Sasha had been solving competitive programming problems with his friends for a long time, and they had sandwiches as a snack. All of Sasha’s guests have already left. Sasha threw away all the crumbs, and now he needs to wash the dishes. When he started washing the dishes, he looked at the dryer. The plates in the dryer reminded him of a bracket sequence. Depending on which way a plate is turned, it looks like an opening ‘(’ or closing ‘)’ bracket. The dryer may not be completely filled with plates; that is, some places may be empty. Sasha wondered which way it is better to place the washed plates. He is interested in which prefixes of the dryer he can turn into a correct bracket sequence.

The dryer can be represented as a string of length N consisting of the characters ‘(’, ‘)’ and ‘?’ . The character ‘?’ denotes an empty place where a plate can be placed. Sasha has Q independent questions, and in the i-th of them, one number k_i is given. For each question, determine whether in the prefix of length k_i it is possible to replace each character ‘?’ with ‘(’ or ‘)’ so that the resulting prefix becomes a correct bracket sequence.

Recall that a string is called a correct bracket sequence if it is either empty or has the form (S₁)S₂, where S₁ and S₂ are correct bracket sequences.

The first line contains the number N (1 ≤ N ≤ 10⁵) — the number of places in the dryer.

The second line contains a string of length N consisting of the characters ‘(’, ‘)’ and ‘?’ , describing the dryer.

The third line contains the number Q (1 ≤ Q ≤ N).

The fourth line contains Q distinct integers k_i (1 ≤ k_i ≤ N), where k_i is the length of the prefix in the i-th question.

Print Q lines. In the i-th line, print “YES”, if the prefix of length k_i can be turned into a correct bracket sequence, and “NO” otherwise.