Matrix Operation

You are a student looking for a job. Today you took an employment examination for an IT company. They asked you to write an efficient program that performs several operations. First, they showed you an $N \times N$ square matrix and a list of operations. All operations but one modify the matrix, and the last operation outputs the character in a specified cell. Remember that you need to output the final matrix after you finish all the operations.

Following are the details of the operations:

• WR r c v: (Write operation) write an integer v into the cell (r,c) ($1 \leq v \leq 1,000,000$)
• CP r1 c1 r2 c2: (Copy operation) copy the character in the cell (r1,c1) into the cell (r2,c2)
• SR r1 r2: (Swap Row operation) swap the r1-th row and r2-th row
• SC c1 c2: (Swap Column operation) swap the c1-th column and c2-th column
• RL: (Rotate Left operation) rotate the whole matrix counter-clockwise by 90 degrees
• RR: (Rotate Right operation) rotate the whole matrix clockwise by 90 degrees
• RH: (Reflect Horizontal operation) reverse the order of the rows
• RV: (Reflect Vertical operation) reverse the order of the columns

The first line of each testcase contains nine integers. The first two integers in the line, N and Q, indicate the size of the matrix and the number of queries, respectively $(1 \leq N,Q \leq 40,000)$. The next three integers, A, B, and C, are coefficients used to calculate the values in the initial matrix $(1 \leq A,B,C \leq 1,000,000)$, and they are used as follows: $A_{r,c} = (r * A + c * B) \bmod C$, where r and c are the row and column indices, respectively $(1\leq r,c\leq N)$. The last four integers, D, E, F, and G, are coefficients used to compute the final hash value mentioned in the next section $(1 \leq D \leq E \leq N, 1 \leq F \leq G \leq N, E - D \leq 1,000, G - F \leq 1,000)$. Each of the next Q lines contains one operation in the format described above.

Output the hash value h computed from the final matrix B using the following pseudocode.

h <- 314159265
for r = D...E
  for c = F...G
    h <- (31 * h + B_{r,c}) mod 1,000,000,007

Here, "<-" is a destructive assignment operator, "for i = S...T" indicates a loop over i from S to T (both inclusive), and "mod" is a remainder operation.