A backstage manager is assembling the final performance roster for a variety show, one act at a time. There are n acts, and they arrive in a fixed order, numbered 0 through n-1 by arrival. When the i-th act arrives, the manager is told a value describing that act and the exact slot in the roster built so far where it must be inserted; every act already occupying that slot or a later one shifts one place to the right to make room. After all n acts have arrived, report the finished roster from left to right.

Input format

Line 1: one integer n -- the number of acts. Line 2: n integers values[0] ... values[n-1] -- the value carried by the act that arrives i-th (0-indexed). Line 3: n integers positions[0] ... positions[n-1] -- the 0-indexed slot at which that act is inserted into the roster at the moment it arrives.

Output format

Print the n values of the final roster, left to right, space-separated on a single line.

Constraints

1 <= n <= 1000 0 <= values[i] <= 1000 0 <= positions[i] <= i, for every i from 0 to n-1 (so positions[i] is always a valid insertion slot for the roster's length just before the i-th act is inserted).

4
4 7 2 9
0 1 0 2

2 4 9 7

1
5
0

5