Sruti is a forgetful student. She forgets almost everything that she sees in her day-to-day life. To improve her memory, she has decided to take part in a memory competition. In this competition, she will be provided a list containing N integers sorted in ascending order. She has to remember this list.

Later, she will be asked Q number of queries. In each query, she will be provided with a number. She has to answer the index of that number in that list.

However, she has opted for high difficulty level. So, after deliberating for a few minutes, the judges introduced one additional step for her. She may receive any number which may or may not be present in the list.

In case the number is present, she has to print YES and the index of the number, separated by a single white-space.

In case the number is absent, she has to print NO and the index where the element should have been present in the list so that the list was still sorted in ascending order.

Input Format

The first line contains a single integer, N, denoting the size of the list. The second line will contain N space separated integers, arr[0], arr[1], ... arr[N-1]. The third line will contain a single integer, Q, denoting the number of queries to be made. Then, Q lines will follow, each having a single integer, R, as the query.

Output Format

There shall be Q lines in total. For each query, if the element is present, print YES and then the index of the element, separated by a single white-space. If the element is absent, print NO and then the index where the element should have been present in the list so that the list was still sorted in ascending order.

Note: All indexes are 0-indexed

Constraints

\( 1 \le N \le 10^7 \)

\( -10^7 \le arr[i] \le 10^7\)

\(1 \le Q \le 10^6 \)

\(-10^7 \le R \le 10^7\)