Controllers

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 $1 ≤ i ≤ n$, 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 $n$ ($1 ≤ n ≤ 2 \cdot 10^5$) — 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 $q$ ($1 ≤ q ≤ 10^5$) — the number of controllers.

The following $q$ lines contain two integers $a\_j$ and $b\_j$ each ($1 ≤ a\_j , b\_j ≤ 10^9$) — 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.