Iahub and Xors

1000ms

262144K

Description:

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 a_i, j.

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

Write a program to perform two following operations:

Query(x₀, y₀, x₁, y₁): print the xor sum of the elements of the submatrix (x₀, y₀, x₁, y₁).
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.

Sample 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

Sample 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.

Informação

Provedor Codeforces

Código CF341D