// https://judge.eluminatis-of-lu.com/contest/676ffd92569fb90008aac7da/1119
use crate::algo_lib::collections::dsu::DSU;
use crate::algo_lib::collections::fx_hash_map::FxHashSet;
use crate::algo_lib::collections::iter_ext::iter_copied::ItersCopied;
use crate::algo_lib::collections::vec_ext::inc_dec::IncDec;
use crate::algo_lib::io::input::Input;
use crate::algo_lib::io::output::Output;
use crate::algo_lib::misc::test_type::TaskType;
use crate::algo_lib::misc::test_type::TestType;
type PreCalc = ();
fn solve(input: &mut Input, out: &mut Output, _test_case: usize, _data: &mut PreCalc) {
    let n = input.read_size();
    let q = input.read_size();
    let a = input.read_size_vec(n).dec();
    let edges = input.read_size_pair_vec(q).dec();
    let mut dsu = DSU::new(n);
    for (u, v) in edges {
        dsu.union(u, v);
    }
    let sets = dsu.parts();
    let mut ans = 0;
    for part in sets {
        let set = part.copy_iter().collect::<FxHashSet<_>>();
        for i in part {
            if set.contains(&a[i]) {
                ans += 1;
            }
        }
    }
    out.print_line(ans);
}
pub static TEST_TYPE: TestType = TestType::MultiNumber;
pub static TASK_TYPE: TaskType = TaskType::Classic;
pub(crate) fn run(mut input: Input, mut output: Output) -> bool {
    let mut pre_calc = ();
    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();
    match TASK_TYPE {
        TaskType::Classic => input.is_empty(),
        TaskType::Interactive => true,
    }
}


fn main() {
    let mut sin = std::io::stdin();
    let input = crate::algo_lib::io::input::Input::new(&mut sin);
    let mut stdout = std::io::stdout();
    let output = crate::algo_lib::io::output::Output::new(&mut stdout);
    run(input, output);
}
pub mod algo_lib {
pub mod collections {
pub mod dsu {
use crate::algo_lib::collections::slice_ext::bounds::Bounds;
use crate::algo_lib::collections::slice_ext::indices::Indices;
use std::cell::Cell;
#[derive(Clone)]
pub struct DSU {
    id: Vec<Cell<i32>>,
    count: usize,
}
impl DSU {
    pub fn new(n: usize) -> Self {
        Self {
            id: vec![Cell::new(- 1); n],
            count: n,
        }
    }
    pub fn size(&self, i: usize) -> usize {
        (-self.id[self.find(i)].get()) as usize
    }
    #[allow(clippy::len_without_is_empty)]
    pub fn len(&self) -> usize {
        self.id.len()
    }
    pub fn iter(&self) -> impl Iterator<Item = usize> + '_ {
        self.id
            .iter()
            .enumerate()
            .filter_map(|(i, id)| if id.get() < 0 { Some(i) } else { None })
    }
    pub fn set_count(&self) -> usize {
        self.count
    }
    pub fn union(&mut self, mut a: usize, mut b: usize) -> bool {
        a = self.find(a);
        b = self.find(b);
        if a == b {
            false
        } else {
            self.id[a].replace(self.id[a].get() + self.id[b].get());
            self.id[b].replace(a as i32);
            self.count -= 1;
            true
        }
    }
    pub fn find(&self, i: usize) -> usize {
        if self.id[i].get() >= 0 {
            let res = self.find(self.id[i].get() as usize);
            self.id[i].replace(res as i32);
            res
        } else {
            i
        }
    }
    pub fn clear(&mut self) {
        self.count = self.id.len();
        self.id.fill(Cell::new(-1));
    }
    pub fn parts(&self) -> Vec<Vec<usize>> {
        let roots: Vec<_> = self.iter().collect();
        let mut res = vec![Vec::new(); roots.len()];
        for i in self.id.indices() {
            res[roots.as_slice().bin_search(&self.find(i)).unwrap()].push(i);
        }
        res
    }
}
}
pub mod fx_hash_map {
use std::cell::Cell;
use std::convert::TryInto;
use std::time::SystemTime;
use std::{
    collections::{HashMap, HashSet},
    hash::{BuildHasherDefault, Hasher},
    ops::BitXor,
};
pub type FxHashMap<K, V> = HashMap<K, V, BuildHasherDefault<FxHasher>>;
pub type FxHashSet<V> = HashSet<V, BuildHasherDefault<FxHasher>>;
#[derive(Default)]
pub struct FxHasher {
    hash: usize,
}
thread_local! {
    static K : Cell < usize > = Cell::new(((SystemTime::UNIX_EPOCH.elapsed().unwrap()
    .as_nanos().wrapping_mul(2) + 1) & 0xFFFFFFFFFFFFFFFF) as usize)
}
impl FxHasher {
    #[inline]
    fn add_to_hash(&mut self, i: usize) {
        self.hash = self.hash.rotate_left(5).bitxor(i).wrapping_mul(K.get());
    }
}
impl Hasher for FxHasher {
    #[inline]
    fn write(&mut self, mut bytes: &[u8]) {
        let read_usize = |bytes: &[u8]| u64::from_ne_bytes(
            bytes[..8].try_into().unwrap(),
        );
        let mut hash = FxHasher { hash: self.hash };
        while bytes.len() >= 8 {
            hash.add_to_hash(read_usize(bytes) as usize);
            bytes = &bytes[8..];
        }
        if bytes.len() >= 4 {
            hash.add_to_hash(
                u32::from_ne_bytes(bytes[..4].try_into().unwrap()) as usize,
            );
            bytes = &bytes[4..];
        }
        if bytes.len() >= 2 {
            hash.add_to_hash(
                u16::from_ne_bytes(bytes[..2].try_into().unwrap()) as usize,
            );
            bytes = &bytes[2..];
        }
        if !bytes.is_empty() {
            hash.add_to_hash(bytes[0] as usize);
        }
        self.hash = hash.hash;
    }
    #[inline]
    fn write_u8(&mut self, i: u8) {
        self.add_to_hash(i as usize);
    }
    #[inline]
    fn write_u16(&mut self, i: u16) {
        self.add_to_hash(i as usize);
    }
    #[inline]
    fn write_u32(&mut self, i: u32) {
        self.add_to_hash(i as usize);
    }
    #[inline]
    fn write_u64(&mut self, i: u64) {
        self.add_to_hash(i as usize);
    }
    #[inline]
    fn write_usize(&mut self, i: usize) {
        self.add_to_hash(i);
    }
    #[inline]
    fn finish(&self) -> u64 {
        self.hash as u64
    }
}
}
pub mod iter_ext {
pub mod iter_copied {
use std::iter::{
    Chain, Copied, Enumerate, Filter, Map, Rev, Skip, StepBy, Sum, Take, Zip,
};
pub trait ItersCopied<'a, T: 'a + Copy>: Sized + 'a
where
    &'a Self: IntoIterator<Item = &'a T>,
{
    fn copy_iter(&'a self) -> Copied<<&'a Self as IntoIterator>::IntoIter> {
        self.into_iter().copied()
    }
    fn copy_enumerate(
        &'a self,
    ) -> Enumerate<Copied<<&'a Self as IntoIterator>::IntoIter>> {
        self.copy_iter().enumerate()
    }
    fn copy_rev(&'a self) -> Rev<Copied<<&'a Self as IntoIterator>::IntoIter>>
    where
        Copied<<&'a Self as IntoIterator>::IntoIter>: DoubleEndedIterator,
    {
        self.copy_iter().rev()
    }
    fn copy_skip(
        &'a self,
        n: usize,
    ) -> Skip<Copied<<&'a Self as IntoIterator>::IntoIter>> {
        self.copy_iter().skip(n)
    }
    fn copy_take(
        &'a self,
        n: usize,
    ) -> Take<Copied<<&'a Self as IntoIterator>::IntoIter>> {
        self.copy_iter().take(n)
    }
    fn copy_chain<V>(
        &'a self,
        chained: &'a V,
    ) -> Chain<
        Copied<<&'a Self as IntoIterator>::IntoIter>,
        Copied<<&'a V as IntoIterator>::IntoIter>,
    >
    where
        &'a V: IntoIterator<Item = &'a T>,
    {
        self.copy_iter().chain(chained.into_iter().copied())
    }
    fn copy_zip<V>(
        &'a self,
        other: &'a V,
    ) -> Zip<
        Copied<<&'a Self as IntoIterator>::IntoIter>,
        Copied<<&'a V as IntoIterator>::IntoIter>,
    >
    where
        &'a V: IntoIterator<Item = &'a T>,
    {
        self.copy_iter().zip(other.into_iter().copied())
    }
    fn copy_max(&'a self) -> T
    where
        T: Ord,
    {
        self.copy_iter().max().unwrap()
    }
    fn copy_max_by_key<B, F>(&'a self, f: F) -> T
    where
        F: FnMut(&T) -> B,
        B: Ord,
    {
        self.copy_iter().max_by_key(f).unwrap()
    }
    fn copy_min(&'a self) -> T
    where
        T: Ord,
    {
        self.copy_iter().min().unwrap()
    }
    fn copy_min_by_key<B, F>(&'a self, f: F) -> T
    where
        F: FnMut(&T) -> B,
        B: Ord,
    {
        self.copy_iter().min_by_key(f).unwrap()
    }
    fn copy_sum(&'a self) -> T
    where
        T: Sum<T>,
    {
        self.copy_iter().sum()
    }
    fn copy_map<F, U>(
        &'a self,
        f: F,
    ) -> Map<Copied<<&'a Self as IntoIterator>::IntoIter>, F>
    where
        F: FnMut(T) -> U,
    {
        self.copy_iter().map(f)
    }
    fn copy_all(&'a self, f: impl FnMut(T) -> bool) -> bool {
        self.copy_iter().all(f)
    }
    fn copy_any(&'a self, f: impl FnMut(T) -> bool) -> bool {
        self.copy_iter().any(f)
    }
    fn copy_step_by(
        &'a self,
        step: usize,
    ) -> StepBy<Copied<<&'a Self as IntoIterator>::IntoIter>> {
        self.copy_iter().step_by(step)
    }
    fn copy_filter<F: FnMut(&T) -> bool>(
        &'a self,
        f: F,
    ) -> Filter<Copied<<&'a Self as IntoIterator>::IntoIter>, F> {
        self.copy_iter().filter(f)
    }
    fn copy_fold<Acc, F>(&'a self, init: Acc, f: F) -> Acc
    where
        F: FnMut(Acc, T) -> Acc,
    {
        self.copy_iter().fold(init, f)
    }
    fn copy_reduce<F>(&'a self, f: F) -> Option<T>
    where
        F: FnMut(T, T) -> T,
    {
        self.copy_iter().reduce(f)
    }
    fn copy_position<P>(&'a self, predicate: P) -> Option<usize>
    where
        P: FnMut(T) -> bool,
    {
        self.copy_iter().position(predicate)
    }
    fn copy_find(&'a self, val: T) -> Option<usize>
    where
        T: PartialEq,
    {
        self.copy_iter().position(|x| x == val)
    }
    fn copy_count(&'a self, val: T) -> usize
    where
        T: PartialEq,
    {
        self.copy_iter().filter(|&x| x == val).count()
    }
}
impl<'a, U: 'a, T: 'a + Copy> ItersCopied<'a, T> for U
where
    &'a U: IntoIterator<Item = &'a T>,
{}
}
}
pub mod slice_ext {
pub mod bounds {
pub trait Bounds<T: PartialOrd> {
    fn lower_bound(&self, el: &T) -> usize;
    fn upper_bound(&self, el: &T) -> usize;
    fn bin_search(&self, el: &T) -> Option<usize>;
    fn more(&self, el: &T) -> usize;
    fn more_or_eq(&self, el: &T) -> usize;
    fn less(&self, el: &T) -> usize {
        self.lower_bound(el)
    }
    fn less_or_eq(&self, el: &T) -> usize {
        self.upper_bound(el)
    }
}
impl<T: PartialOrd> Bounds<T> for [T] {
    fn lower_bound(&self, el: &T) -> usize {
        let mut left = 0;
        let mut right = self.len();
        while left < right {
            let mid = left + ((right - left) >> 1);
            if &self[mid] < el {
                left = mid + 1;
            } else {
                right = mid;
            }
        }
        left
    }
    fn upper_bound(&self, el: &T) -> usize {
        let mut left = 0;
        let mut right = self.len();
        while left < right {
            let mid = left + ((right - left) >> 1);
            if &self[mid] <= el {
                left = mid + 1;
            } else {
                right = mid;
            }
        }
        left
    }
    fn bin_search(&self, el: &T) -> Option<usize> {
        let at = self.lower_bound(el);
        if at == self.len() || &self[at] != el { None } else { Some(at) }
    }
    fn more(&self, el: &T) -> usize {
        self.len() - self.upper_bound(el)
    }
    fn more_or_eq(&self, el: &T) -> usize {
        self.len() - self.lower_bound(el)
    }
}
}
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 inc_dec {
use crate::algo_lib::numbers::num_traits::algebra::{AdditionMonoidWithSub, One};
pub trait IncDec {
    #[must_use]
    fn inc(self) -> Self;
    #[must_use]
    fn dec(self) -> Self;
}
impl<T: AdditionMonoidWithSub + One> IncDec for T {
    fn inc(self) -> Self {
        self + T::one()
    }
    fn dec(self) -> Self {
        self - T::one()
    }
}
impl<T: AdditionMonoidWithSub + One> IncDec for Vec<T> {
    fn inc(mut self) -> Self {
        self.iter_mut().for_each(|i| *i += T::one());
        self
    }
    fn dec(mut self) -> Self {
        self.iter_mut().for_each(|i| *i -= T::one());
        self
    }
}
impl<T: AdditionMonoidWithSub + One> IncDec for Vec<Vec<T>> {
    fn inc(mut self) -> Self {
        self.iter_mut().for_each(|v| v.iter_mut().for_each(|i| *i += T::one()));
        self
    }
    fn dec(mut self) -> Self {
        self.iter_mut().for_each(|v| v.iter_mut().for_each(|i| *i -= T::one()));
        self
    }
}
impl<T: AdditionMonoidWithSub + One, U: AdditionMonoidWithSub + One> IncDec
for Vec<(T, U)> {
    fn inc(mut self) -> Self {
        self.iter_mut()
            .for_each(|(i, j)| {
                *i += T::one();
                *j += U::one();
            });
        self
    }
    fn dec(mut self) -> Self {
        self.iter_mut()
            .for_each(|(i, j)| {
                *i -= T::one();
                *j -= U::one();
            });
        self
    }
}
impl<T: AdditionMonoidWithSub + One, U: AdditionMonoidWithSub + One, V> IncDec
for Vec<(T, U, V)> {
    fn inc(mut self) -> Self {
        self.iter_mut()
            .for_each(|(i, j, _)| {
                *i += T::one();
                *j += U::one();
            });
        self
    }
    fn dec(mut self) -> Self {
        self.iter_mut()
            .for_each(|(i, j, _)| {
                *i -= T::one();
                *j -= U::one();
            });
        self
    }
}
impl<T: AdditionMonoidWithSub + One, U: AdditionMonoidWithSub + One, V, W> IncDec
for Vec<(T, U, V, W)> {
    fn inc(mut self) -> Self {
        self.iter_mut()
            .for_each(|(i, j, ..)| {
                *i += T::one();
                *j += U::one();
            });
        self
    }
    fn dec(mut self) -> Self {
        self.iter_mut()
            .for_each(|(i, j, ..)| {
                *i -= T::one();
                *j -= U::one();
            });
        self
    }
}
impl<T: AdditionMonoidWithSub + One, U: AdditionMonoidWithSub + One, V, W, X> IncDec
for Vec<(T, U, V, W, X)> {
    fn inc(mut self) -> Self {
        self.iter_mut()
            .for_each(|(i, j, ..)| {
                *i += T::one();
                *j += U::one();
            });
        self
    }
    fn dec(mut self) -> Self {
        self.iter_mut()
            .for_each(|(i, j, ..)| {
                *i -= T::one();
                *j -= U::one();
            });
        self
    }
}
impl<T: AdditionMonoidWithSub + One, U: AdditionMonoidWithSub + One> IncDec for (T, U) {
    fn inc(mut self) -> Self {
        self.0 += T::one();
        self.1 += U::one();
        self
    }
    fn dec(mut self) -> Self {
        self.0 -= T::one();
        self.1 -= U::one();
        self
    }
}
}
}
}
pub mod io {
pub mod input {
use crate::algo_lib::collections::vec_ext::default::default_vec;
use std::io::Read;
use std::mem::MaybeUninit;
pub struct Input<'s> {
    input: &'s mut (dyn Read + Send),
    buf: Vec<u8>,
    at: usize,
    buf_read: usize,
    eol: bool,
}
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 + Send)) -> Self {
        Self {
            input,
            buf: default_vec(Self::DEFAULT_BUF_SIZE),
            at: 0,
            buf_read: 0,
            eol: true,
        }
    }
    pub fn new_with_size(input: &'s mut (dyn Read + Send), buf_size: usize) -> Self {
        Self {
            input,
            buf: default_vec(buf_size),
            at: 0,
            buf_read: 0,
            eol: true,
        }
    }
    pub fn get(&mut self) -> Option<u8> {
        if self.refill_buffer() {
            let res = self.buf[self.at];
            self.at += 1;
            if res == b'\r' {
                self.eol = true;
                if self.refill_buffer() && self.buf[self.at] == b'\n' {
                    self.at += 1;
                }
                return Some(b'\n');
            }
            self.eol = res == 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 !b.is_ascii_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 c.is_ascii_whitespace() {
                break;
            }
            res.push(c);
        }
        if res.is_empty() { None } else { Some(res) }
    }
    pub fn is_exhausted(&mut self) -> bool {
        self.peek().is_none()
    }
    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) -> u8 {
        self.skip_whitespace();
        self.get().unwrap()
    }
    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 fn is_eol(&self) -> bool {
        self.eol
    }
}
pub trait Readable {
    fn read(input: &mut Input) -> Self;
}
impl Readable for u8 {
    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)
    }
}
impl<T: Readable, const SIZE: usize> Readable for [T; SIZE] {
    fn read(input: &mut Input) -> Self {
        unsafe {
            let mut res = MaybeUninit::<[T; SIZE]>::uninit();
            for i in 0..SIZE {
                let ptr: *mut T = (*res.as_mut_ptr()).as_mut_ptr();
                ptr.add(i).write(input.read::<T>());
            }
            res.assume_init()
        }
    }
}
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 $t; if sgn { res -= d; } else { res += d; } match input.get() {
        None => break, Some(ch) => { if ch.is_ascii_whitespace() { break; } else { c =
        ch; } } } } res } })+
    };
}
read_integer!(i8 i16 i32 i64 i128 isize u16 u32 u64 u128 usize);
macro_rules! tuple_readable {
    ($($name:ident)+) => {
        impl <$($name : Readable),+> Readable for ($($name,)+) { fn read(input : & mut
        Input) -> Self { ($($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::cmp::Reverse;
use std::io::{stderr, Stderr, 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,
    precision: Option<usize>,
    separator: u8,
}
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,
            precision: None,
            separator: b' ',
        }
    }
    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,
            precision: None,
            separator: b' ',
        }
    }
    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]) {
        self.print_per_line_iter(arg.iter());
    }
    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(self.separator);
            }
            e.write(self);
        }
    }
    pub fn print_line_iter<T: Writable, I: Iterator<Item = T>>(&mut self, iter: I) {
        self.print_iter(iter);
        self.put(b'\n');
    }
    pub fn print_per_line_iter<T: Writable, I: Iterator<Item = T>>(&mut self, iter: I) {
        for e in iter {
            e.write(self);
            self.put(b'\n');
        }
    }
    pub fn set_bool_output(&mut self, bool_output: BoolOutput) {
        self.bool_output = bool_output;
    }
    pub fn set_precision(&mut self, precision: usize) {
        self.precision = Some(precision);
    }
    pub fn reset_precision(&mut self) {
        self.precision = None;
    }
    pub fn get_precision(&self) -> Option<usize> {
        self.precision
    }
    pub fn separator(&self) -> u8 {
        self.separator
    }
    pub fn set_separator(&mut self, separator: u8) {
        self.separator = separator;
    }
}
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 Writable for u8 {
    fn write(&self, output: &mut Output) {
        output.put(*self);
    }
}
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 + ?Sized> 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 $t { fn write(& self, output : & mut Output) { self
        .to_string().write(output); } })+
    };
}
write_to_string!(u16 u32 u64 u128 usize i8 i16 i32 i64 i128 isize);
macro_rules! tuple_writable {
    ($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); $(out.put(out
        .separator); self.$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)
    }
}
impl<T: Writable> Writable for Reverse<T> {
    fn write(&self, output: &mut Output) {
        self.0.write(output);
    }
}
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 test_type {
pub enum TestType {
    Single,
    MultiNumber,
    MultiEof,
}
pub enum TaskType {
    Classic,
    Interactive,
}
}
}
pub mod numbers {
pub mod num_traits {
pub mod algebra {
use crate::algo_lib::numbers::num_traits::invertible::Invertible;
use std::ops::{
    Add, AddAssign, Div, DivAssign, Mul, MulAssign, Neg, Rem, RemAssign, Sub, 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 invertible {
pub trait Invertible {
    type Output;
    fn inv(&self) -> Option<Self::Output>;
}
}
}
}
}