There is a table with rows and columns. Some cells contain balls, while others are empty. You are given a ball to move and the destination cell for this ball. In each step, the ball can move to an adjacent empty cell horizontally or vertically. Determine whether it is possible to move the ball from its initial position to the given destination, and if so, find a path with the minimum number of steps.
The first line contains an integer (2 \leq n \leq 40). The next lines each contain characters. A dot () denotes an empty cell, an uppercase letter indicates a ball, marks the starting position of the ball to be moved, and an uppercase letter marks the destination cell for the ball.
Print Y on the first line if it is possible to move the ball, or N otherwise. If it is possible, then output lines of characters each — in the same format as the input, but such that and all dots on the found path are replaced with plus signs (+).
Example 1
Example 2
Example 3