SDE - 1

Ninja has been given two sparse matrices ‘MAT1’ and ‘MAT2’ of integers having size ‘N’ x ‘M’ and ‘M’ x ‘P’, respectively.

A sparse matrix is a matrix that contains very few non-zero elements.

Ninja has to find the matrix formed by the multiplication of ‘MAT1’ and ‘MAT2’. As Ninja is busy with some other tasks so he needs your help. Can you help Ninja to find the matrix formed by the multiplication of ‘MAT1’ and ‘MAT2’?

Note: The number of columns in ‘MAT1’ i.e ‘M’ is equal to the number of rows in ‘MAT2’ i.e ‘M’. It means we can always multiply ‘MAT1’ with ‘MAT2’.

For example:

For the ‘MAT1’ and ‘MAT2’ given below, ‘MAT3’ is the matrix formed by multiplying ‘MAT1’ and ‘MAT2’. 

1. MAT3[0][0] = MAT1[0][0] * MAT2[0][0] + MAT1[0][1] * MAT2[1][0]  ie. 2 * 1 + 1 * 4 = 6
2. MAT3[1][0] = MAT1[1][0] * MAT2[1][0] + MAT1[1][1] * MAT2[1][0] ie. 0 * 6 + 0 * 4 = 0

Tanmay and Rohit are best buddies. One day Tanmay gives Rohit a problem to test his intelligence and skills. He gives him an array of N natural numbers and asks him to solve the following queries:-

Query 0 :

0 x y

This operation modifies the element present at index x to y.

Query 1 :

1 x y 

This operation counts the number of even numbers in range x to y inclusive.

Query 2 :

2 x y 

This operation counts the number of odd numbers in range x to y inclusive.

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