B'A long time ago, Spyofgame invented the famous array a ( 1 -indexed) of length n that contains information about the world and life. After that, he decided to convert it into the matrix b ( 0 -indexed) of size (n + 1) x (n + 1) which contains information about the world, life and beyond. Spyofgame converted a into b with the following rules. Here oplus denotes the bitwise XOR operation. Today, archaeologists have discovered the famous matrix b . However, many elements of the matrix has been lost. They only know the values of b_{i,n} for 1 <= q i <= q n (note that these are some elements of the last column, not the last row). The archaeologists want to know what a possible array of a is. Can you help them reconstruct any array that could be a ? The first line contains a single integer n ( 1 <= q n <= q 5 cdot 10^5 ). The second line contains n integers b_{1,n}, b_{2,n}, ldots, b_{n,n} ( 0 <= q b_{i,n} < 2^{30} ). If some array a is consistent with the information, print a line containing n integers a_1, a_2, ldots, a_n . If there are multiple solutions, output any. If such an array does not exist, output -1 instead. If we let a = [1,2,3] , then b will be: The values of b_{1,n}, b_{2,n}, ldots, b_{n,n} generated are [0,2,1] which is consistent with what the archaeologists have discovered. '...