Vincent and Tommy are playing English pool. The game is played with 15 coloured object balls (two groups of seven balls – red and yellow – and a black 8-ball) and a white cue ball, where they take turns to pocket their own set of coloured balls, followed by the 8-ball, by using the pool cue to strike the cue ball to collide with those object balls.
Before each game, they will have to pick the balls from under the table, and with the help of a rack set up the 15 object balls on the table in the following specific colour pattern, which is of the shape of an equilateral triangle of side-length 5:
Vincent finds it to be a very natural hand gesture to grab three balls at a time in the form of a triangle of side-length 2 (call it a "3-ball-triangle"), with those three balls tightly packed with each other and fit right in the size of his palm. He is also too lazy to rearrange the balls once they have been placed inside the rack. Vincent therefore wonders, if the colours of the balls are to be ignored, whether he can directly fill up the triangular rack with 3-ball-triangle's given the side-length of the rack. Can you help him solve the problem?
The only line of input contains a single integer $$$N$$$ $$$(1 \le N \le 100)$$$, the length of the side of the triangular rack.
If it is impossible to fill up the triangular rack of side-length $$$N$$$ with 3-ball-triangle's, output Impossible.
Otherwise, output $$$N$$$ lines, with the $$$k$$$-th line containing $$$k$$$ characters, that represent the resulting rack to be divided into 3-ball-triangle's. All the outputted characters must be either L or 7.
The rack is to be presented as if all the rows are left-aligned, and should be able to be divided into 'L'-shaped and '7'-shaped regions each with three corresponding characters. Three Ls form a L-shaped region to represent a 3-ball-triangle pointing upward, and three 7s form a 7-shaped region to represent a 3-ball-triangle pointing downward. To illustrate this, consider the following (failed) attempts when $$$N = 3$$$ (Sample 2): (Note that the Os are placeholders that should not appear in your output)
2
L LL
3
Impossible
