# H :: Hanging Hats

Time Limit: 10 Seconds Memory Limit: 131072 KB

It is a well-known fact that all mages wear pointed hats. However, contrary to popular belief, mages do not sleep in them, and those of the Unheard University hang them on one common, very large wall before going to bed. Mages' hats come only in two shapes: a wide one and a narrow one.

The mages go to sleep one after another (it is easily assured
as due to a tight budget, they have only one bathroom and one towel).
Before going to bed, the *i*-th mage takes its hat and chooses an
arbitrary position
(*x*_{i}, *y*_{i}) on the wall, where *y*_{i} is the
(positive) distance from the ground. Then he hammers a nail at
position
(*x*_{i}, *y*_{i}) and hangs his hat on this nail.

Not surprisingly, the hats are magical, which means that they magically
unfold to a given height. Hence, when hung, a hat looks exactly like a
isosceles triangle of height *y*_{i}, i.e., its left and right
edges are of equal length. Its top vertex is exactly at the nail and its
bottom edge touches the ﬂoor. If the hat is narrow, then the length
of its bottom edge is *y*_{i}; if it is wide, it is equal to 2*y*_{i}.

All nails are provided by the university and they have nice heads which glow in the dark. If a nail becomes covered by a hat hung later (even by its boundary), its glow is no longer visible. Moreover, if a mage tries to hammer a nail at an already hanging hat (also even at its boundary), this nail and his hat are thrown away, and he himself becomes expelled from the university. The Chancellor of the University (apparently not having more important things to worry about) wants to know how the number of visible glowing nail heads changes in time.

An example consisting of 7 hats is presented below. Dots correspond to glowing nail heads; numbers represent the order in which they are hung. Hats 2 and 6 are narrow, the remaining ones are wide. Mages 3 and 4 were expelled while trying to hang their hats (their hats were not hung). After mage 7 hung his hat, hats of mages 1, 2 and 7 were visible.

## Input

The input contains several test cases. The first line of the input
contains a positive integer *Z* <= 30, denoting the number of test
cases. Then *Z* test cases follow, each conforming to the format
described below.

The first line of the input instance contains
*n* є [1, 10^{5}], the
number of mages. The *i*-th of the following *n* lines contains two
space-separated integers
*x*_{i} є [- 10^{9}, 10^{9}] and *y*_{i} є [1, 10^{9}], followed by a letter `W` or `N`. These numbers
are the coordinates where the *i*-th mage tries to hammer a nail; the
letter denotes whether his hat is wide or narrow.

## Output

For each test case, your program has to write an output conforming to the format described below.

For each input instance you should output *n* lines. The *i*-th line
should contain the word ``FAIL`' if by hammering the nail the
*i*-th mage got himself expelled from the university. Otherwise, it
should contain a positive integer, the number of nail heads visible
after the *i*-th mage hangs his hat.

## Sample Input

2 3 0 1 W 0 2 N 0 1 W 7 4 3 W 8 8 N 3 2 W 9 5 W 12 1 W 14 2 N 13 4 W

## Sample Output

1 1 FAIL 1 2 FAIL FAIL 3 4 3Submit

Source: Central European Regional Contest 2010