In what concerns the continuous evaluation solving exercises grade during the semester, you should submit until 23:59 of October 26th
(this exercise will still be available for submission after that deadline, but without couting towards your grade)
[to understand the context of this problem, you should read the class #03 exercise sheet]

[AED006] Lower Bound

Tom needs your help again!

The Problem

Given a sorted sequence of N integer numbers and Q queries, each one indicating a number to search for, your task is to find the position of the first number in the sequence that is bigger or equal than the query number (or to find that all numbers are lower).

Input

The first line of input contains an integer N, the quantity of numbers in the sorted sequence. The second line contains the sequence itself with N space separated integers (we denote each one by S_i). It is guaranteed that these come in increasing order, but there might be repeated numbers.

The third line contains an integer Q, the quantity of queries to consider. Each of the following Q lines contains a query in the form of a single integer X_i, indicating the number we are querying.

Output

The output should contain exactly Q lines. The i-th line should contain the position of the first number in the sequence that is bigger or equal than X_i or -1 if all sequence numbers are smaller than X_i. Note that the positions in the sequence go from 0 to N-1.

Constraints

The following limits are guaranteed in all the test cases that will be given to your program:

10
2 2 2 3 5 5 8 8 8 8
6
2
8
5
1
4
9

0
6
4
0
4
-1

Explanation of the example:

• The first number ≥2 is S₀
• The first number ≥8 is S₆
• The first number ≥5 is S₄
• The first number ≥1 is S₀
• The first number ≥4 is S₄
• There is no number ≥9