Problem3111--Iahub and Xors

3111: Iahub and Xors

Time Limit: 2 Sec  Memory Limit: 256 MB
Submit: 0  Solved: 0
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Description

time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

Iahub does not like background stories, so he'll tell you exactly what this problem asks you for.

You are given a matrix a with n rows and n columns. Initially, all values of the matrix are zeros. Both rows and columns are 1-based, that is rows are numbered 1, 2, ..., n and columns are numbered 1, 2, ..., n. Let's denote an element on the i-th row and j-th column as ai,j.

We will call a submatrix (x0,y0,x1,y1) such elements ai,j for which two inequalities hold: x0≤i≤x1, y0≤j≤y1.

Write a program to perform two following operations:

  1. Query(x0, y0, x1, y1): print the xor sum of the elements of the submatrix (x0,y0,x1,y1).
  2. Update(x0, y0, x1, y1, v): each element from submatrix (x0,y0,x1,y1) gets xor-ed by value v.
Input

The first line contains two integers: n (1≤n≤1000) and m (1≤m≤105). The number m represents the number of operations you need to perform. Each of the next m lines contains five or six integers, depending on operation type.

If the i-th operation from the input is a query, the first number from i-th line will be 1. It will be followed by four integers x0, y0, x1, y1. If the i-th operation is an update, the first number from the i-th line will be 2. It will be followed by five integers x0, y0, x1, y1, v.

It is guaranteed that for each update operation, the following inequality holds: 0≤v<262. It is guaranteed that for each operation, the following inequalities hold: 1≤x0≤x1≤n, 1≤y0≤y1≤n.

Output

For each query operation, output on a new line the result.

Examples
Input
3 5
2 1 1 2 2 1
2 1 3 2 3 2
2 3 1 3 3 3
1 2 2 3 3
1 2 2 3 2
Output
3
2
Note

After the first 3 operations, the matrix will look like this: 


1 1 2
1 1 2
3 3 3

The fourth operation asks us to compute 1 xor 2 xor 3 xor 3 = 3.

The fifth operation asks us to compute 1 xor 3 = 2.

Source/Category

 
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