Time Limit: 2000/1000 MS (Java/Others)

Memory Limit: 65536/32768 K (Java/Others)

In addition fond of programing, Jack also loves painting. He likes to draw many interesting graphics on the paper.

One day,Jack found a new interesting graph called Palindrome graph. No matter how many times to flip or rotate 90 degrees, the palindrome graph are always unchanged.

Jack took a paper with n*n grid and K kinds of pigments.Some of the grid has been filled with color and can not be modified.Jack want to know:how many ways can he paint a palindrome graph?

One day,Jack found a new interesting graph called Palindrome graph. No matter how many times to flip or rotate 90 degrees, the palindrome graph are always unchanged.

Jack took a paper with n*n grid and K kinds of pigments.Some of the grid has been filled with color and can not be modified.Jack want to know:how many ways can he paint a palindrome graph?

There are several test cases.

For each test case,there are three integer n m k(0<n<=10000,0<=m<=2000,0<k<=1000000), indicate n*n grid and k kinds of pigments.

Then follow m lines,for each line,there are 2 integer i,j.indicated that grid(i,j) (0<=i,j<n) has been filled with color.

You can suppose that jack have at least one way to paint a palindrome graph.

For each test case,there are three integer n m k(0<n<=10000,0<=m<=2000,0<k<=1000000), indicate n*n grid and k kinds of pigments.

Then follow m lines,for each line,there are 2 integer i,j.indicated that grid(i,j) (0<=i,j<n) has been filled with color.

You can suppose that jack have at least one way to paint a palindrome graph.

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