You are an expert competitive programmer. You will be given a problem statement, test case constraints and example test inputs and outputs. Please reason step by step about the solution (that must respect memory and time limits), then provide a complete implementation in python3.

Your solution must read input from standard input (cin), write output to standard output (cout).
Do not include any debug prints or additional output.

Put your final solution within a single code block:
```python
<your code here>
```

Execution time limit: 2.0 seconds
Memory limit: 256.0 MB

# Problem
Alperen has two strings, $$$s$$$ and $$$t$$$ which are both initially equal to "a".

He will perform $$$q$$$ operations of two types on the given strings:

- $$$1 \;\; k \;\; x$$$ — Append the string $$$x$$$ exactly $$$k$$$ times at the end of string $$$s$$$. In other words, $$$s := s + \underbrace{x + \dots + x}_{k \text{ times}}$$$.
- $$$2 \;\; k \;\; x$$$ — Append the string $$$x$$$ exactly $$$k$$$ times at the end of string $$$t$$$. In other words, $$$t := t + \underbrace{x + \dots + x}_{k \text{ times}}$$$.

After each operation, determine if it is possible to rearrange the characters of $$$s$$$ and $$$t$$$ such that $$$s$$$ is lexicographically smaller$$$^{\dagger}$$$ than $$$t$$$.

Note that the strings change after performing each operation and don't go back to their initial states.

$$$^{\dagger}$$$ Simply speaking, the lexicographical order is the order in which words are listed in a dictionary. A formal definition is as follows: string $$$p$$$ is lexicographically smaller than string $$$q$$$ if there exists a position $$$i$$$ such that $$$p_i < q_i$$$, and for all $$$j < i$$$, $$$p_j = q_j$$$. If no such $$$i$$$ exists, then $$$p$$$ is lexicographically smaller than $$$q$$$ if the length of $$$p$$$ is less than the length of $$$q$$$. For example, $$$\texttt{abdc} < \texttt{abe}$$$ and $$$\texttt{abc} < \texttt{abcd}$$$, where we write $$$p < q$$$ if $$$p$$$ is lexicographically smaller than $$$q$$$.

## Input Format
The first line of the input contains an integer $$$t$$$ ($$$1 \leq t \leq 10^4$$$) — the number of test cases.

The first line of each test case contains an integer $$$q$$$ $$$(1 \leq q \leq 10^5)$$$ — the number of operations Alperen will perform.

Then $$$q$$$ lines follow, each containing two positive integers $$$d$$$ and $$$k$$$ ($$$1 \leq d \leq 2$$$; $$$1 \leq k \leq 10^5$$$) and a non-empty string $$$x$$$ consisting of lowercase English letters — the type of the operation, the number of times we will append string $$$x$$$ and the string we need to append respectively.

It is guaranteed that the sum of $$$q$$$ over all test cases doesn't exceed $$$10^5$$$ and that the sum of lengths of all strings $$$x$$$ in the input doesn't exceed $$$5 \cdot 10^5$$$.

## Output Format
For each operation, output "YES", if it is possible to arrange the elements in both strings in such a way that $$$s$$$ is lexicographically smaller than $$$t$$$ and "NO" otherwise.

## Examples
```input
3
5
2 1 aa
1 2 a
2 3 a
1 2 b
2 3 abca
2
1 5 mihai
2 2 buiucani
3
1 5 b
2 3 a
2 4 paiu
```
```output
YES
NO
YES
NO
YES
NO
YES
NO
NO
YES
```

## Note
In the first test case, the strings are initially $$$s = $$$ "a" and $$$t = $$$ "a".

After the first operation the string $$$t$$$ becomes "aaa". Since "a" is already lexicographically smaller than "aaa", the answer for this operation should be "YES".

After the second operation string $$$s$$$ becomes "aaa", and since $$$t$$$ is also equal to "aaa", we can't arrange $$$s$$$ in any way such that it is lexicographically smaller than $$$t$$$, so the answer is "NO".

After the third operation string $$$t$$$ becomes "aaaaaa" and $$$s$$$ is already lexicographically smaller than it so the answer is "YES".

After the fourth operation $$$s$$$ becomes "aaabb" and there is no way to make it lexicographically smaller than "aaaaaa" so the answer is "NO".

After the fifth operation the string $$$t$$$ becomes "aaaaaaabcaabcaabca", and we can rearrange the strings to: "bbaaa" and "caaaaaabcaabcaabaa" so that $$$s$$$ is lexicographically smaller than $$$t$$$, so we should answer "YES".

Now solve the problem and return the code.