While rummaging through things in a distant drawer, Anya found a beautiful string $$$s$$$ consisting only of zeros and ones.

Now she wants to make it even more beautiful by performing $$$q$$$ operations on it.

Each operation is described by two integers $$$i$$$ ($$$1 \le i \le |s|$$$) and $$$v$$$ ($$$v \in \{0, 1\}$$$) and means that the $$$i$$$-th character of the string is assigned the value $$$v$$$ (that is, the assignment $$$s_i = v$$$ is performed).

But Anya loves the number $$$1100$$$, so after each query, she asks you to tell her whether the substring "1100" is present in her string (i.e. there exist such $$$1 \le i \le |s| - 3$$$ that $$$s_{i}s_{i + 1}s_{i + 2}s_{i + 3} = \texttt{1100}$$$).

Input format:
The first line contains one integer $$$t$$$ ($$$1 \leq t \leq 10^4$$$) — the number of test cases.

The first line of the test case contains the string $$$s$$$ ($$$1 \leq |s| \leq 2 \cdot 10^5$$$), consisting only of the characters "0" and "1". Here $$$|s|$$$ denotes the length of the string $$$s$$$.

The next line contains an integer $$$q$$$ ($$$1 \leq q \leq 2 \cdot 10^5$$$) — the number of queries.

The following $$$q$$$ lines contain two integers $$$i$$$ ($$$1 \leq i \leq |s|$$$) and $$$v$$$ ($$$v \in \{0, 1\}$$$), describing the query.

It is guaranteed that the sum of $$$|s|$$$ across all test cases does not exceed $$$2 \cdot 10^5$$$. It is also guaranteed that the sum of $$$q$$$ across all test cases does not exceed $$$2 \cdot 10^5$$$.
Output format:
For each query, output "YES", if "1100" is present in Anya's string; otherwise, output "NO".

You can output the answer in any case (upper or lower). For example, the strings "yEs", "yes", "Yes", and "YES" will be recognized as positive responses.
Example Input 0:
4
100
4
1 1
2 0
2 0
3 1
1100000
3
6 1
7 1
4 1
111010
4
1 1
5 0
4 1
5 0
0100
4
3 1
1 1
2 0
2 1

Example Output 0:
NO
NO
NO
NO
YES
YES
NO
NO
YES
YES
YES
NO
NO
NO
NO



Example input:
4
100
4
1 1
2 0
2 0
3 1
1100000
3
6 1
7 1
4 1
111010
4
1 1
5 0
4 1
5 0
0100
4
3 1
1 1
2 0
2 1


Example output:
NO
NO
NO
NO
YES
YES
NO
NO
YES
YES
YES
NO
NO
NO
NO