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 \times 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:
Sereja chooses five integers x1,y1,x2,y2,v (x1 \le x2,y1 \le y2) and adds v candies to each matrix cell (i,j) (x1 \le i \le x2;y1 \le j \le y2). Sereja chooses four integers x1,y1,x2,y2 (x1 \le x2,y1 \le y2). Then he asks Dima to calculate the total number of candies in cells (i,j) (x1 \le i \le x2;y1 \le j \le y2) 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 \lt x1 OR p \gt x2) AND (q \lt y1 OR q \gt y2). 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 \le n,m \le 4 \cdot 106;1 \le w \le 105).

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, x1, y1, x2, y2 and v (1 \le x1 \le x2 \le n;1 \le y1 \le y2 \le m;1 \le v \le 109). A line that describes an event of the second type contains 5 integers: 1, x1, y1, x2, y2 (2 \le x1 \le x2 \le n-1;2 \le y1 \le y2 \le 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 109 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:

22200
22200 
00000
00000

After the second one it is:

22200
25500
03300 
00000

After the third one it is:

22201
25501
03301
00001

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.