3365: Inna and Large Sweet Matrix
题目描述
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:
- Sereja chooses five integers x1,y1,x2,y2,v (x1≤x2,y1≤y2) and adds v candies to each matrix cell (i,j) (x1≤i≤x2;y1≤j≤y2).
- Sereja chooses four integers x1,y1,x2,y2 (x1≤x2,y1≤y2). Then he asks Dima to calculate the total number of candies in cells (i,j) (x1≤i≤x2;y1≤j≤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<x1 OR p>x2) AND (q<y1 OR q>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≤n,m≤4·106;1≤w≤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≤x1≤x2≤n;1≤y1≤y2≤m;1≤v≤109).
- A line that describes an event of the second type contains 5 integers: 1, x1, y1, x2, y2 (2≤x1≤x2≤n-1;2≤y1≤y2≤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.
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
2
-21
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.