Problem Statement

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.

Input

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

Output

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

Constraints

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

Sample Input 1

((a)ba)

Sample Output 1

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.

Sample Input 2

(a(ba))

Sample Output 2

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.

Sample Input 3

(((())))

Sample Output 3

Yes

Sample Input 4

abca

Sample Output 4

No

见题面 Input 部分

见题面 Output 部分