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E. Inna and Large Sweet Matrix

time limit per test

1 secondmemory limit per test

512 megabytesinput

standard inputoutput

standard outputInna 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:

- 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}). - 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!

Input

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.

Output

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

Examples

Input

4 5 5

0 1 1 2 3 2

0 2 2 3 3 3

0 1 5 4 5 1

1 2 3 3 4

1 3 4 3 4

Output

2

-21

Note

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.

Codeforces (c) Copyright 2010-2018 Mike Mirzayanov

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