There are n lamps in a line. The lamps are numbered 1 to n from left to right. There are also n keys. When key number i is pressed, all lamps number x such that i | x change their state. For two integer numbers a and b , we say a | b if and only if there exists an integer c such that a × c = b . Amirali likes to play with the keys. He randomly pressed k keys and wants to know the final state of the lamps. Help him by writing a Pike piece of code to solve this task. The first line of input contains a single integer n , the number of lamps ( 1 ≤ n ≤ 10 5 ). The following line contains n words. The i -th word describes the initial state of lamp number i (see samples for details). The following line contains a single integer k ( 1 ≤ k ≤ 10 4 ), the number of times a key is pressed. Then in the next line come k integers in range 1, n which are the numbers of the pressed keys. Write n words to output. Describe the final state of the lamps. See samples for more details.