lines for the puzzle contains exactly c uppercase letters, with no spaces. The next input line for each puzzle contains a positive integer s, the number of words to search for. Each of the next s input lines contains a string of uppercase letters (length between 3 and 100 letters, inclusive) which is a word to search for. It is not necessarily a real word in any language.

Each of the s words will appear exactly once in the grid, meaning it has exactly one starting location and goes only in one direction. None of the words will be palindromes (same letters backwards and forwards). Assume that the input is valid as described here.

#### Output

For each word search puzzle, output the line “Word search puzzle #p:” where p is the puzzle number (counting from 1 in the input). Then, for each word given in that puzzle (and in the order given), output a line of the form “d r c w” where w is the word, r is the row in the grid where the first letter of the word is located (counting from 1), c is the column in the grid where the first letter is located (counting from 1), and d is the direction where the remaining letters of the word can be found, relative to the first letter, as given below. Output exactly one space after each of d, r, and c. For the direction d, use the following 1-letter codes:

Leave a blank line after the output for each puzzle.

#### Samples

Input Copy
2
6 12
JARWORDEPIDG
IWAXLOEAHNOK
KPEPSORTHGIN
ZASFCOFABEMW
QEHEZIUSRSTY
MWCORMNELTOS
5
WORD
SEARCH
KNIGHTRO
UNDERFUND
INGESTING
3 7
UCFAEHT
KNIGHTS
CODETRY
2
AGE
THETHETHETHETH
Output
Word search puzzle #1:
R 1 4 WORD
U 4 3 SEARCH
L 3 1 KNIGHTRO
D 5 7 UNDERFUND
D 1 10 INGESTING

Word search puzzle #2:
D 1 4 AGE
U 3 5 THETHETHETHETH


#### Source

UCF2016
##### Problem Information

 Time Limit: 1000MS (C/C++,Others×2) Memory Limit: 128MB (C/C++,Others×2) Special Judge: No AC/Submit: 1 / 1 Tags:
##### Contests involved

 1032. UCF 2016