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ZOJ Problem Set - 2609
Crazy Painter

Time Limit: 10 Seconds      Memory Limit: 32768 KB      Special Judge

Crazy painter Henry Daub is planning to draw his new masterpiece. Like all paintings of Henry, the new masterpiece is going to be a rectangle of size m��n inches, each unit square of which will be painted with some color.

Henry would like to minimize the time needed to paint his masterpiece. He has already created the painting sketch and now he is planning the process of drawing. There are three technical tricks that Henry uses in creating his paintings.

In a turn he can paint either a horizontal line, a vertical line or a single unit square. Painting a horizontal line colors a number of horizontally adjacent unit squares to some color, painting a vertical lines colors a number of vertically adjacent squares, and painting a square just colors this square. Painting a horizontal line takes Henry h seconds, a vertical line can be painted in v seconds, and a single square is painted in s seconds.

Since the resulting picture must be accurate, it is not allowed to change the color of the square, that is, a single square may be painted several times, but it must be painted the same color each time. Help Henry to determine the time needed to paint the picture. Initially the canvas is empty, so each square must be colored.

Input

Input contains multiple test cases. The first line of the input is a single integer T (1 <= T <= 40) which is the number of test cases. T test cases follow, each preceded by a single blank line.

The first line of each case contains m, n, h, v and s (1 <= m, n <= 30, 1 <= h, v, s <= 105). Next m lines contain n characters each and describe the future masterpiece. The colors of the squares are identified using small letters of English alphabet.

Output

For each test case, on the first line print t - the time needed to paint the masterpiece and k - the number of turns needed to do this. Next k lines must contain the description of the turns. Each turn is first described with one of the letters 'h', 'v' or 's'. In the first two cases four integers numbers must follow - the coordinates of the leftmost topmost and the rightmost bottommost square of the line painted; in the last case just two integers are needed - the coordinates of the square painted. The last character of each line must be the color used in the turn.

Sample Input

2

4 4 3 5 2
aabc
aabc
bbbb
ccbc

3 4 11 8 3
aaaa
aaaa
aaaa


Sample Output

23 8
h 1 1 1 2 a
h 2 1 2 2 a
h 3 1 3 4 b
v 1 3 4 3 b
h 4 1 4 2 c
s 1 4 c
s 2 4 c
s 4 4 c

32 4
v 1 1 3 1 a
v 1 2 3 2 a
v 1 3 3 3 a
v 1 4 3 4 a


Author: Andrew Stankevich
Source: Andrew Stankevich's Contest #7
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