A Flea on a Chessboard

An infinite chessboard is obtained by extending a finite chessboard infinitely to the right and up. Each square is either black or white and has side length $S$ millimeters ($0 < S \le 1000$). The bottom-left square is black. A flea sits on the board at the point $(x, y)$ (in millimeters) and, with each jump, moves $dx$ millimeters to the right and $dy$ millimeters up ($0 < dx,\ dy$); that is, a flea at $(x, y)$ lands at $(x+dx,\ y+dy)$ after one jump.

Given the flea's starting position, determine how many jumps it takes for the flea to reach a white square. If the flea lands on the boundary between two squares, that does not count as landing on a white square. It is possible that the flea never reaches a white square.

The input consists of several test cases. Each test case is one line containing five non-negative integers $S$, $x$, $y$, $dx$, and $dy$ separated by whitespace. A line containing five zeros follows the last test case and is not processed.

For each test case print one line. If the flea first reaches a white square at $(a, b)$ after $n$ jumps, print After n jumps the flea lands at (a, b).. If the flea never reaches a white square, print The flea cannot escape from black squares..