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

use std::cmp::max;
use std::cmp::min;
use std::collections::HashMap;

#[allow(unused)]
use crate::dbg;
use crate::algo_lib::io::input::Input;
use crate::algo_lib::io::output::Output;
use crate::algo_lib::misc::binary_search::binary_search_first_true;
use crate::algo_lib::misc::rand::Random;

#[derive(Clone, Copy, Debug)]
struct Submission {
    time: i64,
    ok: bool,
}

#[derive(Clone, Debug)]
struct Team {
    by_task: HashMap<u8, Vec<Submission>>,
    name: String,
}

#[derive(Debug)]
struct TeamScore {
    cur: Score,
    best: Score,
    worst: Score,
}

impl std::ops::Add for Score {
    type Output = Score;

    fn add(self, other: Score) -> Score {
        Score {
            tasks_solved: self.tasks_solved + other.tasks_solved,
            rev_penalty: self.rev_penalty + other.rev_penalty,
        }
    }
}

impl Team {
    fn worst_single(&self) -> Score {
        let mut res = Score {
            tasks_solved: 1,
            rev_penalty: i64::MAX,
        };
        for (_, submissions) in self.by_task.iter() {
            let mut penalty = 20 * (submissions.len() - 1) as i64;
            penalty += submissions[submissions.len() - 1].time;
            let rev_penalty = -penalty;
            if rev_penalty < res.rev_penalty {
                res.rev_penalty = rev_penalty;
            }
        }
        if res.rev_penalty == i64::MAX {
            res.tasks_solved = 0;
        }
        res
    }

    fn calc_scores(&self) -> TeamScore {
        let mut cur = Score {
            tasks_solved: 0,
            rev_penalty: 0,
        };
        let mut best = Score {
            tasks_solved: 0,
            rev_penalty: 0,
        };
        let mut worst = Score {
            tasks_solved: 0,
            rev_penalty: 0,
        };
        for (_, submissions) in &self.by_task {
            let mut task_cur = Score {
                tasks_solved: 0,
                rev_penalty: 0,
            };
            let mut task_best = Score {
                tasks_solved: 0,
                rev_penalty: 0,
            };
            let mut task_worst = Score {
                tasks_solved: 0,
                rev_penalty: 0,
            };
            let mut cur_penalty = 0;
            let mut skipped_ok = false;
            for sub in submissions {
                if task_best.tasks_solved == 0 {
                    task_best.tasks_solved = 1;
                    task_best.rev_penalty = -(sub.time);
                }
                if sub.ok {
                    if task_cur.tasks_solved == 0 {
                        task_cur.tasks_solved = 1;
                        task_cur.rev_penalty = -(sub.time + cur_penalty);
                    }
                    if skipped_ok {
                        task_worst.tasks_solved = 1;
                        task_worst.rev_penalty = -(sub.time + cur_penalty);
                        break;
                    } else {
                        skipped_ok = true;
                        cur_penalty += 20;
                    }
                } else {
                    cur_penalty += 20;
                }
            }
            best = max(best + task_cur, cur + task_best);
            worst = min(worst + task_cur, cur + task_worst);
            cur = cur + task_cur;
        }
        TeamScore { cur, best, worst }
    }
}

#[derive(Clone, PartialEq, Eq, PartialOrd, Ord, Copy, Debug)]
struct Score {
    tasks_solved: usize,
    rev_penalty: i64,
}

#[derive(Clone, Copy, PartialEq, Eq, PartialOrd, Ord, Debug)]
struct TeamAndScore {
    score: Score,
    team_id: usize,
}

fn get_gold_medels_cnt(teams: &[TeamAndScore]) -> usize {
    let mut cnt = teams.len();
    while cnt > 0 && teams[cnt - 1].score.tasks_solved == 0 {
        cnt -= 1;
    }
    if cnt == 0 {
        return 0;
    }
    let mut cnt = min(35, (cnt + 9) / 10);
    assert!(cnt > 0);
    let need_score = teams[cnt - 1].score;
    while cnt < teams.len() && teams[cnt].score == need_score {
        cnt += 1;
    }
    cnt
}

fn solve_case(teams: &[Team]) -> Vec<bool> {
    let mut scores = vec![];
    for t in teams.iter() {
        scores.push(t.calc_scores());
    }
    let mut teams_and_scores = vec![];
    for i in 0..scores.len() {
        teams_and_scores.push(TeamAndScore {
            score: scores[i].cur,
            team_id: i,
        });
    }
    teams_and_scores.sort();
    teams_and_scores.reverse();
    let mut can_gold = vec![false; teams.len()];
    let gold_limit = get_gold_medels_cnt(&teams_and_scores);
    for i in 0..gold_limit {
        can_gold[teams_and_scores[i].team_id] = true;
    }
    let mut cnt_non_zero = 0;
    for i in 0..teams.len() {
        if scores[i].cur.tasks_solved > 0 {
            cnt_non_zero += 1;
        }
    }
    for i in 0..teams.len() {
        let team_id = teams_and_scores[i].team_id;
        let best_score = scores[team_id].best;
        if best_score.tasks_solved == 0 {
            continue;
        }
        let mut now_non_zero = cnt_non_zero;
        if scores[team_id].cur.tasks_solved == 0 {
            now_non_zero += 1;
        }
        let cnt_better = binary_search_first_true(0..teams.len(), |pos| {
            teams_and_scores[pos].score <= best_score
        });
        let limit = min(35, (now_non_zero + 9) / 10);
        if cnt_better < limit {
            can_gold[team_id] = true;
        }
    }
    for i in 0..min(40, teams.len()) {
        let mut teams_and_scores = teams_and_scores.clone();
        teams_and_scores[i].score = scores[teams_and_scores[i].team_id].worst;
        teams_and_scores.sort();
        teams_and_scores.reverse();
        let gold_limit = get_gold_medels_cnt(&teams_and_scores);
        for j in 0..gold_limit {
            can_gold[teams_and_scores[j].team_id] = true;
        }
    }
    {
        let mut best_zero = vec![];
        for i in 0..teams.len() {
            if scores[i].cur.tasks_solved == 0 {
                let cur = teams[i].worst_single();
                if cur.tasks_solved == 1 {
                    best_zero.push((cur, i));
                }
            }
        }
        best_zero.sort();
        for best_zero in best_zero[..min(2, best_zero.len())].iter() {
            let mut teams_and_scores = teams_and_scores.clone();
            for pos in 0..teams_and_scores.len() {
                if teams_and_scores[pos].team_id == best_zero.1 {
                    teams_and_scores[pos].score = best_zero.0;
                    break;
                }
            }
            teams_and_scores.sort();
            teams_and_scores.reverse();
            let gold_limit = get_gold_medels_cnt(&teams_and_scores);
            for j in 0..gold_limit {
                can_gold[teams_and_scores[j].team_id] = true;
            }
        }
    }
    can_gold
}

fn solve(input: &mut Input, out: &mut Output, _test_case: usize) {
    let tc = input.usize();
    for _ in 0..tc {
        let m = input.usize();
        let mut teams = vec![];
        let mut by_name = HashMap::new();
        for _ in 0..m {
            let tname = input.string_as_string();
            if !by_name.contains_key(&tname) {
                let new_id = teams.len();
                teams.push(Team {
                    by_task: HashMap::new(),
                    name: tname.clone(),
                });
                by_name.insert(tname.clone(), new_id);
            }
            let t_id = by_name[&tname];
            let task = input.string()[0];
            let time = input.i64();
            let ok = input.string_as_string() == "accepted";
            teams[t_id]
                .by_task
                .entry(task)
                .or_insert_with(Vec::new)
                .push(Submission { time, ok });
        }
        let can_gold = solve_case(&teams);
        let mut cnt_can_gold = 0;
        let mut golds = vec![];
        for i in 0..teams.len() {
            if can_gold[i] {
                cnt_can_gold += 1;
                golds.push(teams[i].name.clone());
            }
        }
        out.println(cnt_can_gold);
        let all_golds = golds.join(" ");
        out.println(all_golds);
        // if 2 + 2 != 5 {
        //     break;
        // }
    }
}

fn solve_slow(teams: &[Team]) -> Vec<bool> {
    let mut res = vec![false; teams.len()];
    let mut update = |teams: &[Team]| {
        let mut teams_and_scores = vec![];
        for i in 0..teams.len() {
            let score = teams[i].calc_scores().cur;
            teams_and_scores.push(TeamAndScore { score, team_id: i });
        }
        teams_and_scores.sort();
        teams_and_scores.reverse();
        let gold_limit = get_gold_medels_cnt(&teams_and_scores);

        for j in 0..gold_limit {
            if !res[teams_and_scores[j].team_id] {
                // dbg!("Found", teams_and_scores[j].team_id);
                // dbg!(gold_limit);
                // for tt in teams_and_scores.iter() {
                //     dbg!(tt);
                // }
            }
            res[teams_and_scores[j].team_id] = true;
        }
    };
    update(teams);
    for t_id in 0..teams.len() {
        for task in teams[t_id].by_task.keys() {
            for sw_id in 0..teams[t_id].by_task[task].len() {
                let mut nteams = teams.to_vec();
                nteams[t_id]
                    .by_task
                    .get_mut(task)
                    .unwrap()
                    .get_mut(sw_id)
                    .unwrap()
                    .ok ^= true;
                update(&nteams);
            }
        }
    }
    res
}

fn stress() {
    for it in 146438.. {
        dbg!(it);
        let mut rnd = Random::new(it);
        const N: usize = 106;
        let teams_num = rnd.gen(1..N);
        let mut teams = vec![
            Team {
                by_task: HashMap::new(),
                name: "A".to_string(),
            };
            teams_num
        ];
        let num_submits = rnd.gen(1..2 * N);
        for _ in 0..num_submits {
            let team_id = rnd.gen(0..teams_num);
            let task = (b'A' + (rnd.gen(0..5)) as u8);
            let time = rnd.gen(1..100);
            let ok = rnd.gen_bool();
            teams[team_id]
                .by_task
                .entry(task)
                .or_insert_with(Vec::new)
                .push(Submission { time, ok });
        }
        for team in teams.iter_mut() {
            for (_, submissions) in team.by_task.iter_mut() {
                submissions.sort_by_key(|s| s.time);
            }
        }
        let teams: Vec<_> = teams.into_iter().filter(|t| t.by_task.len() > 0).collect();
        let ans = solve_case(&teams);
        let ans_slow = solve_slow(&teams);
        if ans != ans_slow {
            for (i, tt) in teams.iter().enumerate() {
                dbg!(i, tt);
            }
            dbg!(ans);
            dbg!(ans_slow);
            for i in 0..ans.len() {
                if ans[i] != ans_slow[i] {
                    dbg!(i, ans[i], ans_slow[i]);
                }
            }
            panic!();
        }
    }
}

pub(crate) fn run(mut input: Input, mut output: Output) -> bool {
    solve(&mut input, &mut output, 1);
    output.flush();
    true
}

}
pub mod algo_lib {
pub mod io {
pub mod input {
use std::fmt::Debug;
use std::io::Read;
use std::marker::PhantomData;
use std::path::Path;
use std::str::FromStr;

pub struct Input {
    input: Box<dyn Read>,
    buf: Vec<u8>,
    at: usize,
    buf_read: usize,
}

macro_rules! read_integer_fun {
    ($t:ident) => {
        #[allow(unused)]
        pub fn $t(&mut self) -> $t {
            self.read_integer()
        }
    };
}

impl Input {
    const DEFAULT_BUF_SIZE: usize = 4096;

    ///
    /// Using with stdin:
    /// ```no_run
    /// use algo_lib::io::input::Input;
    /// let stdin = std::io::stdin();
    /// let input = Input::new(Box::new(stdin));
    /// ```
    ///
    /// For read files use ``new_file`` instead.
    ///
    ///
    pub fn new(input: Box<dyn Read>) -> Self {
        Self {
            input,
            buf: vec![0; Self::DEFAULT_BUF_SIZE],
            at: 0,
            buf_read: 0,
        }
    }

    pub fn new_stdin() -> Self {
        let stdin = std::io::stdin();
        Self::new(Box::new(stdin))
    }

    pub fn new_file<P: AsRef<Path>>(path: P) -> Self {
        let file = std::fs::File::open(&path)
            .unwrap_or_else(|_| panic!("Can't open file: {:?}", path.as_ref().as_os_str()));
        Self::new(Box::new(file))
    }

    pub fn new_with_size(input: Box<dyn Read>, buf_size: usize) -> Self {
        Self {
            input,
            buf: vec![0; buf_size],
            at: 0,
            buf_read: 0,
        }
    }

    pub fn new_file_with_size<P: AsRef<Path>>(path: P, buf_size: usize) -> Self {
        let file = std::fs::File::open(&path)
            .unwrap_or_else(|_| panic!("Can't open file: {:?}", path.as_ref().as_os_str()));
        Self::new_with_size(Box::new(file), buf_size)
    }

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

    pub fn peek(&mut self) -> Option<u8> {
        if self.refill_buffer() {
            Some(self.buf[self.at])
        } else {
            None
        }
    }

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

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

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

    pub fn has_more_elements(&mut self) -> bool {
        !self.is_exhausted()
    }

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

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

    pub fn string_vec(&mut self, size: usize) -> Vec<Vec<u8>> {
        let mut res = Vec::with_capacity(size);
        for _ in 0usize..size {
            res.push(self.string());
        }
        res
    }

    pub fn read_line(&mut self) -> String {
        let mut res = String::new();
        while let Some(c) = self.get() {
            if c == b'\n' {
                break;
            }
            if c == b'\r' {
                if self.peek() == Some(b'\n') {
                    self.get();
                }
                break;
            }
            res.push(c.into());
        }
        res
    }

    #[allow(clippy::should_implement_trait)]
    pub fn into_iter<T: Readable>(self) -> InputIterator<T> {
        InputIterator {
            input: self,
            phantom: Default::default(),
        }
    }

    fn read_integer<T: FromStr>(&mut self) -> T
    where
        <T as FromStr>::Err: Debug,
    {
        let res = self.read_string();
        res.parse::<T>().unwrap()
    }

    fn read_string(&mut self) -> String {
        match self.next_token() {
            None => {
                panic!("Input exhausted");
            }
            Some(res) => unsafe { String::from_utf8_unchecked(res) },
        }
    }

    pub fn string_as_string(&mut self) -> String {
        self.read_string()
    }

    pub fn string(&mut self) -> Vec<u8> {
        self.read_string().into_bytes()
    }

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

    fn read_float(&mut self) -> f64 {
        self.read_string().parse().unwrap()
    }

    pub fn f64(&mut self) -> f64 {
        self.read_float()
    }

    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
        }
    }

    read_integer_fun!(i32);
    read_integer_fun!(i64);
    read_integer_fun!(i128);
    read_integer_fun!(u32);
    read_integer_fun!(u64);
    read_integer_fun!(usize);
}

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

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

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

impl Readable for f64 {
    fn read(input: &mut Input) -> Self {
        input.read_string().parse().unwrap()
    }
}

impl Readable for f32 {
    fn read(input: &mut Input) -> Self {
        input.read_string().parse().unwrap()
    }
}

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

pub struct InputIterator<T: Readable> {
    input: Input,
    phantom: PhantomData<T>,
}

impl<T: Readable> Iterator for InputIterator<T> {
    type Item = T;

    fn next(&mut self) -> Option<Self::Item> {
        self.input.skip_whitespace();
        self.input.peek().map(|_| self.input.read())
    }
}

macro_rules! read_integer {
    ($t:ident) => {
        impl Readable for $t {
            fn read(input: &mut Input) -> Self {
                input.read_integer()
            }
        }
    };
}

read_integer!(i8);
read_integer!(i16);
read_integer!(i32);
read_integer!(i64);
read_integer!(i128);
read_integer!(isize);
read_integer!(u8);
read_integer!(u16);
read_integer!(u32);
read_integer!(u64);
read_integer!(u128);
read_integer!(usize);
}
pub mod output {
use std::io::Write;

pub struct Output {
    output: Box<dyn Write>,
    buf: Vec<u8>,
    at: usize,
    auto_flush: bool,
}

impl Output {
    const DEFAULT_BUF_SIZE: usize = 4096;

    pub fn new(output: Box<dyn Write>) -> Self {
        Self {
            output,
            buf: vec![0; Self::DEFAULT_BUF_SIZE],
            at: 0,
            auto_flush: false,
        }
    }

    pub fn new_stdout() -> Self {
        let stdout = std::io::stdout();
        Self::new(Box::new(stdout))
    }

    pub fn new_file(path: impl AsRef<std::path::Path>) -> Self {
        let file = std::fs::File::create(path).unwrap();
        Self::new(Box::new(file))
    }

    pub fn new_with_auto_flush(output: Box<dyn Write>) -> Self {
        Self {
            output,
            buf: vec![0; Self::DEFAULT_BUF_SIZE],
            at: 0,
            auto_flush: true,
        }
    }

    pub fn flush(&mut self) {
        if self.at != 0 {
            self.output.write_all(&self.buf[..self.at]).unwrap();
            self.at = 0;
            self.output.flush().expect("Couldn't flush output");
        }
    }

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

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

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

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

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

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;
        }
        if self.auto_flush {
            self.flush();
        }
        Ok(buf.len())
    }

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

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

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

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

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

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

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

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

write_to_string!(u8);
write_to_string!(u16);
write_to_string!(u32);
write_to_string!(u64);
write_to_string!(u128);
write_to_string!(usize);
write_to_string!(i8);
write_to_string!(i16);
write_to_string!(i32);
write_to_string!(i64);
write_to_string!(i128);
write_to_string!(isize);
write_to_string!(f32);
write_to_string!(f64);

impl<T: Writable, U: Writable> Writable for (T, U) {
    fn write(&self, output: &mut Output) {
        self.0.write(output);
        output.put(b' ');
        self.1.write(output);
    }
}

impl<T: Writable, U: Writable, V: Writable> Writable for (T, U, V) {
    fn write(&self, output: &mut Output) {
        self.0.write(output);
        output.put(b' ');
        self.1.write(output);
        output.put(b' ');
        self.2.write(output);
    }
}
}
}
pub mod misc {
pub mod binary_search {
use crate::algo_lib::misc::num_traits::Number;
use std::ops::Range;

pub fn binary_search_first_true<T>(range: Range<T>, mut f: impl FnMut(T) -> bool) -> T
where
    T: Number,
{
    // we can't store [range.start - 1] into [left], because it could overflow
    let mut left_plus_one = range.start;
    let mut right = range.end;
    while right > left_plus_one {
        let mid = left_plus_one + (right - left_plus_one) / T::TWO;
        if f(mid) {
            right = mid;
        } else {
            left_plus_one = mid + T::ONE;
        }
    }
    right
}

pub fn binary_search_last_true<T>(range: Range<T>, mut f: impl FnMut(T) -> bool) -> Option<T>
where
    T: Number,
{
    let first_false = binary_search_first_true(range.clone(), |x| !f(x));
    if first_false == range.start {
        None
    } else {
        Some(first_false - T::ONE)
    }
}

#[test]
fn simple_stress() {
    const N: usize = 50;
    for n in 1..N {
        for cnt_false in 0..=n {
            let mut a = vec![false; cnt_false];
            a.resize(n, true);
            let mut max_f_calls = ((n + 1) as f64).log2().ceil() as i32;
            let f_is_true = |id: usize| -> bool {
                max_f_calls -= 1;
                assert!(max_f_calls >= 0);
                a[id]
            };
            let result = binary_search_first_true(0..n, f_is_true);
            assert_eq!(result, cnt_false);
        }
    }
}
}
pub mod dbg_macro {
#[macro_export]
#[allow(unused_macros)]
macro_rules! dbg {
    ($first_val:expr, $($val:expr),+ $(,)?) => {
        eprint!("[{}:{}] {} = {:?}",
                    file!(), line!(), stringify!($first_val), &$first_val);
        ($(eprint!(", {} = {:?}", stringify!($val), &$val)),+,);
        eprintln!();
    };
    ($first_val:expr) => {
        eprintln!("[{}:{}] {} = {:?}",
                    file!(), line!(), stringify!($first_val), &$first_val)
    };
}
}
pub mod gen_vector {
pub fn gen_vec<T>(n: usize, f: impl FnMut(usize) -> T) -> Vec<T> {
    (0..n).map(f).collect()
}
}
pub mod num_traits {
use std::cmp::Ordering;
use std::fmt::Debug;
use std::ops::Add;
use std::ops::AddAssign;
use std::ops::Div;
use std::ops::DivAssign;
use std::ops::Mul;
use std::ops::MulAssign;
use std::ops::Sub;
use std::ops::SubAssign;

pub trait HasConstants<T> {
    const MAX: T;
    const MIN: T;
    const ZERO: T;
    const ONE: T;
    const TWO: T;
}

pub trait ConvSimple<T> {
    fn from_i32(val: i32) -> T;
    fn to_i32(self) -> i32;
    fn to_f64(self) -> f64;
}

pub trait Signum {
    fn signum(&self) -> i32;
}

pub trait Number:
    Copy
    + Add<Output = Self>
    + AddAssign
    + Sub<Output = Self>
    + SubAssign
    + Mul<Output = Self>
    + MulAssign
    + Div<Output = Self>
    + DivAssign
    + PartialOrd
    + PartialEq
    + HasConstants<Self>
    + Default
    + Debug
    + Sized
    + ConvSimple<Self>
{
}

impl<
        T: Copy
            + Add<Output = Self>
            + AddAssign
            + Sub<Output = Self>
            + SubAssign
            + Mul<Output = Self>
            + MulAssign
            + Div<Output = Self>
            + DivAssign
            + PartialOrd
            + PartialEq
            + HasConstants<Self>
            + Default
            + Debug
            + Sized
            + ConvSimple<Self>,
    > Number for T
{
}

macro_rules! has_constants_impl {
    ($t: ident) => {
        impl HasConstants<$t> for $t {
            // TODO: remove `std` for new rust version..
            const MAX: $t = std::$t::MAX;
            const MIN: $t = std::$t::MIN;
            const ZERO: $t = 0;
            const ONE: $t = 1;
            const TWO: $t = 2;
        }

        impl ConvSimple<$t> for $t {
            fn from_i32(val: i32) -> $t {
                val as $t
            }

            fn to_i32(self) -> i32 {
                self as i32
            }

            fn to_f64(self) -> f64 {
                self as f64
            }
        }
    };
}

has_constants_impl!(i32);
has_constants_impl!(i64);
has_constants_impl!(i128);
has_constants_impl!(u32);
has_constants_impl!(u64);
has_constants_impl!(u128);
has_constants_impl!(usize);
has_constants_impl!(u8);

impl ConvSimple<Self> for f64 {
    fn from_i32(val: i32) -> Self {
        val as f64
    }

    fn to_i32(self) -> i32 {
        self as i32
    }

    fn to_f64(self) -> f64 {
        self
    }
}

impl HasConstants<Self> for f64 {
    const MAX: Self = Self::MAX;
    const MIN: Self = -Self::MAX;
    const ZERO: Self = 0.0;
    const ONE: Self = 1.0;
    const TWO: Self = 2.0;
}

impl<T: Number + Ord> Signum for T {
    fn signum(&self) -> i32 {
        match self.cmp(&T::ZERO) {
            Ordering::Greater => 1,
            Ordering::Less => -1,
            Ordering::Equal => 0,
        }
    }
}
}
pub mod rand {
use crate::algo_lib::misc::gen_vector::gen_vec;
use crate::algo_lib::misc::num_traits::Number;
use std::ops::Range;
use std::time::SystemTime;
use std::time::UNIX_EPOCH;

#[allow(dead_code)]
pub struct Random {
    state: u64,
}

impl Random {
    pub fn gen_u64(&mut self) -> u64 {
        let mut x = self.state;
        x ^= x << 13;
        x ^= x >> 7;
        x ^= x << 17;
        self.state = x;
        x
    }

    #[allow(dead_code)]
    pub fn next_in_range(&mut self, from: usize, to: usize) -> usize {
        assert!(from < to);
        (from as u64 + self.gen_u64() % ((to - from) as u64)) as usize
    }

    pub fn gen_index<T>(&mut self, a: &[T]) -> usize {
        self.gen(0..a.len())
    }

    #[allow(dead_code)]
    #[inline(always)]
    pub fn gen_double(&mut self) -> f64 {
        (self.gen_u64() as f64) / (std::usize::MAX as f64)
    }

    #[allow(dead_code)]
    pub fn new(seed: u64) -> Self {
        let state = if seed == 0 { 787788 } else { seed };
        Self { state }
    }

    pub fn new_time_seed() -> Self {
        let time = SystemTime::now();
        let seed = (time.duration_since(UNIX_EPOCH).unwrap().as_nanos() % 1_000_000_000) as u64;
        if seed == 0 {
            Self::new(787788)
        } else {
            Self::new(seed)
        }
    }

    #[allow(dead_code)]
    pub fn gen_permutation(&mut self, n: usize) -> Vec<usize> {
        let mut result: Vec<_> = (0..n).collect();
        for i in 0..n {
            let idx = self.next_in_range(0, i + 1);
            result.swap(i, idx);
        }
        result
    }

    pub fn shuffle<T>(&mut self, a: &mut [T]) {
        for i in 1..a.len() {
            a.swap(i, self.gen(0..i + 1));
        }
    }

    pub fn gen<T>(&mut self, range: Range<T>) -> T
    where
        T: Number,
    {
        let from = T::to_i32(range.start);
        let to = T::to_i32(range.end);
        assert!(from < to);
        let len = (to - from) as usize;
        T::from_i32(self.next_in_range(0, len) as i32 + from)
    }

    pub fn gen_vec<T>(&mut self, n: usize, range: Range<T>) -> Vec<T>
    where
        T: Number,
    {
        gen_vec(n, |_| self.gen(range.clone()))
    }

    pub fn gen_nonempty_range(&mut self, n: usize) -> Range<usize> {
        let x = self.gen(0..n);
        let y = self.gen(0..n);
        if x <= y {
            x..y + 1
        } else {
            y..x + 1
        }
    }

    pub fn gen_bool(&mut self) -> bool {
        self.gen(0..2) == 0
    }
}
}
}
}
fn main() {
    let input = algo_lib::io::input::Input::new_stdin();
    let mut output = algo_lib::io::output::Output::new_stdout();
    crate::solution::run(input, output);
}