// https://contest.ucup.ac/contest/1885/problem/9926
use crate::algo_lib::collections::md_arr::arr2d::{Arr2d, Arr2dRead};
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::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 m = input.read_size();
    let c = input.read_char_table(n, m);
    for &z in b"WB" {
        let mut paths: Arr2d<Vec<Str>> = Arr2d::new(n, m, Vec::new());
        let mut good = true;
        if c[(0, 0)] != z {
            paths[(0, 0)].push(Str::new());
        }
        'outer: for i in 0..n {
            for j in 0..m {
                if i > 0 && paths[(i - 1, j)].len() % 2 == 1 {
                    let mut path = paths[(i - 1, j)].pop().unwrap();
                    path.push(b'D');
                    paths[(i, j)].push(path);
                }
                if (c[(i, j)] == z) != (paths[(i, j)].len() % 2 == 0) {
                    if j == 0 {
                        good = false;
                        break 'outer;
                    }
                    if j > 0 && paths[(i, j - 1)].len() % 2 == 1 {
                        let mut path = paths[(i, j - 1)].pop().unwrap();
                        path.push(b'R');
                        paths[(i, j)].push(path);
                    } else {
                        if i == n - 1 {
                            good = false;
                            break 'outer;
                        }
                        let mut x = 0;
                        let mut y = 0;
                        let mut p1 = Str::new();
                        let mut p2 = Str::new();
                        'inner: for k in (0..=j - 1).rev() {
                            for l in 0..=i {
                                if paths[(l, k)].len() >= 2 {
                                    x = l;
                                    y = k;
                                    p1 = paths[(l, k)].pop().unwrap();
                                    p2 = paths[(l, k)].pop().unwrap();
                                    break 'inner;
                                }
                            }
                        }
                        for _ in x..i {
                            p1.push(b'D');
                            p2.push(b'D');
                        }
                        for _ in y..j - 1 {
                            p1.push(b'R');
                            p2.push(b'R');
                        }
                        p1.push(b'R');
                        paths[(i, j)].push(p1);
                        p2.push(b'D');
                        paths[(i + 1, j - 1)].push(p2);
                    }
                } else if j > 0 && i == n - 1 && paths[(i, j - 1)].len() % 2 == 1 {
                    good = false;
                    break 'outer;
                }
            }
        }
        if !good {
            continue;
        }
        let mut ans = Vec::new();
        for i in 0..n {
            for j in 0..m {
                for mut path in paths[(i, j)].drain(..) {
                    for _ in i + 1..n {
                        path.push(b'D');
                    }
                    for _ in j + 1..m {
                        path.push(b'R');
                    }
                    ans.push(path);
                }
            }
        }
        out.print_line(true);
        out.print_line(ans.len());
        out.print_per_line(&ans);
        return;
    }
    out.print_line(false);
}
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 md_arr {
pub mod arr2d {
use crate::algo_lib::collections::slice_ext::legacy_fill::LegacyFill;
use crate::algo_lib::io::input::{Input, Readable};
use crate::algo_lib::io::output::{Output, Writable};
use std::iter::{Skip, StepBy, Take};
use std::mem::MaybeUninit;
use std::ops::{Index, IndexMut, Range};
use std::slice::{Iter, IterMut};
use std::vec::IntoIter;
#[derive(Clone, Eq, PartialEq, Default, Debug, Hash)]
pub struct Arr2d<T> {
    d1: usize,
    d2: usize,
    data: Vec<T>,
}
impl<T: Clone> Arr2d<T> {
    pub fn new(d1: usize, d2: usize, value: T) -> Self {
        Self {
            d1,
            d2,
            data: vec![value; d1 * d2],
        }
    }
}
impl<T> Arr2d<T> {
    pub fn gen<F>(d1: usize, d2: usize, mut gen: F) -> Self
    where
        F: FnMut(usize, usize) -> T,
    {
        let mut data = Vec::with_capacity(d1 * d2);
        for i in 0usize..d1 {
            for j in 0usize..d2 {
                data.push(gen(i, j));
            }
        }
        Self { d1, d2, data }
    }
    pub fn d1(&self) -> usize {
        self.d1
    }
    pub fn d2(&self) -> usize {
        self.d2
    }
    pub fn iter(&self) -> Iter<'_, T> {
        self.data.iter()
    }
    pub fn iter_mut(&mut self) -> IterMut<'_, T> {
        self.data.iter_mut()
    }
    pub fn row(&self, row: usize) -> Take<Skip<Iter<'_, T>>> {
        assert!(row < self.d1);
        self.data.iter().skip(row * self.d2).take(self.d2)
    }
    pub fn row_mut(&mut self, row: usize) -> Take<Skip<IterMut<'_, T>>> {
        assert!(row < self.d1);
        self.data.iter_mut().skip(row * self.d2).take(self.d2)
    }
    pub fn col(&self, col: usize) -> StepBy<Skip<Iter<'_, T>>> {
        assert!(col < self.d2);
        self.data.iter().skip(col).step_by(self.d2)
    }
    pub fn col_mut(&mut self, col: usize) -> StepBy<Skip<IterMut<'_, T>>> {
        assert!(col < self.d2);
        self.data.iter_mut().skip(col).step_by(self.d2)
    }
    pub fn swap(&mut self, r1: usize, c1: usize, r2: usize, c2: usize) {
        assert!(c1 < self.d2);
        assert!(c2 < self.d2);
        self.data.swap(r1 * self.d2 + c1, r2 * self.d2 + c2);
    }
    pub fn rows(&self) -> Range<usize> {
        0..self.d1
    }
    pub fn cols(&self) -> Range<usize> {
        0..self.d2
    }
    pub fn swap_rows(&mut self, r1: usize, r2: usize) {
        if r1 == r2 {
            assert!(r1 < self.d1);
            return;
        }
        let (r1, r2) = (r1.min(r2), r1.max(r2));
        let (head, tail) = self.data.split_at_mut(r2 * self.d2);
        head[r1 * self.d2..(r1 + 1) * self.d2].swap_with_slice(&mut tail[..self.d2]);
    }
    pub fn rotate_clockwise(self) -> Self {
        unsafe {
            let d1 = self.d1;
            let d2 = self.d2;
            let mut res = MaybeUninit::new(Vec::with_capacity(d1 * d2));
            (*res.as_mut_ptr()).set_len(d1 * d2);
            for (id, element) in self.into_iter().enumerate() {
                let (i, j) = (id / d2, id % d2);
                let ptr: *mut T = (*res.as_mut_ptr()).as_mut_ptr();
                ptr.add(j * d1 + d1 - i - 1).write(element);
            }
            Self {
                d1: d2,
                d2: d1,
                data: res.assume_init(),
            }
        }
    }
    pub fn rotate_counterclockwise(self) -> Self {
        unsafe {
            let d1 = self.d1;
            let d2 = self.d2;
            let mut res = MaybeUninit::new(Vec::with_capacity(d1 * d2));
            (*res.as_mut_ptr()).set_len(d1 * d2);
            for (id, element) in self.into_iter().enumerate() {
                let (i, j) = (id / d2, id % d2);
                let ptr: *mut T = (*res.as_mut_ptr()).as_mut_ptr();
                ptr.add((d2 - j - 1) * d1 + i).write(element);
            }
            Self {
                d1: d2,
                d2: d1,
                data: res.assume_init(),
            }
        }
    }
    pub fn transpose(self) -> Self {
        unsafe {
            let d1 = self.d1;
            let d2 = self.d2;
            let mut res = MaybeUninit::new(Vec::with_capacity(d1 * d2));
            (*res.as_mut_ptr()).set_len(d1 * d2);
            for (id, element) in self.into_iter().enumerate() {
                let (i, j) = (id / d2, id % d2);
                let ptr: *mut T = (*res.as_mut_ptr()).as_mut_ptr();
                ptr.add(j * d1 + i).write(element);
            }
            Self {
                d1: d2,
                d2: d1,
                data: res.assume_init(),
            }
        }
    }
}
impl<T: Clone> Arr2d<T> {
    pub fn fill(&mut self, elem: T) {
        self.data.legacy_fill(elem);
    }
}
impl<T> Index<(usize, usize)> for Arr2d<T> {
    type Output = T;
    fn index(&self, (row, col): (usize, usize)) -> &Self::Output {
        assert!(col < self.d2);
        &self.data[self.d2 * row + col]
    }
}
impl<T> Index<usize> for Arr2d<T> {
    type Output = [T];
    fn index(&self, index: usize) -> &Self::Output {
        &self.data[self.d2 * index..self.d2 * (index + 1)]
    }
}
impl<T> IndexMut<(usize, usize)> for Arr2d<T> {
    fn index_mut(&mut self, (row, col): (usize, usize)) -> &mut T {
        assert!(col < self.d2);
        &mut self.data[self.d2 * row + col]
    }
}
impl<T> IndexMut<usize> for Arr2d<T> {
    fn index_mut(&mut self, index: usize) -> &mut [T] {
        &mut self.data[self.d2 * index..self.d2 * (index + 1)]
    }
}
impl<T> AsRef<Vec<T>> for Arr2d<T> {
    fn as_ref(&self) -> &Vec<T> {
        &self.data
    }
}
impl<T> AsMut<Vec<T>> for Arr2d<T> {
    fn as_mut(&mut self) -> &mut Vec<T> {
        &mut self.data
    }
}
impl<T: Writable> Writable for Arr2d<T> {
    fn write(&self, output: &mut Output) {
        let mut at = 0usize;
        for i in 0usize..self.d1 {
            if i != 0 {
                output.put(b'\n');
            }
            for j in 0usize..self.d2 {
                if j != 0 {
                    output.put(output.separator());
                }
                self.data[at].write(output);
                at += 1;
            }
        }
    }
}
impl<T> IntoIterator for Arr2d<T> {
    type Item = T;
    type IntoIter = IntoIter<T>;
    fn into_iter(self) -> Self::IntoIter {
        self.data.into_iter()
    }
}
impl<'a, T> IntoIterator for &'a Arr2d<T> {
    type Item = &'a T;
    type IntoIter = Iter<'a, T>;
    fn into_iter(self) -> Self::IntoIter {
        self.iter()
    }
}
pub trait Arr2dRead {
    fn read_table<T: Readable>(&mut self, d1: usize, d2: usize) -> Arr2d<T>;
    fn read_int_table(&mut self, d1: usize, d2: usize) -> Arr2d<i32>;
    fn read_long_table(&mut self, d1: usize, d2: usize) -> Arr2d<i64>;
    fn read_size_table(&mut self, d1: usize, d2: usize) -> Arr2d<usize>;
    fn read_char_table(&mut self, d1: usize, d2: usize) -> Arr2d<u8>;
}
impl Arr2dRead for Input<'_> {
    fn read_table<T: Readable>(&mut self, d1: usize, d2: usize) -> Arr2d<T> {
        Arr2d::gen(d1, d2, |_, _| self.read())
    }
    fn read_int_table(&mut self, d1: usize, d2: usize) -> Arr2d<i32> {
        self.read_table(d1, d2)
    }
    fn read_long_table(&mut self, d1: usize, d2: usize) -> Arr2d<i64> {
        self.read_table(d1, d2)
    }
    fn read_size_table(&mut self, d1: usize, d2: usize) -> Arr2d<usize> {
        self.read_table(d1, d2)
    }
    fn read_char_table(&mut self, d1: usize, d2: usize) -> Arr2d<u8> {
        self.read_table(d1, d2)
    }
}
pub trait Arr2dCharWrite {
    fn print_table(&mut self, table: &Arr2d<u8>);
}
impl Arr2dCharWrite for Output<'_> {
    fn print_table(&mut self, table: &Arr2d<u8>) {
        let mut at = 0usize;
        for _ in 0..table.d1 {
            for _ in 0..table.d2 {
                self.put(table.data[at]);
                at += 1;
            }
            self.put(b'\n');
        }
        self.maybe_flush();
    }
}
impl<T: Readable> Readable for Arr2d<T> {
    fn read(input: &mut Input) -> Self {
        let d1 = input.read();
        let d2 = input.read();
        input.read_table(d1, d2)
    }
}
}
}
pub mod slice_ext {
pub mod legacy_fill {
pub trait LegacyFill<T> {
    fn legacy_fill(&mut self, val: T);
}
impl<T: Clone> LegacyFill<T> for [T] {
    fn legacy_fill(&mut self, val: T) {
        for el in self.iter_mut() {
            *el = val.clone();
        }
    }
}
}
}
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;
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 string {
pub mod str {
use crate::algo_lib::io::input::{Input, Readable};
use crate::algo_lib::io::output::{Output, Writable};
use std::fmt::Display;
use std::io::Write;
use std::iter::FromIterator;
use std::ops::{AddAssign, Deref, DerefMut};
use std::str::from_utf8_unchecked;
use std::vec::IntoIter;
#[derive(Eq, PartialEq, Hash, PartialOrd, Ord, Clone, Default)]
pub struct Str(Vec<u8>);
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 Deref for Str {
    type Target = Vec<u8>;
    fn deref(&self) -> &Self::Target {
        &self.0
    }
}
impl DerefMut for Str {
    fn deref_mut(&mut self) -> &mut Self::Target {
        &mut self.0
    }
}
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
    }
}
}
}
}