You are given a set $S$ of $0$ string. There are $q$ queries of the following types:
- Add a string to $S$.
- Determine if there exists a group of $k$ strings having common suffix of length $l$.
- Remove the string added in the $i^{th}$ query, it is guaranteed that the string exists in $S$.
### Input
- The first line contains an integer $q$.
- The next $q$ lines, each line follow the form:
+ `1 s`: Add string $s$ to $S$.
+ `2 k l`: Determine if there exists a group of $k$ strings having common suffix of length $l$.
+ `3 i`: Remove the string added in the $i^{th}$ operation.
### Output
- Print the answer for the query of type $2$. Print `YES` if it exists, otherwise print `NO`.
### Constraints
- $1 \le q \le 10^5$.
- $1 \le k, l \le 10^6$.
- $1 \le i \le q$.
- The sum of string length does not exceed $10^6$.
- $S_i$ contain only lowercase letters.
### Example
Input:
```
9
1 aba
1 accba
2 2 2
2 2 3
1 aaaa
1 ababa
2 3 2
3 1
2 3 2
```
Output:
```
YES
NO
YES
NO
```
