{"raw_statement":[{"iden":"problem statement","content":"A string consisting of lowercase English letters, `(`, and `)` is said to be a **good string** if you can make it an empty string by the following procedure:\n\n*   First, remove all lowercase English letters.\n*   Then, repeatedly remove consecutive `()` while possible.\n\nFor example, `((a)ba)` is a good string, because removing all lowercase English letters yields `(())`, from which we can remove consecutive `()` at the $2$\\-nd and $3$\\-rd characters to obtain `()`, which in turn ends up in an empty string.\nYou are given a good string $S$. We denote by $S_i$ the $i$\\-th character of $S$.\nFor each lowercase English letter `a`, `b`, $\\ldots$, and `z`, we have a ball with the letter written on it. Additionally, we have an empty box.\nFor each $i = 1,2,$ $\\ldots$ $,|S|$ in this order, Takahashi performs the following operation unless he faints.\n\n*   If $S_i$ is a lowercase English letter, put the ball with the letter written on it into the box. If the ball is already in the box, he faints.\n*   If $S_i$ is `(`, do nothing.\n*   If $S_i$ is `)`, take the maximum integer $j$ less than $i$ such that the $j$\\-th through $i$\\-th characters of $S$ form a good string. (We can prove that such an integer $j$ always exists.) Take out from the box all the balls that he has put in the $j$\\-th through $i$\\-th operations.\n\nDetermine if Takahashi can complete the sequence of operations without fainting."},{"iden":"constraints","content":"*   $1 \\leq |S| \\leq 3 \\times 10^5$\n*   $S$ is a good string."},{"iden":"input","content":"The input is given from Standard Input in the following format:\n\n$S$"},{"iden":"sample input 1","content":"((a)ba)"},{"iden":"sample output 1","content":"Yes\n\nFor $i = 1$, he does nothing.  \nFor $i = 2$, he does nothing.  \nFor $i = 3$, he puts the ball with `a` written on it into the box.  \nFor $i = 4$, $j=2$ is the maximum integer less than $4$ such that the $j$\\-th through $4$\\-th characters of $S$ form a good string, so he takes out the ball with `a` written on it from the box.  \nFor $i = 5$, he puts the ball with `b` written on it into the box.  \nFor $i = 6$, he puts the ball with `a` written on it into the box.  \nFor $i = 7$, $j=1$ is the maximum integer less than $7$ such that the $j$\\-th through $7$\\-th characters of $S$ form a good string, so he takes out the ball with `a` written on it, and another with `b`, from the box.\nTherefore, the answer to this case is `Yes`."},{"iden":"sample input 2","content":"(a(ba))"},{"iden":"sample output 2","content":"No\n\nFor $i = 1$, he does nothing.  \nFor $i = 2$, he puts the ball with `a` written on it into the box.  \nFor $i = 3$, he does nothing.  \nFor $i = 4$, he puts the ball with `b` written on it into the box.  \nFor $i = 5$, the ball with `a` written on it is already in the box, so he faints, aborting the sequence of operations.\nTherefore, the answer to this case is `No`."},{"iden":"sample input 3","content":"(((())))"},{"iden":"sample output 3","content":"Yes"},{"iden":"sample input 4","content":"abca"},{"iden":"sample output 4","content":"No"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}