Grid Sum Query and Update

You are given an $N \times N$ chessboard with all cells initially set to $0$. You need to perform the following operations:

1. 1 x y A: Increase the value in cell $(x,y)$ by $A$, where $1\le x,y\le N$ and $A$ is a positive integer.
   
2. 2 x_1 y_1 x_2 y_2: Query the sum of the values in the rectangular region with the top-left cell $(x_1,y_1)$ and the bottom-right cell $(x_2,y_2)$, where $1\le x_1\le x_2\le N$ and $1\le y_1\le y_2\le N$.
   
3. 3: Terminate the program.

inputFormat

The first line of input contains a single integer $N$, the size of the chessboard. Each subsequent line contains an operation in one of the following formats:

1 x y A
2 x1 y1 x2 y2
3 (this operation indicates the termination of the input).

Read operations until a line with operation type 3 is encountered.

outputFormat

For each query operation (operation type 2), output the sum of the values in the specified rectangular region on its own line.

sample

3
1 1 1 5
1 2 2 3
2 1 1 2 2
3

8