B'Luca has a cypher made up of a sequence of n wheels, each with a digit a_i written on it. On the i -th wheel, he made b_i moves. Each move is one of two types: Luca knows the final sequence of wheels and the moves for each wheel. Help him find the original sequence and crack the cypher. The first line contains a single integer t ( 1 <= q t <= q 100 ) -- the number of test cases. The first line of each test case contains a single integer n ( 1 <= q n <= q 100 ) -- the number of wheels. The second line contains n integers a_i ( 0 <= q a_i <= q 9 ) -- the digit shown on the i -th wheel after all moves have been performed. Then n lines follow, the i -th of which contains the integer b_i ( 1 <= q b_i <= q 10 ) and b_i characters that are either texttt{U} or texttt{D} -- the number of moves performed on the i -th wheel, and the moves performed. texttt{U} and texttt{D} represent an up move and a down move respectively. For each test case, output n space-separated digits -- the initial sequence of the cypher. In the first test case, we can prove that initial sequence was [2,1,1] . In that case, the following moves were performed: '...