// https://contest.ucup.ac/contest/1901/problem/8621
use crate::algo_lib::collections::iter_ext::iter_copied::ItersCopied;
use crate::algo_lib::collections::slice_ext::backward::Back;
use crate::algo_lib::collections::slice_ext::indices::Indices;
use crate::algo_lib::collections::vec_ext::gen_vec::VecGen;
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;
use crate::algo_lib::numbers::num_traits::bit_ops::BitOps;
use crate::algo_lib::string::str::Str;
type PreCalc = ();
fn solve(input: &mut Input, out: &mut Output, _test_case: usize, _data: &mut PreCalc) {
    let n = input.read_size();
    let a = input.read_long_vec(n);
    let mut parts = Vec::with_gen(n, |i| (a[i], vec![i]));
    while parts.len() >= 3 {
        parts.sort_unstable();
        for i in 0..parts.len() - 2 {
            if parts[i].0 == parts[i + 2].0 {
                let mut ans = Str::from(vec![b'.'; n]);
                for j in parts[i].1.copy_iter() {
                    ans[j] = b'A';
                }
                for j in parts[i + 1].1.copy_iter() {
                    ans[j] = b'B';
                }
                for j in parts[i + 2].1.copy_iter() {
                    ans[j] = b'C';
                }
                out.print_line(ans);
                return;
            }
        }
        let p0 = parts.indices().filter(|&i| !parts[i].0.is_set(0)).collect::<Vec<_>>();
        let p1 = parts.indices().filter(|&i| parts[i].0.is_set(0)).collect::<Vec<_>>();
        let mut n_parts = Vec::new();
        for p0 in [p0, p1] {
            for i in 0..p0.len() / 2 {
                let a = &parts[p0[i]];
                let b = &parts[p0[Back(i)]];
                let sum = (a.0 + b.0) / 2;
                let ind = a.1.copy_iter().chain(b.1.copy_iter()).collect::<Vec<_>>();
                n_parts.push((sum, ind));
            }
        }
        parts = n_parts;
    }
}
pub static TEST_TYPE: TestType = TestType::Single;
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 input = crate::algo_lib::io::input::Input::stdin();
    let output = crate::algo_lib::io::output::Output::stdout();
    run(input, output);
}
pub mod algo_lib {
pub mod collections {
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 backward {
use std::ops::{Index, IndexMut};
pub struct Back(pub usize);
impl<T> Index<Back> for [T] {
    type Output = T;
    fn index(&self, index: Back) -> &Self::Output {
        &self[self.len() - index.0 - 1]
    }
}
impl<T> IndexMut<Back> for [T] {
    fn index_mut(&mut self, index: Back) -> &mut Self::Output {
        &mut self[self.len() - index.0 - 1]
    }
}
impl<T> Index<Back> for Vec<T> {
    type Output = T;
    fn index(&self, index: Back) -> &Self::Output {
        self.as_slice().index(index)
    }
}
impl<T> IndexMut<Back> for Vec<T> {
    fn index_mut(&mut self, index: Back) -> &mut Self::Output {
        self.as_mut_slice().index_mut(index)
    }
}
}
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 gen_vec {
use crate::algo_lib::collections::vec_ext::default::default_vec;
pub trait VecGen<T> {
    fn with_gen(n: usize, f: impl FnMut(usize) -> T) -> Vec<T>;
    fn with_gen_prefix(n: usize, f: impl FnMut(usize, &Self) -> T) -> Vec<T>;
    fn gen_append(&mut self, n: usize, f: impl FnMut(usize, &Self) -> T);
    fn with_gen_back(n: usize, f: impl FnMut(usize, &Self) -> T) -> Vec<T>
    where
        T: Default;
}
impl<T> VecGen<T> for Vec<T> {
    fn with_gen(n: usize, mut f: impl FnMut(usize) -> T) -> Vec<T> {
        Self::with_gen_prefix(n, |i, _| f(i))
    }
    fn with_gen_prefix(n: usize, f: impl FnMut(usize, &Self) -> T) -> Vec<T> {
        let mut vec = Vec::with_capacity(n);
        vec.gen_append(n, f);
        vec
    }
    fn gen_append(&mut self, n: usize, mut f: impl FnMut(usize, &Self) -> T) {
        self.reserve(n);
        let len = self.len();
        for i in 0..n {
            self.push(f(len + i, self));
        }
    }
    fn with_gen_back(n: usize, mut f: impl FnMut(usize, &Self) -> T) -> Vec<T>
    where
        T: Default,
    {
        let mut vec = default_vec(n);
        for i in (0..n).rev() {
            vec[i] = f(i, &vec);
        }
        vec
    }
}
}
}
}
pub mod io {
pub mod input {
use std::fs::File;
use std::io::{Read, Stdin};
use std::mem::MaybeUninit;
enum InputSource {
    Stdin(Stdin),
    File(File),
    Slice,
    Delegate(Box<dyn Read + Send>),
}
pub struct Input {
    input: InputSource,
    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 Input {
    const DEFAULT_BUF_SIZE: usize = 4096;
    pub fn slice(input: &[u8]) -> Self {
        Self {
            input: InputSource::Slice,
            buf: input.to_vec(),
            at: 0,
            buf_read: input.len(),
            eol: true,
        }
    }
    pub fn stdin() -> Self {
        Self {
            input: InputSource::Stdin(std::io::stdin()),
            buf: vec![0; Self::DEFAULT_BUF_SIZE],
            at: 0,
            buf_read: 0,
            eol: true,
        }
    }
    pub fn file(file: File) -> Self {
        Self {
            input: InputSource::File(file),
            buf: vec![0; Self::DEFAULT_BUF_SIZE],
            at: 0,
            buf_read: 0,
            eol: true,
        }
    }
    pub fn delegate(reader: impl Read + Send + 'static) -> Self {
        Self {
            input: InputSource::Delegate(Box::new(reader)),
            buf: vec![0; Self::DEFAULT_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 = match &mut self.input {
                InputSource::Stdin(stdin) => stdin.read(&mut self.buf).unwrap(),
                InputSource::File(file) => file.read(&mut self.buf).unwrap(),
                InputSource::Delegate(reader) => reader.read(&mut self.buf).unwrap(),
                InputSource::Slice => 0,
            };
            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
}
}
pub mod output {
use std::cmp::Reverse;
use std::fs::File;
use std::io::{Stdout, 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,
        }
    }
}
enum OutputDest<'s> {
    Stdout(Stdout),
    File(File),
    Buf(&'s mut Vec<u8>),
    Delegate(Box<dyn Write + 's>),
}
pub struct Output<'s> {
    output: OutputDest<'s>,
    buf: Vec<u8>,
    at: usize,
    bool_output: BoolOutput,
    precision: Option<usize>,
    separator: u8,
}
impl<'s> Output<'s> {
    pub fn buf(buf: &'s mut Vec<u8>) -> Self {
        Self::new(OutputDest::Buf(buf))
    }
    pub fn delegate(delegate: impl Write + 'static) -> Self {
        Self::new(OutputDest::Delegate(Box::new(delegate)))
    }
    fn new(output: OutputDest<'s>) -> Self {
        Self {
            output,
            buf: vec![0; Self::DEFAULT_BUF_SIZE],
            at: 0,
            bool_output: BoolOutput::YesNoCaps,
            precision: None,
            separator: b' ',
        }
    }
}
impl Output<'static> {
    pub fn stdout() -> Self {
        Self::new(OutputDest::Stdout(std::io::stdout()))
    }
    pub fn file(file: File) -> Self {
        Self::new(OutputDest::File(file))
    }
}
impl Output<'_> {
    const DEFAULT_BUF_SIZE: usize = 4096;
    pub fn flush(&mut self) {
        if self.at != 0 {
            match &mut self.output {
                OutputDest::Stdout(stdout) => {
                    stdout.write_all(&self.buf[..self.at]).unwrap();
                    stdout.flush().unwrap();
                }
                OutputDest::File(file) => {
                    file.write_all(&self.buf[..self.at]).unwrap();
                    file.flush().unwrap();
                }
                OutputDest::Buf(buf) => buf.extend_from_slice(&self.buf[..self.at]),
                OutputDest::Delegate(delegate) => {
                    delegate.write_all(&self.buf[..self.at]).unwrap();
                    delegate.flush().unwrap();
                }
            }
            self.at = 0;
        }
    }
    pub fn print<T: Writable>(&mut self, s: T) {
        s.write(self);
    }
    pub fn print_line<T: Writable>(&mut self, s: T) {
        self.print(s);
        self.put(b'\n');
    }
    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 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;
        }
        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);
    }
}
}
}
pub mod misc {
pub mod test_type {
pub enum TestType {
    Single,
    MultiNumber,
    MultiEof,
}
pub enum TaskType {
    Classic,
    Interactive,
}
}
pub mod transparent_wrapper {
#[macro_export]
macro_rules! transparent_wrapper {
    ($name:ident $(<$($par:ident $(,)?)+>)? = $t:ty $(, derive $($d:ty $(,)?)+)?) => {
        $(#[derive($($d,)+)])? pub struct $name $(<$($par,)+>)? ($t); impl
        $(<$($par,)+>)? Deref for $name $(<$($par,)+>)? { type Target = $t; fn deref(&
        self) -> & Self::Target { & self.0 } } impl $(<$($par,)+>)? DerefMut for $name
        $(<$($par,)+>)? { fn deref_mut(& mut self) -> & mut Self::Target { & mut self.0 }
        }
    };
}
}
}
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 bit_ops {
use crate::algo_lib::numbers::num_traits::algebra::{One, Zero};
use std::ops::{
    BitAnd, BitAndAssign, BitOr, BitOrAssign, BitXor, BitXorAssign, Not, RangeInclusive,
    Shl, Sub,
};
use std::ops::{ShlAssign, Shr, ShrAssign};
pub trait BitOps: Copy + BitAnd<
        Output = Self,
    > + BitAndAssign + BitOr<
        Output = Self,
    > + BitOrAssign + BitXor<
        Output = Self,
    > + BitXorAssign + Not<
        Output = Self,
    > + Shl<
        usize,
        Output = Self,
    > + ShlAssign<
        usize,
    > + Shr<usize, Output = Self> + ShrAssign<usize> + Zero + One + PartialEq {
    #[inline]
    fn bit(at: usize) -> Self {
        Self::one() << at
    }
    #[inline]
    fn is_set(&self, at: usize) -> bool {
        (*self >> at & Self::one()) == Self::one()
    }
    #[inline]
    fn set_bit(&mut self, at: usize) {
        *self |= Self::bit(at);
    }
    #[inline]
    fn unset_bit(&mut self, at: usize) {
        *self &= !Self::bit(at);
    }
    #[must_use]
    #[inline]
    fn with_bit(mut self, at: usize) -> Self {
        self.set_bit(at);
        self
    }
    #[must_use]
    #[inline]
    fn without_bit(mut self, at: usize) -> Self {
        self.unset_bit(at);
        self
    }
    #[inline]
    fn flip_bit(&mut self, at: usize) {
        *self ^= Self::bit(at);
    }
    #[must_use]
    #[inline]
    fn flipped_bit(mut self, at: usize) -> Self {
        self.flip_bit(at);
        self
    }
    fn all_bits(n: usize) -> Self {
        let mut res = Self::zero();
        for i in 0..n {
            res.set_bit(i);
        }
        res
    }
    fn iter_all(n: usize) -> RangeInclusive<Self> {
        Self::zero()..=Self::all_bits(n)
    }
}
pub struct BitIter<T> {
    cur: T,
    all: T,
    ended: bool,
}
impl<T: Copy> BitIter<T> {
    pub fn new(all: T) -> Self {
        Self {
            cur: all,
            all,
            ended: false,
        }
    }
}
impl<T: BitOps + Sub<Output = T>> Iterator for BitIter<T> {
    type Item = T;
    fn next(&mut self) -> Option<Self::Item> {
        if self.ended {
            return None;
        }
        let res = self.cur;
        if self.cur == T::zero() {
            self.ended = true;
        } else {
            self.cur = (self.cur - T::one()) & self.all;
        }
        Some(res)
    }
}
impl<
    T: Copy + BitAnd<Output = Self> + BitAndAssign + BitOr<Output = Self> + BitOrAssign
        + BitXor<Output = Self> + BitXorAssign + Not<Output = Self>
        + Shl<usize, Output = Self> + ShlAssign<usize> + Shr<usize, Output = Self>
        + ShrAssign<usize> + One + Zero + PartialEq,
> BitOps for T {}
pub trait Bits: BitOps {
    fn bits() -> u32;
}
macro_rules! bits_integer_impl {
    ($($t:ident $bits:expr),+) => {
        $(impl Bits for $t { fn bits() -> u32 { $bits } })+
    };
}
bits_integer_impl!(
    i128 128, i64 64, i32 32, i16 16, i8 8, isize 64, u128 128, u64 64, u32 32, u16 16,
    u8 8, usize 64
);
}
pub mod invertible {
pub trait Invertible {
    type Output;
    fn inv(&self) -> Option<Self::Output>;
}
}
}
}
pub mod string {
pub mod str {
use crate::algo_lib::io::input::{Input, Readable};
use crate::algo_lib::io::output::{Output, Writable};
use crate::transparent_wrapper;
use std::fmt::Display;
use std::io::Write;
use std::ops::{AddAssign, Deref, DerefMut};
use std::str::from_utf8_unchecked;
use std::vec::IntoIter;
transparent_wrapper!(
    Str = Vec < u8 >, derive Eq, PartialEq, Hash, PartialOrd, Ord, Clone, Default
);
impl Str {
    pub fn new() -> Self {
        Self(Vec::new())
    }
    pub fn unwrap(self) -> Vec<u8> {
        self.0
    }
}
impl From<Vec<u8>> for Str {
    fn from(v: Vec<u8>) -> Self {
        Self(v)
    }
}
impl From<&[u8]> for Str {
    fn from(v: &[u8]) -> Self {
        Self(v.to_vec())
    }
}
impl<const N: usize> From<&[u8; N]> for Str {
    fn from(v: &[u8; N]) -> Self {
        Self(v.to_vec())
    }
}
impl Readable for Str {
    fn read(input: &mut Input) -> Self {
        let mut res = Vec::new();
        input.skip_whitespace();
        while let Some(c) = input.get() {
            if c.is_ascii_whitespace() {
                break;
            }
            res.push(c);
        }
        Self(res)
    }
}
impl Writable for Str {
    fn write(&self, output: &mut Output) {
        output.write_all(&self.0).unwrap()
    }
}
impl IntoIterator for Str {
    type Item = u8;
    type IntoIter = IntoIter<u8>;
    fn into_iter(self) -> Self::IntoIter {
        self.0.into_iter()
    }
}
impl<'a> IntoIterator for &'a Str {
    type Item = &'a u8;
    type IntoIter = std::slice::Iter<'a, u8>;
    fn into_iter(self) -> Self::IntoIter {
        self.iter()
    }
}
impl<'a> IntoIterator for &'a mut Str {
    type Item = &'a mut u8;
    type IntoIter = std::slice::IterMut<'a, u8>;
    fn into_iter(self) -> Self::IntoIter {
        self.iter_mut()
    }
}
impl FromIterator<u8> for Str {
    fn from_iter<T: IntoIterator<Item = u8>>(iter: T) -> Self {
        Self(iter.into_iter().collect())
    }
}
impl AsRef<[u8]> for Str {
    fn as_ref(&self) -> &[u8] {
        &self.0
    }
}
impl AddAssign<&[u8]> for Str {
    fn add_assign(&mut self, rhs: &[u8]) {
        self.0.extend_from_slice(rhs)
    }
}
impl Display for Str {
    fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result {
        unsafe { f.write_str(from_utf8_unchecked(&self.0)) }
    }
}
pub trait StrReader {
    fn read_str(&mut self) -> Str;
    fn read_str_vec(&mut self, n: usize) -> Vec<Str>;
    fn read_line(&mut self) -> Str;
    fn read_line_vec(&mut self, n: usize) -> Vec<Str>;
    fn read_lines(&mut self) -> Vec<Str>;
}
impl StrReader for Input {
    fn read_str(&mut self) -> Str {
        self.read()
    }
    fn read_str_vec(&mut self, n: usize) -> Vec<Str> {
        self.read_vec(n)
    }
    fn read_line(&mut self) -> Str {
        let mut res = Str::new();
        while let Some(c) = self.get() {
            if self.is_eol() {
                break;
            }
            res.push(c);
        }
        res
    }
    fn read_line_vec(&mut self, n: usize) -> Vec<Str> {
        let mut res = Vec::with_capacity(n);
        for _ in 0..n {
            res.push(self.read_line());
        }
        res
    }
    fn read_lines(&mut self) -> Vec<Str> {
        let mut res = Vec::new();
        while !self.is_exhausted() {
            res.push(self.read_line());
        }
        if let Some(s) = res.last() {
            if s.is_empty() {
                res.pop();
            }
        }
        res
    }
}
}
}
}