Little Q and Big Integers#9285
Little Q likes positive big integers in base notation, but not all of them. He doesn't like integers with zeroes, including leading zeroes. Additionally, he is particular about the number of occurrences of each digit. Formally, his preferences can be described as a binary matrix g_{1..k-1,0..n}, where for every digit from to k - 1, if g_{i,j} = 0, he doesn't like integers which contain exactly copies of digit . He also can't accept any digit appearing more than times. The integer must contain at least one digit.
Little Q's taste changes every day. There are days in total, and on day , the value g_{u_i,v_i} is flipped ( becomes and becomes ). Let denote the number of big integers which Little Q likes after -th day's change, and denote the answer before all changes. Your task is to calculate the following:
The first line contains three integers , and : the base, the upper limit and the number of days (3 \leq k \leq 10, 1 \leq n \leq 1.4 \cdot 10^4, 1 \leq m \leq 200). In the next k - 1 lines, line contains n + 1 integers g_{i,0}, g_{i,1}, \ldots, g_{i,n} (0 \leq g_{i,j} \leq 1). Together they provide the initial matrix . After that follow lines, -th line contains two integers u_i and v_i which mean that on -th day, the value g_{u_i,v_i} is flipped (1 \leq u_i \leq k - 1, 0 \leq v_i \leq n).
Print a single integer: the answer to the problem.
Example 1