Senor Vorpal Kickass'o invented an innovative method to encrypt integer sequences of length n . To encrypt a sequence, one has to choose a secret sequence , that acts as a key. Vorpal is very selective, so the key should be such a sequence b i , that its cyclic shifts are linearly independent, that is, there is no non-zero set of coefficients x 0 , x 1 , ..., x n - 1 , such that for all k at the same time. After that for a sequence you should build the following cipher: In other words, you are to compute the quadratic deviation between each cyclic shift of b i and the sequence a i . The resulting sequence is the Kickass's cipher. The cipher is in development right now and Vorpal wants to decipher a sequence after it has been encrypted. You are to solve this problem for him. You are given sequences c i and b i . You are to find all suitable sequences a i . The first line contains a single integer n ( ). The second line contains n integers b 0 , b 1 , ..., b n - 1 ( ). The third line contains n integers c 0 , c 1 , ..., c n - 1 ( ). It is guaranteed that all cyclic shifts of sequence b i are linearly independent. In the first line print a single integer k — the number of sequences a i , such that after encrypting them with key b i you get the sequence c i . After that in each of k next lines print n integers a 0 , a 1 , ..., a n - 1 . Print the sequences in lexicographical order. Note that k could be equal to 0 .