Lamps in a Line
Description
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 ≤ 105).
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 ≤ 104), 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.
Input
The first line of input contains a single integer n, the number of lamps (1 ≤ n ≤ 105).
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 ≤ 104), 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.
Output
Write n words to output. Describe the final state of the lamps. See samples for more details.
Samples
2
off off
2
1 2
on off
3
off off on
6
1 1 1 1 2 2
off off on