// 
pub mod solution {
//{"name":"u25_k","group":"Manual","url":"","interactive":false,"timeLimit":2000,"tests":[{"input":"","output":""}],"testType":"single","input":{"type":"stdin","fileName":null,"pattern":null},"output":{"type":"stdout","fileName":null,"pattern":null},"languages":{"java":{"taskClass":"u25_k"}}}

use crate::algo_lib::io::input::Input;
use crate::algo_lib::io::output::Output;
use crate::algo_lib::misc::random::random;
use crate::algo_lib::misc::value::DynamicValue;
use crate::algo_lib::misc::value_ref::ValueRef;
use crate::algo_lib::numbers::mod_int::ModInt;
use crate::algo_lib::numbers::num_traits::algebra::One;
use crate::algo_lib::numbers::num_traits::invertible::Invertible;
use crate::algo_lib::numbers::primes::prime::next_prime;
use crate::dynamic_value;
use crate::value_ref;

type PreCalc = ();

fn solve(input: &mut Input, out: &mut Output, _test_case: usize, _data: &mut PreCalc) {
let n1 = input.read_size();
let a = input.read_long_vec(n1);
let n2 = input.read_size();
let b = input.read_long_vec(n2);

dynamic_value!(HM: i64);
type HashMod = ModInt<i64, HM>;

value_ref!(HashBaseContainer HBCS: HashBase);

struct HashBase {
multiplier: HashMod,
inv_multiplier: HashMod,
power: Vec<HashMod>,
inv_power: Vec<HashMod>,
}

impl HashBase {
pub fn init() {
if unsafe { HBCS.is_some() } {
return;
}
HM::set_val(next_prime(
random().next_bounds(10i64.pow(18), 2 * 10i64.pow(18)),
));
let multiplier =
HashMod::new(random().next_bounds(4 * 10i64.pow(17), 5 * 10i64.pow(17)));
let inv_multiplier = multiplier.inv().unwrap();
HashBaseContainer::set_val(Self {
multiplier,
inv_multiplier,
power: vec![HashMod::one()],
inv_power: vec![HashMod::one()],
});
}

pub fn ensure_capacity(&mut self, n: usize) {
if self.power.len() < n {
self.power.reserve(n - self.power.len());
while self.power.len() < n {
self.power
.push(*self.power.last().unwrap() * self.multiplier);
}
self.inv_power.reserve(n - self.inv_power.len());
while self.inv_power.len() < n {
self.inv_power
.push(*self.inv_power.last().unwrap() * self.inv_multiplier);
}
}
}

pub fn get_power(n: usize) -> HashMod {
HashBaseContainer::val_mut().ensure_capacity(n + 1);
HashBaseContainer::val().power[n]
}
}

HashBase::init();
struct Node {
hash: HashMod,
max: i64,
qty: usize,
from: usize,
to: usize,
left_hash: HashMod,
left_qty: usize,
left: Option<Box<Node>>,
right: Option<Box<Node>>,
}

impl Node {
fn new(from: usize, to: usize, a: &[i64]) -> Self {
if from + 1 == to {
return Self {
hash: a[from].into(),
max: a[from],
qty: 1,
from,
to,
left_hash: 0.into(),
left_qty: 0,
left: None,
right: None,
};
}
let mid = (from + to) / 2;
let left = Self::new(from, mid, a);
let right = Self::new(mid, to, a);
let mut res = Self {
hash: 0.into(),
max: 0,
qty: 0,
from,
to,
left_hash: 0.into(),
left_qty: 0,
left: Some(Box::new(left)),
right: Some(Box::new(right)),
};
res.recalculate();
res
}

fn recalculate(&mut self) {
self.max = self
.left
.as_ref()
.unwrap()
.max
.max(self.right.as_ref().unwrap().max);
let right_max = self.right.as_ref().unwrap().max;
let (hash, qty) = self.left.as_ref().unwrap().more_than(right_max);
self.left_hash = hash;
self.left_qty = qty;
let right_qty = self.right.as_ref().unwrap().qty;
self.hash = hash * HashBase::get_power(right_qty) + self.right.as_ref().unwrap().hash;
self.qty = qty + right_qty;
}

fn more_than(&self, outer_max: i64) -> (HashMod, usize) {
if self.max < outer_max {
return (0.into(), 0);
}
if self.from + 1 == self.to {
return (self.hash, self.qty);
}
if self.right.as_ref().unwrap().max >= outer_max {
let (hash, qty) = self.right.as_ref().unwrap().more_than(outer_max);
(
self.left_hash * HashBase::get_power(qty) + hash,
self.left_qty + qty,
)
} else {
self.left.as_ref().unwrap().more_than(outer_max)
}
}

fn update(&mut self, pos: usize, val: i64) {
if self.from + 1 == self.to {
self.hash = val.into();
self.max = val;
self.qty = 1;
return;
}
let mid = (self.from + self.to) / 2;
if pos < mid {
self.left.as_mut().unwrap().update(pos, val);
} else {
self.right.as_mut().unwrap().update(pos, val);
}
self.recalculate();
}
}

let mut first = Node::new(0, n1, &a);
let mut second = Node::new(0, n2, &b);

let m = input.read_size();
for _ in 0..m {
let o = input.read_size();
let x = input.read_size() - 1;
let y = input.read_long();
if o == 1 {
first.update(x, y);
} else {
second.update(x, y);
}
out.print_line(first.hash == second.hash);
}
}

pub(crate) fn run(mut input: Input, mut output: Output) -> bool {
let mut pre_calc = ();

#[allow(dead_code)]
enum TestType {
Single,
MultiNumber,
MultiEof,
}
let test_type = TestType::Single;
match test_type {
TestType::Single => solve(&mut input, &mut output, 1, &mut pre_calc),
TestType::MultiNumber => {
let t = input.read();
for i in 1..=t {
solve(&mut input, &mut output, i, &mut pre_calc);
}
}
TestType::MultiEof => {
let mut i = 1;
while input.peek().is_some() {
solve(&mut input, &mut output, i, &mut pre_calc);
i += 1;
}
}
}
output.flush();
if false {
true
} else {
input.skip_whitespace();
input.peek().is_none()
}
}

}
pub mod algo_lib {
pub mod collections {
pub mod slice_ext {
pub mod indices {
use std::ops::Range;

pub trait Indices {
fn indices(&self) -> Range<usize>;
}

impl<T> Indices for [T] {
fn indices(&self) -> Range<usize> {
0..self.len()
}
}
}
}
pub mod vec_ext {
pub mod default {
pub fn default_vec<T: Default>(len: usize) -> Vec<T> {
let mut v = Vec::with_capacity(len);
for _ in 0..len {
v.push(T::default());
}
v
}
}
}
}
pub mod io {
pub mod input {
use crate::algo_lib::collections::vec_ext::default::default_vec;
use std::io::Read;

pub struct Input<'s> {
input: &'s mut dyn Read,
buf: Vec<u8>,
at: usize,
buf_read: usize,
}

macro_rules! read_impl {
($t: ty, $read_name: ident, $read_vec_name: ident) => {
pub fn $read_name(&mut self) -> $t {
self.read()
}

pub fn $read_vec_name(&mut self, len: usize) -> Vec<$t> {
self.read_vec(len)
}
};

($t: ty, $read_name: ident, $read_vec_name: ident, $read_pair_vec_name: ident) => {
read_impl!($t, $read_name, $read_vec_name);

pub fn $read_pair_vec_name(&mut self, len: usize) -> Vec<($t, $t)> {
self.read_vec(len)
}
};
}

impl<'s> Input<'s> {
const DEFAULT_BUF_SIZE: usize = 4096;

pub fn new(input: &'s mut dyn Read) -> Self {
Self {
input,
buf: default_vec(Self::DEFAULT_BUF_SIZE),
at: 0,
buf_read: 0,
}
}

pub fn new_with_size(input: &'s mut dyn Read, buf_size: usize) -> Self {
Self {
input,
buf: default_vec(buf_size),
at: 0,
buf_read: 0,
}
}

pub fn get(&mut self) -> Option<u8> {
if self.refill_buffer() {
let res = self.buf[self.at];
self.at += 1;
if res == b'\r' {
if self.refill_buffer() && self.buf[self.at] == b'\n' {
self.at += 1;
}
return Some(b'\n');
}
Some(res)
} else {
None
}
}

pub fn peek(&mut self) -> Option<u8> {
if self.refill_buffer() {
let res = self.buf[self.at];
Some(if res == b'\r' { b'\n' } else { res })
} else {
None
}
}

pub fn skip_whitespace(&mut self) {
while let Some(b) = self.peek() {
if !char::from(b).is_whitespace() {
return;
}
self.get();
}
}

pub fn next_token(&mut self) -> Option<Vec<u8>> {
self.skip_whitespace();
let mut res = Vec::new();
while let Some(c) = self.get() {
if char::from(c).is_whitespace() {
break;
}
res.push(c);
}
if res.is_empty() {
None
} else {
Some(res)
}
}

//noinspection RsSelfConvention
pub fn is_exhausted(&mut self) -> bool {
self.peek().is_none()
}

//noinspection RsSelfConvention
pub fn is_empty(&mut self) -> bool {
self.skip_whitespace();
self.is_exhausted()
}

pub fn read<T: Readable>(&mut self) -> T {
T::read(self)
}

pub fn read_vec<T: Readable>(&mut self, size: usize) -> Vec<T> {
let mut res = Vec::with_capacity(size);
for _ in 0..size {
res.push(self.read());
}
res
}

pub fn read_char(&mut self) -> char {
self.skip_whitespace();
self.get().unwrap().into()
}

read_impl!(u32, read_unsigned, read_unsigned_vec);
read_impl!(u64, read_u64, read_u64_vec);
read_impl!(usize, read_size, read_size_vec, read_size_pair_vec);
read_impl!(i32, read_int, read_int_vec, read_int_pair_vec);
read_impl!(i64, read_long, read_long_vec, read_long_pair_vec);
read_impl!(i128, read_i128, read_i128_vec);

fn refill_buffer(&mut self) -> bool {
if self.at == self.buf_read {
self.at = 0;
self.buf_read = self.input.read(&mut self.buf).unwrap();
self.buf_read != 0
} else {
true
}
}
}

pub trait Readable {
fn read(input: &mut Input) -> Self;
}

impl Readable for char {
fn read(input: &mut Input) -> Self {
input.read_char()
}
}

impl<T: Readable> Readable for Vec<T> {
fn read(input: &mut Input) -> Self {
let size = input.read();
input.read_vec(size)
}
}

macro_rules! read_integer {
($($t:ident)+) => {$(
impl Readable for $t {
fn read(input: &mut Input) -> Self {
input.skip_whitespace();
let mut c = input.get().unwrap();
let sgn = match c {
b'-' => {
c = input.get().unwrap();
true
}
b'+' => {
c = input.get().unwrap();
false
}
_ => false,
};
let mut res = 0;
loop {
assert!(c.is_ascii_digit());
res *= 10;
let d = (c - b'0') as $t;
if sgn {
res -= d;
} else {
res += d;
}
match input.get() {
None => break,
Some(ch) => {
if ch.is_ascii_whitespace() {
break;
} else {
c = ch;
}
}
}
}
res
}
}
)+};
}

read_integer!(i8 i16 i32 i64 i128 isize u8 u16 u32 u64 u128 usize);

macro_rules! tuple_readable {
($($name:ident)+) => {
impl<$($name: Readable), +> Readable for ($($name,)+) {
fn read(input: &mut Input) -> Self {
($($name::read(input),)+)
}
}
}
}

tuple_readable! {T}
tuple_readable! {T U}
tuple_readable! {T U V}
tuple_readable! {T U V X}
tuple_readable! {T U V X Y}
tuple_readable! {T U V X Y Z}
tuple_readable! {T U V X Y Z A}
tuple_readable! {T U V X Y Z A B}
tuple_readable! {T U V X Y Z A B C}
tuple_readable! {T U V X Y Z A B C D}
tuple_readable! {T U V X Y Z A B C D E}
tuple_readable! {T U V X Y Z A B C D E F}

impl Read for Input<'_> {
fn read(&mut self, buf: &mut [u8]) -> std::io::Result<usize> {
if self.at == self.buf_read {
self.input.read(buf)
} else {
let mut i = 0;
while i < buf.len() && self.at < self.buf_read {
buf[i] = self.buf[self.at];
i += 1;
self.at += 1;
}
Ok(i)
}
}
}
}
pub mod output {
use crate::algo_lib::collections::vec_ext::default::default_vec;
use std::io::stderr;
use std::io::Stderr;
use std::io::Write;

#[derive(Copy, Clone)]
pub enum BoolOutput {
YesNo,
YesNoCaps,
PossibleImpossible,
Custom(&'static str, &'static str),
}

impl BoolOutput {
pub fn output(&self, output: &mut Output, val: bool) {
(if val { self.yes() } else { self.no() }).write(output);
}

fn yes(&self) -> &str {
match self {
BoolOutput::YesNo => "Yes",
BoolOutput::YesNoCaps => "YES",
BoolOutput::PossibleImpossible => "Possible",
BoolOutput::Custom(yes, _) => yes,
}
}

fn no(&self) -> &str {
match self {
BoolOutput::YesNo => "No",
BoolOutput::YesNoCaps => "NO",
BoolOutput::PossibleImpossible => "Impossible",
BoolOutput::Custom(_, no) => no,
}
}
}

pub struct Output<'s> {
output: &'s mut dyn Write,
buf: Vec<u8>,
at: usize,
auto_flush: bool,
bool_output: BoolOutput,
}

impl<'s> Output<'s> {
const DEFAULT_BUF_SIZE: usize = 4096;

pub fn new(output: &'s mut dyn Write) -> Self {
Self {
output,
buf: default_vec(Self::DEFAULT_BUF_SIZE),
at: 0,
auto_flush: false,
bool_output: BoolOutput::YesNoCaps,
}
}

pub fn new_with_auto_flush(output: &'s mut dyn Write) -> Self {
Self {
output,
buf: default_vec(Self::DEFAULT_BUF_SIZE),
at: 0,
auto_flush: true,
bool_output: BoolOutput::YesNoCaps,
}
}

pub fn flush(&mut self) {
if self.at != 0 {
self.output.write_all(&self.buf[..self.at]).unwrap();
self.output.flush().unwrap();
self.at = 0;
}
}

pub fn print<T: Writable>(&mut self, s: T) {
s.write(self);
self.maybe_flush();
}

pub fn print_line<T: Writable>(&mut self, s: T) {
self.print(s);
self.put(b'\n');
self.maybe_flush();
}

pub fn put(&mut self, b: u8) {
self.buf[self.at] = b;
self.at += 1;
if self.at == self.buf.len() {
self.flush();
}
}

pub fn maybe_flush(&mut self) {
if self.auto_flush {
self.flush();
}
}

pub fn print_per_line<T: Writable>(&mut self, arg: &[T]) {
for i in arg {
i.write(self);
self.put(b'\n');
}
}

pub fn print_iter<T: Writable, I: Iterator<Item = T>>(&mut self, iter: I) {
let mut first = true;
for e in iter {
if first {
first = false;
} else {
self.put(b' ');
}
e.write(self);
}
}

pub fn set_bool_output(&mut self, bool_output: BoolOutput) {
self.bool_output = bool_output;
}
}

impl Write for Output<'_> {
fn write(&mut self, buf: &[u8]) -> std::io::Result<usize> {
let mut start = 0usize;
let mut rem = buf.len();
while rem > 0 {
let len = (self.buf.len() - self.at).min(rem);
self.buf[self.at..self.at + len].copy_from_slice(&buf[start..start + len]);
self.at += len;
if self.at == self.buf.len() {
self.flush();
}
start += len;
rem -= len;
}
self.maybe_flush();
Ok(buf.len())
}

fn flush(&mut self) -> std::io::Result<()> {
self.flush();
Ok(())
}
}

pub trait Writable {
fn write(&self, output: &mut Output);
}

impl Writable for &str {
fn write(&self, output: &mut Output) {
output.write_all(self.as_bytes()).unwrap();
}
}

impl Writable for String {
fn write(&self, output: &mut Output) {
output.write_all(self.as_bytes()).unwrap();
}
}

impl Writable for char {
fn write(&self, output: &mut Output) {
output.put(*self as u8);
}
}

impl<T: Writable> Writable for [T] {
fn write(&self, output: &mut Output) {
output.print_iter(self.iter());
}
}

impl<T: Writable, const N: usize> Writable for [T; N] {
fn write(&self, output: &mut Output) {
output.print_iter(self.iter());
}
}

impl<T: Writable> Writable for &T {
fn write(&self, output: &mut Output) {
T::write(self, output)
}
}

impl<T: Writable> Writable for Vec<T> {
fn write(&self, output: &mut Output) {
self.as_slice().write(output);
}
}

impl Writable for () {
fn write(&self, _output: &mut Output) {}
}

macro_rules! write_to_string {
($($t:ident)+) => {$(
impl Writable for $t {
fn write(&self, output: &mut Output) {
self.to_string().write(output);
}
}
)+};
}

write_to_string!(u8 u16 u32 u64 u128 usize i8 i16 i32 i64 i128 isize);

macro_rules! tuple_writable {
($name0:ident $($name:ident: $id:tt )*) => {
impl<$name0: Writable, $($name: Writable,)*> Writable for ($name0, $($name,)*) {
fn write(&self, out: &mut Output) {
self.0.write(out);
$(
out.put(b' ');
self.$id.write(out);
)*
}
}
}
}

tuple_writable! {T}
tuple_writable! {T U:1}
tuple_writable! {T U:1 V:2}
tuple_writable! {T U:1 V:2 X:3}
tuple_writable! {T U:1 V:2 X:3 Y:4}
tuple_writable! {T U:1 V:2 X:3 Y:4 Z:5}
tuple_writable! {T U:1 V:2 X:3 Y:4 Z:5 A:6}
tuple_writable! {T U:1 V:2 X:3 Y:4 Z:5 A:6 B:7}
tuple_writable! {T U:1 V:2 X:3 Y:4 Z:5 A:6 B:7 C:8}

impl<T: Writable> Writable for Option<T> {
fn write(&self, output: &mut Output) {
match self {
None => (-1).write(output),
Some(t) => t.write(output),
}
}
}

impl Writable for bool {
fn write(&self, output: &mut Output) {
let bool_output = output.bool_output;
bool_output.output(output, *self)
}
}

static mut ERR: Option<Stderr> = None;

pub fn err() -> Output<'static> {
unsafe {
if ERR.is_none() {
ERR = Some(stderr());
}
Output::new_with_auto_flush(ERR.as_mut().unwrap())
}
}
}
}
pub mod misc {
pub mod random {
use crate::algo_lib::collections::slice_ext::indices::Indices;
use crate::algo_lib::numbers::num_traits::algebra::IntegerSemiRingWithSub;
use crate::algo_lib::numbers::num_traits::primitive::Primitive;
use std::ops::Rem;
use std::time::SystemTime;

const NN: usize = 312;
const MM: usize = 156;
const MATRIX_A: u64 = 0xB5026F5AA96619E9;
const UM: u64 = 0xFFFFFFFF80000000;
const LM: u64 = 0x7FFFFFFF;
const F: u64 = 6364136223846793005;
const MAG01: [u64; 2] = [0, MATRIX_A];

pub struct Random {
mt: [u64; NN],
index: usize,
}

impl Random {
pub fn new(seed: u64) -> Self {
let mut res = Self {
mt: [0u64; NN],
index: NN,
};
res.mt[0] = seed;
for i in 1..NN {
res.mt[i] = F
.wrapping_mul(res.mt[i - 1] ^ (res.mt[i - 1] >> 62))
.wrapping_add(i as u64);
}
res
}

pub fn gen(&mut self) -> u64 {
if self.index == NN {
for i in 0..(NN - MM) {
let x = (self.mt[i] & UM) | (self.mt[i + 1] & LM);
self.mt[i] = self.mt[i + MM] ^ (x >> 1) ^ MAG01[(x & 1) as usize];
}
for i in (NN - MM)..(NN - 1) {
let x = (self.mt[i] & UM) | (self.mt[i + 1] & LM);
self.mt[i] = self.mt[i + MM - NN] ^ (x >> 1) ^ MAG01[(x & 1) as usize];
}
let x = (self.mt[NN - 1] & UM) | (self.mt[0] & LM);
self.mt[NN - 1] = self.mt[MM - 1] ^ (x >> 1) ^ MAG01[(x & 1) as usize];
self.index = 0;
}
let mut x = self.mt[self.index];
self.index += 1;
x ^= (x >> 29) & 0x5555555555555555;
x ^= (x << 17) & 0x71D67FFFEDA60000;
x ^= (x << 37) & 0xFFF7EEE000000000;
x ^= x >> 43;
x
}

pub fn next<T: Rem<Output = T> + Primitive<u64>>(&mut self, n: T) -> T
where
u64: Primitive<T>,
{
(self.gen() % n.to()).to()
}

pub fn next_bounds<T: IntegerSemiRingWithSub + Primitive<u64>>(&mut self, f: T, t: T) -> T
where
u64: Primitive<T>,
{
f + self.next(t - f + T::one())
}
}

static mut RAND: Option<Random> = None;

pub fn random() -> &'static mut Random {
unsafe {
if RAND.is_none() {
RAND = Some(Random::new(
(SystemTime::UNIX_EPOCH.elapsed().unwrap().as_nanos() & 0xFFFFFFFFFFFFFFFF) as u64,
));
}
RAND.as_mut().unwrap()
}
}

pub trait Shuffle {
fn shuffle(&mut self);
}

impl<T> Shuffle for [T] {
fn shuffle(&mut self) {
for i in self.indices() {
let at = random().next(i + 1);
self.swap(i, at);
}
}
}
}
pub mod value {
use std::hash::Hash;

pub trait Value<T>: Copy + Eq + Hash {
fn val() -> T;
}

pub trait ConstValue<T>: Value<T> {
const VAL: T;
}

impl<T, V: ConstValue<T>> Value<T> for V {
fn val() -> T {
Self::VAL
}
}

#[macro_export]
macro_rules! value {
($name: ident: $t: ty = $val: expr) => {
#[derive(Copy, Clone, Eq, PartialEq, Hash, Ord, PartialOrd, Default)]
pub struct $name {}

impl $crate::algo_lib::misc::value::ConstValue<$t> for $name {
const VAL: $t = $val;
}
};
}

pub trait DynamicValue<T>: Value<T> {
//noinspection RsSelfConvention
fn set_val(t: T);
}

#[macro_export]
macro_rules! dynamic_value {
($name: ident: $t: ty) => {
static mut VAL: Option<$t> = None;

#[derive(Copy, Clone, Eq, PartialEq, Hash, Default)]
struct $name {}

impl $crate::algo_lib::misc::value::DynamicValue<$t> for $name {
fn set_val(t: $t) {
unsafe {
VAL = Some(t);
}
}
}

impl $crate::algo_lib::misc::value::Value<$t> for $name {
fn val() -> $t {
unsafe { VAL.unwrap() }
}
}
};
($name: ident: $t: ty = $val: expr) => {
dynamic_value!($name: $t);

$name::set_val($val);
};
}
}
pub mod value_ref {
pub trait ConstValueRef<T: ?Sized + 'static> {
fn val() -> &'static T;
}

pub trait ValueRef<T: 'static> {
fn val() -> &'static T;
fn set_val(t: T);
fn val_mut() -> &'static mut T;
}

#[macro_export]
macro_rules! const_value_ref {
($name: ident $val_name: ident: $int_t: ty as $ext_t: ty = $base: expr) => {
const $val_name: $int_t = $base;

#[derive(Copy, Clone, Eq, PartialEq, Hash)]
pub struct $name {}

impl $crate::algo_lib::misc::value_ref::ConstValueRef<$ext_t> for $name {
fn val() -> &'static $ext_t {
&$val_name
}
}
};
}

#[macro_export]
macro_rules! value_ref {
($name: ident $val_name: ident: $t: ty) => {
static mut $val_name: Option<$t> = None;

#[derive(Copy, Clone, Eq, PartialEq, Hash)]
struct $name {}

impl $crate::algo_lib::misc::value_ref::ValueRef<$t> for $name {
fn val() -> &'static $t {
unsafe { $val_name.as_ref().unwrap() }
}

fn set_val(t: $t) {
unsafe {
$val_name = Some(t);
}
}

fn val_mut() -> &'static mut $t {
unsafe { $val_name.as_mut().unwrap() }
}
}
};
}
}
pub mod when {
#[macro_export]
macro_rules! when {
{$($cond: expr => $then: expr,)*} => {
match () {
$(_ if $cond => $then,)*
_ => unreachable!(),
}
};
{$($cond: expr => $then: expr,)* else $(=>)? $else: expr,} => {
match () {
$(_ if $cond => $then,)*
_ => $else,
}
};
}
}
}
pub mod numbers {
pub mod gcd {
use crate::algo_lib::numbers::num_traits::algebra::IntegerMultiplicationMonoid;
use crate::algo_lib::numbers::num_traits::algebra::IntegerSemiRingWithSub;
use crate::algo_lib::numbers::num_traits::algebra::One;
use crate::algo_lib::numbers::num_traits::algebra::SemiRingWithSub;
use crate::algo_lib::numbers::num_traits::algebra::Zero;
use crate::algo_lib::numbers::num_traits::wideable::Wideable;
use std::mem::swap;

pub fn extended_gcd<T: IntegerSemiRingWithSub + Wideable + Copy>(a: T, b: T) -> (T, T::W, T::W)
where
T::W: Copy + SemiRingWithSub,
{
if a == T::zero() {
(b, T::W::zero(), T::W::one())
} else {
let (d, y, mut x) = extended_gcd(b % a, a);
x -= T::W::from(b / a) * y;
(d, x, y)
}
}

pub fn gcd<T: Copy + Zero + IntegerMultiplicationMonoid>(mut a: T, mut b: T) -> T {
while b != T::zero() {
a %= b;
swap(&mut a, &mut b);
}
a
}

pub fn lcm<T: Copy + Zero + IntegerMultiplicationMonoid>(a: T, b: T) -> T {
(a / gcd(a, b)) * b
}
}
pub mod mod_int {
use crate::algo_lib::io::input::Input;
use crate::algo_lib::io::input::Readable;
use crate::algo_lib::io::output::Output;
use crate::algo_lib::io::output::Writable;
use crate::algo_lib::misc::value::Value;
use crate::algo_lib::numbers::gcd::extended_gcd;
use crate::algo_lib::numbers::num_traits::algebra::Field;
use crate::algo_lib::numbers::num_traits::algebra::IntegerRing;
use crate::algo_lib::numbers::num_traits::algebra::One;
use crate::algo_lib::numbers::num_traits::algebra::Ring;
use crate::algo_lib::numbers::num_traits::algebra::Zero;
use crate::algo_lib::numbers::num_traits::as_index::AsIndex;
use crate::algo_lib::numbers::num_traits::invertible::Invertible;
use crate::algo_lib::numbers::num_traits::wideable::Wideable;
use crate::value;
use crate::when;
use std::collections::HashMap;
use std::fmt::Display;
use std::fmt::Formatter;
use std::hash::Hash;
use std::marker::PhantomData;
use std::ops::Add;
use std::ops::AddAssign;
use std::ops::Div;
use std::ops::DivAssign;
use std::ops::Mul;
use std::ops::MulAssign;
use std::ops::Neg;
use std::ops::Sub;
use std::ops::SubAssign;

pub trait BaseModInt: Field + Copy {
type W: IntegerRing + Copy + From<Self::T>;
type T: IntegerRing + Ord + Copy + Wideable<W = Self::W>;

fn from(v: Self::T) -> Self;
fn module() -> Self::T;
}

#[derive(Copy, Clone, Eq, PartialEq, Hash, Default)]
pub struct ModInt<T, V: Value<T>> {
n: T,
phantom: PhantomData<V>,
}

impl<T: Copy, V: Value<T>> ModInt<T, V> {
pub fn val(&self) -> T {
self.n
}
}

impl<T: Ring + Ord + Copy, V: Value<T>> ModInt<T, V> {
unsafe fn unchecked_new(n: T) -> Self {
debug_assert!(n >= T::zero() && n < V::val());
Self {
n,
phantom: Default::default(),
}
}

unsafe fn maybe_subtract_mod(mut n: T) -> T {
debug_assert!(n < V::val() + V::val() && n >= T::zero());
if n >= V::val() {
n -= V::val();
}
n
}
}

impl<T: IntegerRing + Ord + Copy, V: Value<T>> ModInt<T, V> {
pub fn new(n: T) -> Self {
unsafe { Self::unchecked_new(Self::maybe_subtract_mod(n % (V::val()) + V::val())) }
}
}

impl<T: Copy + IntegerRing + Ord + Wideable + Hash, V: Value<T>> ModInt<T, V>
where
T::W: Copy + IntegerRing,
{
pub fn log(&self, alpha: Self) -> T {
let mut base = HashMap::new();
let mut exp = T::zero();
let mut pow = Self::one();
let mut inv = *self;
let alpha_inv = alpha.inv().unwrap();
while exp * exp < Self::module() {
if inv == Self::one() {
return exp;
}
base.insert(inv, exp);
exp += T::one();
pow *= alpha;
inv *= alpha_inv;
}
let step = pow;
let mut i = T::one();
loop {
if let Some(b) = base.get(&pow) {
break exp * i + *b;
}
pow *= step;
i += T::one();
}
}
}

impl<T: Wideable + Ring + Ord + Copy, V: Value<T>> ModInt<T, V>
where
T::W: IntegerRing,
{
pub fn new_from_wide(n: T::W) -> Self {
unsafe {
Self::unchecked_new(Self::maybe_subtract_mod(
T::downcast(n % (V::val()).into()) + V::val(),
))
}
}
}

impl<T: Copy + IntegerRing + Ord + Wideable, V: Value<T>> Invertible for ModInt<T, V>
where
T::W: Copy + IntegerRing,
{
type Output = Self;

fn inv(&self) -> Option<Self> {
let (g, x, _) = extended_gcd(self.n, V::val());
if g != T::one() {
None
} else {
Some(Self::new_from_wide(x))
}
}
}

impl<T: IntegerRing + Ord + Copy + Wideable, V: Value<T>> BaseModInt for ModInt<T, V>
where
T::W: IntegerRing + Copy,
{
type W = T::W;
type T = T;

fn from(v: Self::T) -> Self {
Self::new(v)
}

fn module() -> T {
V::val()
}
}

impl<T: IntegerRing + Ord + Copy, V: Value<T>> From<T> for ModInt<T, V> {
fn from(n: T) -> Self {
Self::new(n)
}
}

impl<T: Ring + Ord + Copy, V: Value<T>> AddAssign for ModInt<T, V> {
fn add_assign(&mut self, rhs: Self) {
self.n = unsafe { Self::maybe_subtract_mod(self.n + rhs.n) };
}
}

impl<T: Ring + Ord + Copy, V: Value<T>> Add for ModInt<T, V> {
type Output = Self;

fn add(mut self, rhs: Self) -> Self::Output {
self += rhs;
self
}
}

impl<T: Ring + Ord + Copy, V: Value<T>> SubAssign for ModInt<T, V> {
fn sub_assign(&mut self, rhs: Self) {
self.n = unsafe { Self::maybe_subtract_mod(self.n + V::val() - rhs.n) };
}
}

impl<T: Ring + Ord + Copy, V: Value<T>> Sub for ModInt<T, V> {
type Output = Self;

fn sub(mut self, rhs: Self) -> Self::Output {
self -= rhs;
self
}
}

impl<T: IntegerRing + Ord + Copy + Wideable, V: Value<T>> MulAssign for ModInt<T, V>
where
T::W: IntegerRing + Copy,
{
fn mul_assign(&mut self, rhs: Self) {
self.n = T::downcast(T::W::from(self.n) * T::W::from(rhs.n) % T::W::from(V::val()));
}
}

impl<T: IntegerRing + Ord + Copy + Wideable, V: Value<T>> Mul for ModInt<T, V>
where
T::W: IntegerRing + Copy,
{
type Output = Self;

fn mul(mut self, rhs: Self) -> Self::Output {
self *= rhs;
self
}
}

impl<T: IntegerRing + Ord + Copy + Wideable, V: Value<T>> DivAssign for ModInt<T, V>
where
T::W: IntegerRing + Copy,
{
#[allow(clippy::suspicious_op_assign_impl)]
fn div_assign(&mut self, rhs: Self) {
*self *= rhs.inv().unwrap();
}
}

impl<T: IntegerRing + Ord + Copy + Wideable, V: Value<T>> Div for ModInt<T, V>
where
T::W: IntegerRing + Copy,
{
type Output = Self;

fn div(mut self, rhs: Self) -> Self::Output {
self /= rhs;
self
}
}

impl<T: Ring + Ord + Copy, V: Value<T>> Neg for ModInt<T, V> {
type Output = Self;

fn neg(mut self) -> Self::Output {
self.n = unsafe { Self::maybe_subtract_mod(V::val() - self.n) };
self
}
}

impl<T: Display, V: Value<T>> Display for ModInt<T, V> {
fn fmt(&self, f: &mut Formatter<'_>) -> std::fmt::Result {
<T as Display>::fmt(&self.n, f)
}
}

impl<T: IntegerRing + Ord + Copy + Readable, V: Value<T>> Readable for ModInt<T, V> {
fn read(input: &mut Input) -> Self {
Self::new(T::read(input))
}
}

impl<T: Writable, V: Value<T>> Writable for ModInt<T, V> {
fn write(&self, output: &mut Output) {
self.n.write(output);
}
}

impl<T: Ring + Ord + Copy, V: Value<T>> Zero for ModInt<T, V> {
fn zero() -> Self {
unsafe { Self::unchecked_new(T::zero()) }
}
}

impl<T: IntegerRing + Ord + Copy, V: Value<T>> One for ModInt<T, V> {
fn one() -> Self {
Self::new(T::one())
}
}

impl<T, V: Value<T>> Wideable for ModInt<T, V> {
type W = Self;

fn downcast(w: Self::W) -> Self {
w
}
}

impl<T: IntegerRing + Ord + Copy + Wideable + Display + AsIndex, V: Value<T>> std::fmt::Debug
for ModInt<T, V>
where
T::W: IntegerRing + Copy,
{
fn fmt(&self, f: &mut Formatter) -> std::fmt::Result {
let max = T::from_index(100);
when! {
self.n <= max => write!(f, "{}", self.n),
self.n >= V::val() - max => write!(f, "{}", self.n - V::val()),
else => {
let mut denominator = T::one();
while denominator < max {
let mut num = T::one();
while num < max {
if Self::new(num) / Self::new(denominator) == *self {
return write!(f, "{}/{}", num, denominator);
}
if -Self::new(num) / Self::new(denominator) == *self {
return write!(f, "-{}/{}", num, denominator);
}
num += T::one();
}
denominator += T::one();
}
write!(f, "(?? {} ??)", self.n)
},
}
}
}

impl<T: IntegerRing + Ord + Copy + AsIndex, V: Value<T>> AsIndex for ModInt<T, V> {
fn from_index(idx: usize) -> Self {
Self::new(T::from_index(idx))
}

fn to_index(self) -> usize {
self.n.to_index()
}
}

value!(Val7: i32 = 1_000_000_007);
pub type ModInt7 = ModInt<i32, Val7>;

value!(Val9: i32 = 1_000_000_009);
pub type ModInt9 = ModInt<i32, Val9>;

value!(ValF: i32 = 998_244_353);
pub type ModIntF = ModInt<i32, ValF>;
}
pub mod num_traits {
pub mod algebra {
use crate::algo_lib::numbers::num_traits::invertible::Invertible;
use std::ops::Add;
use std::ops::AddAssign;
use std::ops::Div;
use std::ops::DivAssign;
use std::ops::Mul;
use std::ops::MulAssign;
use std::ops::Neg;
use std::ops::Rem;
use std::ops::RemAssign;
use std::ops::Sub;
use std::ops::SubAssign;

pub trait Zero {
fn zero() -> Self;
}

pub trait One {
fn one() -> Self;
}

pub trait AdditionMonoid: Add<Output = Self> + AddAssign + Zero + Eq + Sized {}

impl<T: Add<Output = Self> + AddAssign + Zero + Eq> AdditionMonoid for T {}

pub trait AdditionMonoidWithSub: AdditionMonoid + Sub<Output = Self> + SubAssign {}

impl<T: AdditionMonoid + Sub<Output = Self> + SubAssign> AdditionMonoidWithSub for T {}

pub trait AdditionGroup: AdditionMonoidWithSub + Neg<Output = Self> {}

impl<T: AdditionMonoidWithSub + Neg<Output = Self>> AdditionGroup for T {}

pub trait MultiplicationMonoid: Mul<Output = Self> + MulAssign + One + Eq + Sized {}

impl<T: Mul<Output = Self> + MulAssign + One + Eq> MultiplicationMonoid for T {}

pub trait IntegerMultiplicationMonoid:
MultiplicationMonoid + Div<Output = Self> + Rem<Output = Self> + DivAssign + RemAssign
{
}

impl<T: MultiplicationMonoid + Div<Output = Self> + Rem<Output = Self> + DivAssign + RemAssign>
IntegerMultiplicationMonoid for T
{
}

pub trait MultiplicationGroup:
MultiplicationMonoid + Div<Output = Self> + DivAssign + Invertible<Output = Self>
{
}

impl<T: MultiplicationMonoid + Div<Output = Self> + DivAssign + Invertible<Output = Self>>
MultiplicationGroup for T
{
}

pub trait SemiRing: AdditionMonoid + MultiplicationMonoid {}

impl<T: AdditionMonoid + MultiplicationMonoid> SemiRing for T {}

pub trait SemiRingWithSub: AdditionMonoidWithSub + SemiRing {}

impl<T: AdditionMonoidWithSub + SemiRing> SemiRingWithSub for T {}

pub trait Ring: SemiRing + AdditionGroup {}

impl<T: SemiRing + AdditionGroup> Ring for T {}

pub trait IntegerSemiRing: SemiRing + IntegerMultiplicationMonoid {}

impl<T: SemiRing + IntegerMultiplicationMonoid> IntegerSemiRing for T {}

pub trait IntegerSemiRingWithSub: SemiRingWithSub + IntegerSemiRing {}

impl<T: SemiRingWithSub + IntegerSemiRing> IntegerSemiRingWithSub for T {}

pub trait IntegerRing: IntegerSemiRing + Ring {}

impl<T: IntegerSemiRing + Ring> IntegerRing for T {}

pub trait Field: Ring + MultiplicationGroup {}

impl<T: Ring + MultiplicationGroup> Field for T {}

macro_rules! zero_one_integer_impl {
($($t: ident)+) => {$(
impl Zero for $t {
fn zero() -> Self {
0
}
}

impl One for $t {
fn one() -> Self {
1
}
}
)+};
}

zero_one_integer_impl!(i128 i64 i32 i16 i8 isize u128 u64 u32 u16 u8 usize);
}
pub mod as_index {
pub trait AsIndex {
fn from_index(idx: usize) -> Self;
fn to_index(self) -> usize;
}

macro_rules! from_index_impl {
($($t: ident)+) => {$(
impl AsIndex for $t {
fn from_index(idx: usize) -> Self {
idx as $t
}

fn to_index(self) -> usize {
self as usize
}
}
)+};
}

from_index_impl!(i128 i64 i32 i16 i8 isize u128 u64 u32 u16 u8 usize);
}
pub mod invertible {
pub trait Invertible {
type Output;

fn inv(&self) -> Option<Self::Output>;
}
}
pub mod primitive {
pub trait Primitive<T>: Copy {
fn to(self) -> T;
}

macro_rules! primitive_one {
($t: ident, $($u: ident)+) => {$(
impl Primitive<$u> for $t {
fn to(self) -> $u {
self as $u
}
}
)+};
}

macro_rules! primitive {
($($t: ident)+) => {$(
primitive_one!($t, u8 u16 u32 u64 u128 usize i8 i16 i32 i64 i128 isize);
)+}
}

primitive!(u8 u16 u32 u64 u128 usize i8 i16 i32 i64 i128 isize);
}
pub mod wideable {
use std::convert::From;

pub trait Wideable: Sized {
type W: From<Self>;

fn downcast(w: Self::W) -> Self;
}

macro_rules! wideable_impl {
($($t: ident $w: ident),+) => {$(
impl Wideable for $t {
type W = $w;

fn downcast(w: Self::W) -> Self {
w as $t
}
}
)+};
}

wideable_impl!(i64 i128, i32 i64, i16 i32, i8 i16, u64 u128, u32 u64, u16 u32, u8 u16);
}
}
pub mod number_ext {
use crate::algo_lib::numbers::num_traits::algebra::IntegerSemiRing;
use crate::algo_lib::numbers::num_traits::algebra::MultiplicationMonoid;
use crate::algo_lib::numbers::num_traits::as_index::AsIndex;
use std::ops::Mul;

pub trait Power {
#[must_use]
fn power<T: IntegerSemiRing + Copy>(&self, exp: T) -> Self;
}

impl<S: MultiplicationMonoid + Copy> Power for S {
fn power<T: IntegerSemiRing + Copy>(&self, exp: T) -> Self {
if exp == T::zero() {
S::one()
} else {
let mut res = self.power(exp / (T::one() + T::one()));
res *= res;
if exp % (T::one() + T::one()) == T::one() {
res *= *self;
}
res
}
}
}

pub trait NumDigs {
fn num_digs(&self) -> usize;
}

impl<S: IntegerSemiRing + AsIndex + Copy> NumDigs for S {
fn num_digs(&self) -> usize {
let mut copy = *self;
let ten = S::from_index(10);
let mut res = 0;
while copy != S::zero() {
copy /= ten;
res += 1;
}
res
}
}

pub trait Square {
fn square(self) -> Self;
}

impl<T: Mul<Output = T> + Copy> Square for T {
fn square(self) -> Self {
self * self
}
}
}
pub mod primes {
pub mod prime {
use crate::algo_lib::misc::random::random;
use crate::algo_lib::misc::value::DynamicValue;
use crate::algo_lib::numbers::gcd::gcd;
use crate::algo_lib::numbers::mod_int::ModInt;
use crate::algo_lib::numbers::num_traits::algebra::One;
use crate::algo_lib::numbers::num_traits::algebra::Zero;
use crate::algo_lib::numbers::num_traits::primitive::Primitive;
use crate::algo_lib::numbers::number_ext::Power;
use crate::dynamic_value;
use crate::when;

pub fn is_prime(n: impl Primitive<i64>) -> bool {
let n = n.to();
if n <= 1 {
return false;
}
let mut s = 0;
let mut d = n - 1;
while d % 2 == 0 {
s += 1;
d >>= 1;
}
if s == 0 {
return n == 2;
}
dynamic_value!(IsPrimeModule: i64 = n);
type Mod = ModInt<i64, IsPrimeModule>;
for _ in 0..20 {
let a = Mod::new(random().next(n as u64) as i64);
if a == Mod::zero() {
continue;
}
if a.power(d) == Mod::one() {
continue;
}
let mut dd = d;
let mut good = true;
for _ in 0..s {
if a.power(dd) == -Mod::one() {
good = false;
break;
}
dd *= 2;
}
if good {
return false;
}
}
true
}

pub fn next_prime(mut n: i64) -> i64 {
if n <= 2 {
return 2;
}
n += 1 - (n & 1);
while !is_prime(n) {
n += 2;
}
n
}

fn brent(n: i64, x0: i64, c: i64) -> i64 {
dynamic_value!(ModVal: i64 = n);
type Mod = ModInt<i64, ModVal>;
let mut x = Mod::new(x0);
let c = Mod::new(c);
let mut g = 1;
let mut q = Mod::one();
let mut xs = Mod::zero();
let mut y = Mod::zero();
let m = 128i64;
let mut l = 1;
while g == 1 {
y = x;
for _ in 1..l {
x = x * x + c;
}
let mut k = 0;
while k < l && g == 1 {
xs = x;
for _ in 0..m.min(l - k) {
x = x * x + c;
q *= y - x;
}
g = gcd(q.val(), n);
k += m;
}
l *= 2;
}
if g == n {
loop {
xs = xs * xs + c;
g = gcd((xs - y).val(), n);
if g != 1 {
break;
}
}
}
g
}

pub fn find_divisor(n: i64) -> i64 {
when! {
n == 1 => 1,
n % 2 == 0 => 2,
is_prime(n) => n,
else => {
loop {
let res = brent(
n,
random().next_bounds(2, n as u64 - 1) as i64,
random().next_bounds(1, n as u64 - 1) as i64,
);
if res != n {
return res;
}
}
},
}
}
}
}
}
}
fn main() {
    let mut sin = std::io::stdin();
    let input = algo_lib::io::input::Input::new(&mut sin);
    let mut stdout = std::io::stdout();
    let output = algo_lib::io::output::Output::new(&mut stdout);
    solution::run(input, output);
}