CF390E.Inna and Large Sweet Matrix

Inna loves sweets very much. That's why she wants to play the "Sweet Matrix" game with Dima and Sereja. But Sereja is a large person, so the game proved small for him. Sereja suggested playing the "Large Sweet Matrix" game.

The "Large Sweet Matrix" playing field is an $n×m$ matrix. Let's number the rows of the matrix from $1$ to $n$ , and the columns — from $1$ to $m$ . Let's denote the cell in the $i$ -th row and $j$ -th column as $(i,j)$ . Each cell of the matrix can contain multiple candies, initially all cells are empty. The game goes in $w$ moves, during each move one of the two following events occurs:

1. Sereja chooses five integers $x_{1},y_{1},x_{2},y_{2},v$ $(x_{1}<=x_{2},y_{1}<=y_{2})$ and adds $v$ candies to each matrix cell $(i,j)$ $(x_{1}<=i<=x_{2}; y_{1}<=j<=y_{2})$ .
2. Sereja chooses four integers $x_{1},y_{1},x_{2},y_{2}$ $(x_{1}<=x_{2},y_{1}<=y_{2})$ . Then he asks Dima to calculate the total number of candies in cells $(i,j)$ $(x_{1}<=i<=x_{2}; y_{1}<=j<=y_{2})$ and he asks Inna to calculate the total number of candies in the cells of matrix $(p,q)$ , which meet the following logical criteria: ( p<x_{1} OR p>x_{2} ) AND ( q<y_{1} OR q>y_{2} ). Finally, Sereja asks to write down the difference between the number Dima has calculated and the number Inna has calculated (D - I).

Unfortunately, Sereja's matrix is really huge. That's why Inna and Dima aren't coping with the calculating. Help them!

The first line of the input contains three integers $n$ , $m$ and $w$ $(3<=n,m<=4·10^{6}; 1<=w<=10^{5})$ .

The next $w$ lines describe the moves that were made in the game.

• A line that describes an event of the first type contains 6 integers: $0$ , $x_{1}$ , $y_{1}$ , $x_{2}$ , $y_{2}$ and $v$ $(1<=x_{1}<=x_{2}<=n; 1<=y_{1}<=y_{2}<=m; 1<=v<=10^{9})$ .
• A line that describes an event of the second type contains 5 integers: $1$ , $x_{1}$ , $y_{1}$ , $x_{2}$ , $y_{2}$ $(2<=x_{1}<=x_{2}<=n-1; 2<=y_{1}<=y_{2}<=m-1)$ .

It is guaranteed that the second type move occurs at least once. It is guaranteed that a single operation will not add more than $10^{9}$ candies.

Be careful, the constraints are very large, so please use optimal data structures. Max-tests will be in pretests.

For each second type move print a single integer on a single line — the difference between Dima and Inna's numbers.

Note to the sample. After the first query the matrix looks as:

<br></br>22200<br></br>22200 <br></br>00000<br></br>00000<br></br>After the second one it is:

<br></br>22200<br></br>25500<br></br>03300 <br></br>00000<br></br>After the third one it is:

<br></br>22201<br></br>25501<br></br>03301<br></br>00001<br></br>For the fourth query, Dima's sum equals 5 + 0 + 3 + 0 = 8 and Inna's sum equals 4 + 1 + 0 + 1 = 6. The answer to the query equals 8 - 6 = 2. For the fifth query, Dima's sum equals 0 and Inna's sum equals 18 + 2 + 0 + 1 = 21. The answer to the query is 0 - 21 = -21.