Little Chris is a huge fan of linear algebra. This time he has been given a homework about the unusual square of a square matrix. The dot product of two integer number vectors x and y of size n is the sum of the products of the corresponding components of the vectors. The unusual square of an n × n square matrix A is defined as the sum of n dot products. The i -th of them is the dot product of the i -th row vector and the i -th column vector in the matrix A . Fortunately for Chris, he has to work only in GF (2) ! This means that all operations (addition, multiplication) are calculated modulo 2. In fact, the matrix A is binary: each element of A is either 0 or 1. For example, consider the following matrix A : The unusual square of A is equal to (1·1 + 1·0 + 1·1) + (0·1 + 1·1 + 1·0) + (1·1 + 0·1 + 0·0) = 0 + 1 + 1 = 0 . However, there is much more to the homework. Chris has to process q queries; each query can be one of the following: given a row index i , flip all the values in the i -th row in A ; given a column index i , flip all the values in the i -th column in A ; find the unusual square of A . To flip a bit value w means to change it to 1 - w , i.e., 1 changes to 0 and 0 changes to 1. Given the initial matrix A , output the answers for each query of the third type! Can you solve Chris's homework? The first line of input contains an integer n ( 1 ≤ n ≤ 1000 ), the number of rows and the number of columns in the matrix A . The next n lines describe the matrix: the i -th line contains n space-separated bits and describes the i -th row of A . The j -th number of the i -th line a ij ( 0 ≤ a ij ≤ 1 ) is the element on the intersection of the i -th row and the j -th column of A . The next line of input contains an integer q ( 1 ≤ q ≤ 10 6 ), the number of queries. Each of the next q lines describes a single query, which can be one of the following: 1 i — flip the values of the i -th row; 2 i — flip the values of the i -th column; 3 — output the unusual squar