Labyrinth P79535

You are given an $R \times C$ grid. Some cells, marked with ‘#’, have a wall. The rest of cells are free, and they are marked with ‘.’. There are two exceptions: one free cell is marked with ‘S’ (it is your starting position), and another free cell is marked with ‘T’ (it has a treasure).

Your goal is to reach the treasure as fast as possible. Every second, you can either move to an adjancent free cell, or hit an adjancent wall with a hammer. You know that every wall vanishes after $H$ hits.

Input

Input consists of several cases, each with $R$, $C$ and $H$, followed by $R$ lines with $C$ characters each. Assume that $R$ and $C$ are between 1 and 1000, and that $H$ is between 1 and $10^5$.

Output

For every case, print the minimum time to reach the treasure from the starting position.