There are $N$ terrorist and $N$ soldiers . Every terrorist has a value and a power which is given by array $A$ and $P$ where $A[i]$ and $P[i]$ represents the value and power of i^th terrorist respectively. Every soldier also has some value which is given by array $B$ where $B[i]$ represents the value of i^th soldier. Soldiers want to kill terrorists obviously But, a soldier can decrease power of a terrorist $i$ by atmost $1$ only if $A[1] & A[2]......&A[i]$ (Here "&" is $bitwise AND$) is greater than or equal to value of that soldier. And soldiers do the work (reducing power) according to their arrival. more formally, firstly soldier 1 finishes his work then soldier 2, then soldier 3,........ so on. 

Terrorist gets killed when it's power becomes $0$.For every terrorist you have to tell the $minimum$ possible index(1-based) of soldier(who reduced the power from $1$ to $0$)  by which it will be killed and if this terrorist will alive forever then print $-1$.

Input

First line contains $N$.Next three line will contain array $A$,$P$ and $B$ respectively.
Output

Print $N$ integers(space separated) where i^th integer represents the answer of i^thterrorist.

Constrains

1 <= $N$ <= 10⁵

1 <= $A[i]$ <= 10⁹

1 <= $P[i]$ <= 10⁵

1 <= $B[i]$ <= 10⁹