Two players are playing a board game on an 8 \times 8 square maze. Some of the cells in the maze contain walls. One player controls the terminator piece, while the other controls the escapee piece. Players take turns moving; skipping a turn is not allowed (it is guaranteed that a move is always possible). On a turn, a player may move their piece to any adjacent free cell, either horizontally, vertically, or diagonally (that is, a king's move in chess).
Additionally, the terminator can shoot missiles at the escapee. The missile travels in a straight line in any direction: horizontally, vertically, or diagonally. If the escapee is on the terminator's line of fire and not blocked by any walls, the terminator immediately shoots (regardless of whose turn it is), and the escapee loses.
The initial positions of both pieces are given. The escapee moves first. The escapee wins if they move from the eighth row off the board (since the remaining edges of the board are surrounded by walls).
The question: Can the escapee win if both players play optimally?
The input file describes the board. A free cell is denoted by the digit , a cell with a wall by , the escapee's cell by , and the terminator's cell by .
Output if the escapee wins, and otherwise.
Example 1