Similar to speed dating, during speed interviewing, you rapidly do a bunch of interviews!

The interviewers are situated in a grid formation (\(R\) by ). Each interviewer has a rating score (from to ). However, due to certain events, interviewers will occasionally change in rating.

Hungry for interviews, Reyno will interview with everyone in a square area. Being both ambitious and lazy, he wants to achieve a certain total summed score with interviewers.

#### Input Specification

The first line contains three numbers, \(Q\), the rows and column of the grid and the number of queries to answer.

The next lines will each contain numbers, representing the scores of the interviewers within the grid.

The next lines will contain a query of the following form:

`U r c s`

– the interviewer at location now has a rating of .`S r c s`

– Reyno wants to know the side length of the square starting at that has a total summed rating closest to \((0 \le s \le 100RC)\). If multiple squares are equally close, output the larger side length.

\(1 \le R, C \le 500\)

\(1 \le Q \le 10^5\)

#### Output Specification

Output the answer to each `S`

type query on its own line.

#### Sample Input

```
3 3 7
1 2 6
3 5 7
4 8 9
S 1 1 27
S 1 1 28
U 2 2 50
S 1 2 33
S 1 2 34
S 3 2 100
S 3 2 0
```

#### Sample Output

```
2
3
1
2
1
1
```

#### Explanation for Sample Output

The sum of the ratings for the answers of the `S`

type queries are: , , , , , .

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