Gahui's Sweet Potato Eating

Gahui really likes sweet potatoes.

This time too, the smell of sweet potatoes is unmistakable, yet no sweet potato is in sight. Her older brother has hidden sweet potatoes in the room.

Her brother proposes a game to Gahui and explains the rules. The rules are as follows.

• Every second, Gahui may move one cell in one of the four directions (up, down, left, right), or stay in place without moving.
• If Gahui moves to a cell containing a sweet potato, she eats it. Eating a sweet potato is assumed to take no time.
• Once Gahui eats a sweet potato, it does not reappear in that cell.

Starting from her current position, Gahui wants to eat as many sweet potatoes as possible over T seconds. Tell her the maximum number of sweet potatoes she can eat.

The first line gives the map's height R, width C, and the time T Gahui moves.

From the second line to the R+1-th line, a string of length C is given.

Each character in the given strings is one of 'G' for Gahui, 'S' for a sweet potato, '.' for an empty cell, or '#' for an obstacle.

Print the answer to the problem.

• 2 ≤ R ≤ 100
• 2 ≤ C ≤ 100
• 1 ≤ T ≤ 10
• The character 'G', representing Gahui, appears exactly once in the map. The position of 'G' is Gahui's current position.
• Each position with 'S' contains one sweet potato.
• There is at least one sweet potato and at least one obstacle.
• Gahui cannot jump over or pass through obstacles.
• Gahui cannot leave the map.