PEG Judge - T-800's Escape

Mock CCC 2010 by A.J. and Brian

T-800's Escape

T-800, our friendly neighbourhood technologically advanced android, is trying to get away from the not-so-friendly T-1000s. He has to manoeuvre through a maze of buildings to reach his escape pod. However, there is a slight problem: T-800 can only move a certain number of steps before running out of power. So, T-800 has to recharge every so often on one of the recharging pads on the way to his escape pod. Given a map of the maze, help T-800 reach his escape pod as fast as possible.

Input

The input starts with a line containing the integers R, C, and K (1 ≤ R,C ≤ 50; 1 ≤ K ≤ 100), representing the number of rows and columns in the maze and the maximum number of steps T-800 can take before having to recharge, respectively. The next R lines contain C characters each describing the actual maze: '.' represents a free space, '#' represents a building, 'T' represents T-800's initial position, 'R' represents a recharging pad, and 'E' represents the escape pod. Note that T-800 can step onto a recharging pad to completely recharge himself even on his K^th step, however he cannot take more than K steps at a time without recharging first. Also note that T-800 can only take a step to any square adjacent to his current position (no diagonal moves permitted).

Output

Output the minimum number of steps T-800 has to take in order to reach his escape pod. If it is impossible for him to reach his escape pod, output "T-800 Terminated."