You are at your grandparents' house and you are playing an old video game on a strange console. Your controller has only two buttons and each button has a number written on it. Initially, your score is (0). The game is composed of (n) rounds. For each (1\le i\le n), the (i)-th round works as follows. On the screen, a symbol (s_i) appears, which is either (+) ( plus ) or (-) ( minus ). Then you must press one of the two buttons on the controller once . Suppose you press a button with the number (x) written on it: your score will increase by (x) if the symbol was (+) and will decrease by (x) if the symbol was (-). After you press the button, the round ends. After you have played all (n) rounds, you win if your score is (0). Over the years, your grandparents bought many different controllers, so you have (q) of them. The two buttons on the (j)-th controller have the numbers (a_j) and (b_j) written on them. For each controller, you must compute whether you can win the game playing with that controller. The first line contains a single integer (n) ((1 \le n \le 2\cdot 10^5)) — the number of rounds. The second line contains a string (s) of length (n) — where (s_i) is the symbol that will appear on the screen in the (i)-th round. It is guaranteed that (s) contains only the characters (+) and (-). The third line contains an integer (q) ((1 \le q \le 10^5)) — the number of controllers. The following (q) lines contain two integers (a_j) and (b_j) each ((1 \le a_j, b_j \le 10^9)) — the numbers on the buttons of controller (j). Output (q) lines. On line (j) print (YES) if the game is winnable using controller (j), otherwise print (NO). In the first sample , one possible way to get score (0) using the first controller is by pressing the butt