A8965 | String Theory

The first line of input contains two space-separated integers numbers $n$ and $m$ ( $1<=n,m<=10^{5}$ ), the height and width of the harp in units. Each of the following $n+m$ lines contains 4 space-separated tokens, describing a single string: two symbols $a_{i}$ , $b_{i}$ and two integer numbers $p_{i}$ , $q_{i}$ . The pair $a_{i}$ , $p_{i}$ describes the first pin, and the pair $b_{i}$ , $q_{i}$ describes the second pin of the string;

A pair $s$ , $x$ describes the position of a single pin in a following way:

1. $s$ is equal to one of the symbols "L", "T", "R" or "B" (without quotes), which means that the pin is positioned on the left, top, right or bottom side of the harp accordingly;
2. $x$ is equal to the number of the row, if the pin is on the left or right border of the harp, and to the number of the column, if the pin is on the top or bottom border of the harp.

It is guaranteed that no two different strings are connected to the same pin.

If it is possible to rearrange the rows and columns to fix the harp, on the first line output $n$ space-separated integers — the old numbers of rows now placed from top to bottom in the fixed harp. On the second line, output $m$ space-separated integers — the old numbers of columns now placed from left to right in the fixed harp.

If it is impossible to rearrange the rows and columns to fix the harp, output "No solution" (without quotes).

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