A warehouse assigns distinct integer bin labels. Starting from an empty binary search tree, insert the labels in the order given, using the standard BST rule: to insert a key x, walk down from the root, going left if x is smaller than the current node and right if x is larger, until an empty spot is reached, where a new node is created. No rebalancing is performed.

For each of q arriving packages, you are given its target label t. The package must be stored in the ceiling bin: the smallest existing bin label that is greater than or equal to t. If no such bin exists, report -1 for that query.

Input format

Line 1: an integer n. Line 2: n space-separated distinct integers — the bin labels, in insertion order. Line 3: an integer q. Line 4: q space-separated integers t_1 ... t_q — the query targets.

Output format

q lines. Line i contains the ceiling of t_i, or -1 if no bin label is greater than or equal to t_i.

Constraints

• 1 ≤ n ≤ 40
• -1000 ≤ each bin label ≤ 1000, all labels distinct
• 1 ≤ q ≤ 40
• -2000 ≤ t_i ≤ 2000

5
5 3 8 1 4
3
4 6 9

4
8
-1

4
10 20 5 15
2
-100 20

5
20