Given two sequences of positive integers $a$ and $b$ of lengths $n$ and $m$ respectively, write a program to perform the following queries. All indices start from 1.

• 1 y z: Perform $a[y] = z$ and then output $F(a, b)$. ($1 \le y \le n$, $1 \le z \le 10^5$)
• 2 y z: Output $F(a[y..z], b)$. ($1 \le y \le z \le n$)
• 3 y z: Output $f(b[y..m], b[z..m])$. ($1 \le y, z \le m$)
• 4 p q r s: If the sequence $[b_p, b_{p+1}, \ldots, b_q, b_r, b_{r+1}, \ldots, b_s]$ is a contiguous subsequence of $b$, then output "yes", otherwise output "no". ($1 \le p \le q \le m$, $1 \le r \le s \le m$)

$a[l..r]$ is the subsequence $[a_l, a_{l+1}, \ldots, a_r]$. A similar definition holds for $b$.

For two sequences $x, y$:

• $f(x, y)$ denotes the length of the longest common prefix of $x$ and $y$.
• $F(x, y)$ is a pair of integers $(p, q)$, where $p$ is the maximum value of $f(z, y)$ over all suffixes $z$ of $x$, and $q$ is the number of $z$ that achieve this maximum.

Input

The first line contains an integer $n$, the length of $a$. ($1 \le n \le 10^5$)

The next line contains $n$ integers $a_1, a_2, \ldots, a_n$. ($1 \le a_i \le 10^5$)

The next line contains an integer $m$, the length of $b$. ($1 \le m \le 10^5$)

The next line contains $m$ integers $b_1, b_2, \ldots, b_m$. ($1 \le b_i \le 10^5$)

The next line contains an integer $q$, the number of queries. ($1 \le q \le 10^5$)

The next $q$ lines each contain a query as described above.

Output

For each query, output the result in order, each on its own line.

Examples

Input 1

10
1 2 3 3 3 1 2 3 2 1
3
1 3 1
10
3 1 3
4 3 3 2 2
2 2 10
1 3 2
2 7 9
2 7 10
2 3 9
2 2 8
1 7 1
1 4 2

Output 1

1
yes
1 2
1 3
0 3
1 1
1 1
1 1
2 1
2 1