Inna and Large Sweet Matrix

1000ms

524288K

Description:

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!

Input:

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.

Output:

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

Sample 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

Sample Output:

2
-21

Note:

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

After the second one it is:

After the third one it is:

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.

Informação

Provedor Codeforces

Código CF390E