Problem Statement

Let us define a correct parenthesis sequence as a string that satisfies one of the following conditions.

• It is an empty string.
• It is a concatenation of (, A, ), in this order, for some correct parenthesis sequence A.
• It is a concatenation of A, B, in this order, for some correct parenthesis sequences A and B.

We have a string S of length N consisting of ( and ).
Given $Q queries \text{Query}_1,\text{Query}_2,\ldots,\text{Query}_Q,$ process them in order. There are two kinds of queries, with the following formats and content.

• 1 l r: Swap the l-th and r-th characters of S.
• 2 l r: Determine whether the contiguous substring from the l-th through the r-th character is a correct parenthesis sequence.

Input

Input is given from Standard Input in the following format:
N Q
S
$\text{Query}_1$
$\text{Query}_2$
$\vdots$
$\text{Query}_Q$

Output

For each query in the format 2 l r, print Yes if the contiguous substring is a correct parenthesis sequence, and No otherwise, followed by a newline.

Constraints

• $1 \leq N,Q \leq 2 \times 10^5$
• S is a string of length N consisting of ( and ).
• $1 \leq l < r \leq N$
• N,Q,l,r are all integers.
• Each query is in the format 1 l r or 2 l r.
• There is at least one query in the format 2 l r.

Sample Input 1

5 3
(())(
2 1 4
2 1 2
2 4 5

Sample Output 1

Yes
No
No

In the first query, (()) is a correct parenthesis sequence.
In the second query, (( is not a correct parenthesis sequence.
In the third query, )( is not a correct parenthesis sequence.

Sample Input 2

5 3
(())(
2 1 4
1 1 4
2 1 4

Sample Output 2

Yes
No

In the first query, (()) is a correct parenthesis sequence.
In the second query, S becomes )()((.
In the third query, )()( is not a correct parenthesis sequence.

Sample Input 3

8 8
(()(()))
2 2 7
2 2 8
1 2 5
2 3 4
1 3 4
1 3 5
1 1 4
1 6 8

Sample Output 3

Yes
No
No

见题面 Input 部分

见题面 Output 部分