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:

-   First, remove all lowercase English letters.
-   Then, repeatedly remove consecutive `()` while possible.

For 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.

You are given a good string $S$. We denote by $S_i$ the $i$-th character of $S$.

For 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.

For each $i = 1,2,$ $\ldots$ $,|S|$ in this order, Takahashi performs the following operation unless he faints.

-   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.
-   If $S_i$ is `(`, do nothing.
-   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.

Determine if Takahashi can complete the sequence of operations without fainting.

The input is given from Standard Input in the following format:

```
$S$
```

Print `Yes` if he can complete the sequence of operations without fainting; print `No` otherwise.

-   $1 \leq |S| \leq 3 \times 10^5$
-   $S$ is a good string.

Yes

For i=1, he does nothing.
For i=2, he does nothing.
For i=3, he puts the ball with a written on it into the box.
For 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.
For i=5, he puts the ball with b written on it into the box.
For i=6, he puts the ball with a written on it into the box.
For 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.
Therefore, the answer to this case is Yes.

No

For i=1, he does nothing.
For i=2, he puts the ball with a written on it into the box.
For i=3, he does nothing.
For i=4, he puts the ball with b written on it into the box.
For i=5, the ball with a written on it is already in the box, so he faints, aborting the sequence of operations.
Therefore, the answer to this case is No.