Important: All possible tests are in the pretest, so you shouldn't hack on this problem. So, if you passed pretests, you will also pass the system test. You are an adventurer currently journeying inside an evil temple. After defeating a couple of weak monsters, you arrived at a square room consisting of tiles forming an n × n grid, surrounded entirely by walls. At the end of the room lies a door locked with evil magical forces. The following inscriptions are written on the door: Being a very senior adventurer, you immediately realize what this means. In the room next door lies an infinite number of magical rocks. There are four types of rocks: ' ^ ': this rock moves upwards; ' < ': this rock moves leftwards; ' > ': this rock moves rightwards; ' v ': this rock moves downwards. To open the door, you first need to place the rocks on some of the tiles (one tile can be occupied by at most one rock). Then, you select a single rock that you have placed and activate it. The activated rock will then move in its direction until it hits another rock or hits the walls of the room (the rock will not move if something already blocks it in its chosen direction). The rock then deactivates. If it hits the walls, or if there have been already 10 7 events of rock becoming activated, the movements end. Otherwise, the rock that was hit becomes activated and this procedure is repeated. If a rock moves at least one cell before hitting either the wall or another rock, the hit produces a sound. The door will open once the number of produced sounds is at least x . It is okay for the rocks to continue moving after producing x sounds. The following picture illustrates the four possible scenarios of moving rocks. Moves at least one cell, then hits another rock. A sound is produced, the hit rock becomes activated. Moves at least one cell, then hits the wall (i.e., the side of the room). A sound is produced, the movements end. Does not move because a rock is already standing in the path