An Insect Problem
A \(100 \times 100 \) board is divided into unit squares.
In every square there is an arrow that points up, down, left or right. The board square is surrounded by a wall, except for the right side of the top right corner square.
An insect is placed in one of the squares. Each second, the insect moves one unit in the direction of the arrow in its square. When the insect moves, the arrow of the square it was in moves 90 degrees clockwise.
If the indicated movement cannot be done, the insect does not move that second, but the arrow in its squares does move.
Find the number of ways in which the insect is trapped in the chessboard .