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!

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.

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.