CF1776L.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 $1\le i\le n$, 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.

你正在祖父母家，玩一款老式电子游戏，而游戏机的控制器十分奇特：它只有两个按钮，每个按钮上都标有一个数字。

初始时，你的得分为 $0$。游戏共包含 $n$ 轮。对每个 $1\le i\le n$，第 $i$ 轮的规则如下：

屏幕上会显示一个符号 $s_i$，该符号要么是 $\texttt{+}$（加号），要么是 $\texttt{-}$（减号）。接着，你必须按下控制器上的两个按钮之一，且仅能按一次。假设你按下的按钮上标有数字 $x$：若屏幕上显示的是 $\texttt{+}$，则你的得分增加 $x$；若显示的是 $\texttt{-}$，则你的得分减少 $x$。按下按钮后，本轮结束。

当你完成全部 $n$ 轮后，若最终得分为 $0$，则获胜。

多年来，祖父母购买了许多不同的控制器，因此你一共有 $q$ 个控制器。第 $j$ 个控制器的两个按钮上分别标有数字 $a_j$ 和 $b_j$。对每个控制器，你需要判断：使用该控制器是否能够赢得游戏。

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 $\texttt{+}$ 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 $j$.

第一行包含一个整数 $n$（$1 \le n \le 2\cdot 10^5$）—— 表示回合数。

第二行包含一个长度为 $n$ 的字符串 $s$ —— 其中 $s_i$ 表示第 $i$ 回合屏幕上将显示的符号。保证字符串 $s$ 仅由字符 $\texttt{+}$ 和 $\texttt{-}$ 组成。

第三行包含一个整数 $q$（$1 \le q \le 10^5$）—— 表示控制器的数量。

接下来的 $q$ 行每行包含两个整数 $a_j$ 和 $b_j$（$1 \le a_j, b_j \le 10^9$）—— 分别表示第 $j$ 个控制器上两个按钮的数字。

Output $q$ lines. On line $j$ print $\texttt{YES}$ if the game is winnable using controller $j$, otherwise print $\texttt{NO}$.

输出 $q$ 行。在第 $j$ 行，如果使用控制器 $j$ 可以赢得游戏，则输出 $\texttt{YES}$，否则输出 $\texttt{NO}$。

In 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.

在第一个样例中，使用第一个控制器得到分数 $0$ 的一种可能方式是：在第 $1$、$2$、$4$、$5$、$6$ 和 $8$ 轮按下编号为 $1$ 的按钮，在第 $3$ 和 $7$ 轮按下编号为 $2$ 的按钮。可以证明，使用第二个控制器无法得到分数 $0$。