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.

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