L. Controllerstime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputYou 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 \texttt{+} (plus) or \texttt{-} (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 \texttt{+} and will decrease by x if the symbol was \texttt{-}. 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.InputThe 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 \texttt{+} and \texttt{-}.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. OutputOutput q lines. On line j print \texttt{YES} if the game is winnable using controller j, otherwise print \texttt{NO}.ExamplesInput
8
+-+---+-
5
2 1
10 3
7 9
10 10
5 3
Output
YES
NO
NO
NO
YES
Input
6
+-++--
2
9 7
1 1
Output
YES
YES
Input
20
+-----+--+--------+-
2
1000000000 99999997
250000000 1000000000
Output
NO
YES
NoteIn the first sample, one possible way to get score 0 using the first controller is by pressing the button with numnber 1 in rounds 1, 2, 4, 5, 6 and 8, and pressing the button with number 2 in rounds 3 and 7. It is possible to show that there is no way to get a score of 0 using the second controller.
8
+-+---+-
5
2 1
10 3
7 9
10 10
5 3

YES NO NO NO YES 
['binary search', 'math', '*1500']