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.
## 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]
有一排 #cf_span[n] 盏灯，从左到右编号为 #cf_span[1] 到 #cf_span[n]。同时有 #cf_span[n] 个按键。当按下第 #cf_span[i] 个按键时，所有满足 #cf_span[i|x] 的灯 #cf_span[x] 都会改变状态。
对于两个整数 #cf_span[a] 和 #cf_span[b]，我们说 #cf_span[a|b] 当且仅当存在整数 #cf_span[c] 使得 #cf_span[a × c = b]。
Amirali 喜欢玩这些按键。他随机按下了 #cf_span[k] 个按键，想知道灯的最终状态。请帮他写一段 #cf_span(class=[tex-font-style-underline], body=[Pike]) 代码来解决这个问题。
输入的第一行包含一个整数 #cf_span[n]，表示灯的数量（#cf_span[1 ≤ n ≤ 105]）。
第二行包含 #cf_span[n] 个单词，第 #cf_span[i] 个单词描述第 #cf_span[i] 盏灯的初始状态（详见样例）。
第三行包含一个整数 #cf_span[k]（#cf_span[1 ≤ k ≤ 104]），表示按键被按下的次数。接下来一行包含 #cf_span[k] 个在范围 #cf_span[[1, n]] 内的整数，表示被按下的按键编号。
请输出 #cf_span[n] 个单词，描述灯的最终状态。详见样例。
## Input
输入的第一行包含一个整数 #cf_span[n]，表示灯的数量（#cf_span[1 ≤ n ≤ 105]）。第二行包含 #cf_span[n] 个单词，第 #cf_span[i] 个单词描述第 #cf_span[i] 盏灯的初始状态（详见样例）。第三行包含一个整数 #cf_span[k]（#cf_span[1 ≤ k ≤ 104]），表示按键被按下的次数。接下来一行包含 #cf_span[k] 个在范围 #cf_span[[1, n]] 内的整数，表示被按下的按键编号。
## Output
请输出 #cf_span[n] 个单词，描述灯的最终状态。详见样例。
[samples]
**Definitions**
Let $ n \in \mathbb{Z}^+ $ be the number of lamps and keys.
Let $ s = (s_1, s_2, \dots, s_n) \in \{0,1\}^n $ be the initial state of the lamps, where $ s_i \in \{0,1\} $ represents the initial state of lamp $ i $.
Let $ K = (k_1, k_2, \dots, k_k) \in \{1, 2, \dots, n\}^k $ be the sequence of pressed keys, with $ k \in \mathbb{Z}^+ $ being the number of presses.
**Constraints**
1. $ 1 \leq n \leq 10^5 $
2. $ 1 \leq k \leq 10^4 $
3. For all $ i \in \{1, \dots, n\} $, $ s_i \in \{0,1\} $
4. For all $ j \in \{1, \dots, k\} $, $ 1 \leq k_j \leq n $
**Objective**
For each lamp $ i \in \{1, \dots, n\} $, let $ f(i) $ denote the number of keys $ k_j \in K $ such that $ k_j \mid i $.
The final state of lamp $ i $ is:
$$
s_i' = s_i \oplus (f(i) \bmod 2)
$$
Output $ (s_1', s_2', \dots, s_n') $.