// https://contest.ucup.ac/contest/1894/problem/9982
use crate::algo_lib::collections::slice_ext::backward::Back;
use crate::algo_lib::collections::slice_ext::bounds::Bounds;
use crate::algo_lib::collections::slice_ext::compress::{compress, Compressed};
use crate::algo_lib::collections::vec_ext::detuple::Detuple;
use crate::algo_lib::collections::vec_ext::gen_vec::VecGen;
use crate::algo_lib::collections::vec_ext::inc_dec::IncDec;
use crate::algo_lib::io::input::Input;
use crate::algo_lib::io::output::Output;
use crate::algo_lib::misc::memo::memoization_2d::Memoization2d;
use crate::algo_lib::misc::recursive_function::Callable2;
use crate::algo_lib::misc::test_type::TaskType;
use crate::algo_lib::misc::test_type::TestType;
type PreCalc = ();
fn solve(input: &mut Input, out: &mut Output, _test_case: usize, _data: &mut PreCalc) {
    let n = input.read_size();
    let lr = input.read_size_pair_vec(n).dec();
    let (l, r) = lr.detuple();
    let r = r.inc();
    let Compressed { arrs: [l, r], .. } = compress([&l, &r]);
    let m = r[Back(0)];
    let mut at = 0;
    let d = Vec::with_gen(
        m,
        |i, _| {
            while r[at] < i {
                at += 1;
            }
            at
        },
    );
    at = n;
    let u = Vec::with_gen_back(
        m,
        |i, _| {
            while l[at - 1] > i {
                at -= 1;
            }
            at
        },
    );
    let c1 = r[0];
    let c2 = u[0];
    let ways = [[l, r], [d, u]];
    let end = [m, n];
    let mut mem = Memoization2d::new(
        2,
        n.max(m) + 1,
        |mem, t, pos| -> usize {
            if pos == end[t] {
                1
            } else {
                let p1 = ways[t][1].upper_bound(&pos);
                let res = 1
                    + mem
                        .call(t, ways[t][1][p1])
                        .max(mem.call(1 - t, ways[1 - t][1][p1]));
                res
            }
        },
    );
    out.print_line(mem.call(0, c1).max(mem.call(1, c2)));
}
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 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 md_arr {
pub mod arr2d {
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, Ord, PartialOrd)]
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 with_gen<F>(d1: usize, d2: usize, mut g: 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(g(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.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::with_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');
        }
    }
}
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 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 bounds {
use std::ops::{Bound, RangeBounds};
pub trait Bounds<T: PartialOrd> {
    fn lower_bound(&self, el: &T) -> usize;
    fn upper_bound(&self, el: &T) -> usize;
    fn bin_search(&self, el: &T) -> Option<usize>;
    fn more(&self, el: &T) -> usize;
    fn more_or_eq(&self, el: &T) -> usize;
    fn less(&self, el: &T) -> usize {
        self.lower_bound(el)
    }
    fn less_or_eq(&self, el: &T) -> usize {
        self.upper_bound(el)
    }
    fn inside<'a>(&self, bounds: impl RangeBounds<&'a T>) -> usize
    where
        T: 'a;
}
impl<T: PartialOrd> Bounds<T> for [T] {
    fn lower_bound(&self, el: &T) -> usize {
        let mut left = 0;
        let mut right = self.len();
        while left < right {
            let mid = left + ((right - left) >> 1);
            if &self[mid] < el {
                left = mid + 1;
            } else {
                right = mid;
            }
        }
        left
    }
    fn upper_bound(&self, el: &T) -> usize {
        let mut left = 0;
        let mut right = self.len();
        while left < right {
            let mid = left + ((right - left) >> 1);
            if &self[mid] <= el {
                left = mid + 1;
            } else {
                right = mid;
            }
        }
        left
    }
    fn bin_search(&self, el: &T) -> Option<usize> {
        let at = self.lower_bound(el);
        if at == self.len() || &self[at] != el { None } else { Some(at) }
    }
    fn more(&self, el: &T) -> usize {
        self.len() - self.upper_bound(el)
    }
    fn more_or_eq(&self, el: &T) -> usize {
        self.len() - self.lower_bound(el)
    }
    fn inside<'a>(&self, bounds: impl RangeBounds<&'a T>) -> usize
    where
        T: 'a,
    {
        let to = match bounds.end_bound() {
            Bound::Included(el) => self.less_or_eq(el),
            Bound::Excluded(el) => self.less(el),
            Bound::Unbounded => self.len(),
        };
        let from = match bounds.start_bound() {
            Bound::Included(el) => self.less(el),
            Bound::Excluded(el) => self.less_or_eq(el),
            Bound::Unbounded => 0,
        };
        to - from
    }
}
}
pub mod compress {
use crate::algo_lib::collections::slice_ext::bounds::Bounds;
use std::mem::MaybeUninit;
#[derive(Eq, PartialEq, Debug)]
pub struct Compressed<T, const N: usize> {
    pub order: Vec<T>,
    pub arrs: [Vec<usize>; N],
}
pub fn compress<T: Ord + Clone, const N: usize>(vs: [&[T]; N]) -> Compressed<T, N> {
    let mut size = 0;
    for v in &vs {
        size += v.len();
    }
    let mut all = Vec::with_capacity(size);
    for v in &vs {
        all.extend_from_slice(v);
    }
    all.sort();
    all.dedup();
    let arrs = unsafe {
        let mut arr: MaybeUninit<[Vec<usize>; N]> = MaybeUninit::uninit();
        for (i, v) in vs.iter().enumerate() {
            let mut cur = Vec::with_capacity(vs[i].len());
            for vv in *v {
                cur.push(all.bin_search(vv).unwrap());
            }
            arr.as_mut_ptr().cast::<Vec<usize>>().add(i).write(cur);
        }
        arr.assume_init()
    };
    Compressed { order: all, arrs }
}
}
}
pub mod vec_ext {
pub mod detuple {
pub trait Detuple {
    type Res;
    fn detuple(self) -> Self::Res;
}
impl<A, B, C, D> Detuple for Vec<(A, B, C, D)> {
    type Res = (Vec<A>, Vec<B>, Vec<C>, Vec<D>);
    fn detuple(self) -> Self::Res {
        let mut a = Vec::with_capacity(self.len());
        let mut b = Vec::with_capacity(self.len());
        let mut c = Vec::with_capacity(self.len());
        let mut d = Vec::with_capacity(self.len());
        for (aa, bb, cc, dd) in self {
            a.push(aa);
            b.push(bb);
            c.push(cc);
            d.push(dd);
        }
        (a, b, c, d)
    }
}
impl<A, B, C> Detuple for Vec<(A, B, C)> {
    type Res = (Vec<A>, Vec<B>, Vec<C>);
    fn detuple(self) -> Self::Res {
        let mut a = Vec::with_capacity(self.len());
        let mut b = Vec::with_capacity(self.len());
        let mut c = Vec::with_capacity(self.len());
        for (aa, bb, cc) in self {
            a.push(aa);
            b.push(bb);
            c.push(cc);
        }
        (a, b, c)
    }
}
impl<A, B> Detuple for Vec<(A, B)> {
    type Res = (Vec<A>, Vec<B>);
    fn detuple(self) -> Self::Res {
        let mut a = Vec::with_capacity(self.len());
        let mut b = Vec::with_capacity(self.len());
        for (aa, bb) in self {
            a.push(aa);
            b.push(bb);
        }
        (a, b)
    }
}
}
pub mod gen_vec {
pub trait VecGen<T> {
    fn with_gen(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 + Clone;
}
impl<T> VecGen<T> for Vec<T> {
    fn with_gen(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 + Clone,
    {
        let mut vec = vec![T::default(); n];
        for i in (0..n).rev() {
            vec[i] = f(i, &vec);
        }
        vec
    }
}
}
pub mod inc_dec {
use crate::algo_lib::numbers::num_traits::algebra::{AdditionMonoidWithSub, One};
pub trait IncDec {
    #[must_use]
    fn inc(self) -> Self;
    #[must_use]
    fn dec(self) -> Self;
}
impl<T: AdditionMonoidWithSub + One> IncDec for T {
    fn inc(self) -> Self {
        self + T::one()
    }
    fn dec(self) -> Self {
        self - T::one()
    }
}
impl<T: AdditionMonoidWithSub + One> IncDec for Vec<T> {
    fn inc(mut self) -> Self {
        self.iter_mut().for_each(|i| *i += T::one());
        self
    }
    fn dec(mut self) -> Self {
        self.iter_mut().for_each(|i| *i -= T::one());
        self
    }
}
impl<T: AdditionMonoidWithSub + One> IncDec for Vec<Vec<T>> {
    fn inc(mut self) -> Self {
        self.iter_mut().for_each(|v| v.iter_mut().for_each(|i| *i += T::one()));
        self
    }
    fn dec(mut self) -> Self {
        self.iter_mut().for_each(|v| v.iter_mut().for_each(|i| *i -= T::one()));
        self
    }
}
impl<T: AdditionMonoidWithSub + One, U: AdditionMonoidWithSub + One> IncDec
for Vec<(T, U)> {
    fn inc(mut self) -> Self {
        self.iter_mut()
            .for_each(|(i, j)| {
                *i += T::one();
                *j += U::one();
            });
        self
    }
    fn dec(mut self) -> Self {
        self.iter_mut()
            .for_each(|(i, j)| {
                *i -= T::one();
                *j -= U::one();
            });
        self
    }
}
impl<T: AdditionMonoidWithSub + One, U: AdditionMonoidWithSub + One, V> IncDec
for Vec<(T, U, V)> {
    fn inc(mut self) -> Self {
        self.iter_mut()
            .for_each(|(i, j, _)| {
                *i += T::one();
                *j += U::one();
            });
        self
    }
    fn dec(mut self) -> Self {
        self.iter_mut()
            .for_each(|(i, j, _)| {
                *i -= T::one();
                *j -= U::one();
            });
        self
    }
}
impl<T: AdditionMonoidWithSub + One, U: AdditionMonoidWithSub + One, V, W> IncDec
for Vec<(T, U, V, W)> {
    fn inc(mut self) -> Self {
        self.iter_mut()
            .for_each(|(i, j, ..)| {
                *i += T::one();
                *j += U::one();
            });
        self
    }
    fn dec(mut self) -> Self {
        self.iter_mut()
            .for_each(|(i, j, ..)| {
                *i -= T::one();
                *j -= U::one();
            });
        self
    }
}
impl<T: AdditionMonoidWithSub + One, U: AdditionMonoidWithSub + One, V, W, X> IncDec
for Vec<(T, U, V, W, X)> {
    fn inc(mut self) -> Self {
        self.iter_mut()
            .for_each(|(i, j, ..)| {
                *i += T::one();
                *j += U::one();
            });
        self
    }
    fn dec(mut self) -> Self {
        self.iter_mut()
            .for_each(|(i, j, ..)| {
                *i -= T::one();
                *j -= U::one();
            });
        self
    }
}
impl<T: AdditionMonoidWithSub + One, U: AdditionMonoidWithSub + One> IncDec for (T, U) {
    fn inc(mut self) -> Self {
        self.0 += T::one();
        self.1 += U::one();
        self
    }
    fn dec(mut self) -> Self {
        self.0 -= T::one();
        self.1 -= U::one();
        self
    }
}
}
}
}
pub mod io {
pub mod input {
use 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 memo {
pub mod memoization_2d {
use crate::algo_lib::collections::md_arr::arr2d::Arr2d;
use crate::algo_lib::misc::recursive_function::Callable2;
pub struct Memoization2d<F, Output>
where
    F: FnMut(&mut dyn Callable2<usize, usize, Output>, usize, usize) -> Output,
{
    f: std::cell::UnsafeCell<F>,
    res: Arr2d<Option<Output>>,
}
impl<F, Output: Clone> Memoization2d<F, Output>
where
    F: FnMut(&mut dyn Callable2<usize, usize, Output>, usize, usize) -> Output,
{
    pub fn new(d1: usize, d2: usize, f: F) -> Self {
        Self {
            f: std::cell::UnsafeCell::new(f),
            res: Arr2d::new(d1, d2, None),
        }
    }
}
impl<F, Output: Clone> Callable2<usize, usize, Output> for Memoization2d<F, Output>
where
    F: FnMut(&mut dyn Callable2<usize, usize, Output>, usize, usize) -> Output,
{
    fn call(&mut self, n: usize, m: usize) -> Output {
        match self.res[(n, m)].as_ref() {
            None => {
                let res = unsafe { (*self.f.get())(self, n, m) };
                self.res[(n, m)] = Some(res.clone());
                res
            }
            Some(res) => res.clone(),
        }
    }
}
}
}
pub mod recursive_function {
use std::marker::PhantomData;
macro_rules! recursive_function {
    ($name:ident, $trait:ident, ($($type:ident $arg:ident,)*)) => {
        pub trait $trait <$($type,)* Output > { fn call(& mut self, $($arg : $type,)*) ->
        Output; } pub struct $name < F, $($type,)* Output > where F : FnMut(& mut dyn
        $trait <$($type,)* Output >, $($type,)*) -> Output, { f : std::cell::UnsafeCell <
        F >, $($arg : PhantomData <$type >,)* phantom_output : PhantomData < Output >, }
        impl < F, $($type,)* Output > $name < F, $($type,)* Output > where F : FnMut(&
        mut dyn $trait <$($type,)* Output >, $($type,)*) -> Output, { pub fn new(f : F)
        -> Self { Self { f : std::cell::UnsafeCell::new(f), $($arg :
        Default::default(),)* phantom_output : Default::default(), } } } impl < F,
        $($type,)* Output > $trait <$($type,)* Output > for $name < F, $($type,)* Output
        > where F : FnMut(& mut dyn $trait <$($type,)* Output >, $($type,)*) -> Output, {
        fn call(& mut self, $($arg : $type,)*) -> Output { unsafe { (* self.f.get())
        (self, $($arg,)*) } } }
    };
}
recursive_function!(RecursiveFunction0, Callable0, ());
recursive_function!(RecursiveFunction, Callable, (Arg arg,));
recursive_function!(RecursiveFunction2, Callable2, (Arg1 arg1, Arg2 arg2,));
recursive_function!(RecursiveFunction3, Callable3, (Arg1 arg1, Arg2 arg2, Arg3 arg3,));
recursive_function!(
    RecursiveFunction4, Callable4, (Arg1 arg1, Arg2 arg2, Arg3 arg3, Arg4 arg4,)
);
recursive_function!(
    RecursiveFunction5, Callable5, (Arg1 arg1, Arg2 arg2, Arg3 arg3, Arg4 arg4, Arg5
    arg5,)
);
recursive_function!(
    RecursiveFunction6, Callable6, (Arg1 arg1, Arg2 arg2, Arg3 arg3, Arg4 arg4, Arg5
    arg5, Arg6 arg6,)
);
recursive_function!(
    RecursiveFunction7, Callable7, (Arg1 arg1, Arg2 arg2, Arg3 arg3, Arg4 arg4, Arg5
    arg5, Arg6 arg6, Arg7 arg7,)
);
recursive_function!(
    RecursiveFunction8, Callable8, (Arg1 arg1, Arg2 arg2, Arg3 arg3, Arg4 arg4, Arg5
    arg5, Arg6 arg6, Arg7 arg7, Arg8 arg8,)
);
recursive_function!(
    RecursiveFunction9, Callable9, (Arg1 arg1, Arg2 arg2, Arg3 arg3, Arg4 arg4, Arg5
    arg5, Arg6 arg6, Arg7 arg7, Arg8 arg8, Arg9 arg9,)
);
}
pub mod test_type {
pub enum TestType {
    Single,
    MultiNumber,
    MultiEof,
}
pub enum TaskType {
    Classic,
    Interactive,
}
}
}
pub mod numbers {
pub mod num_traits {
pub mod algebra {
use crate::algo_lib::numbers::num_traits::invertible::Invertible;
use std::ops::{
    Add, AddAssign, Div, DivAssign, Mul, MulAssign, Neg, Rem, RemAssign, Sub, SubAssign,
};
pub trait Zero {
    fn zero() -> Self;
}
pub trait One {
    fn one() -> Self;
}
pub trait AdditionMonoid: Add<Output = Self> + AddAssign + Zero + Eq + Sized {}
impl<T: Add<Output = Self> + AddAssign + Zero + Eq> AdditionMonoid for T {}
pub trait AdditionMonoidWithSub: AdditionMonoid + Sub<Output = Self> + SubAssign {}
impl<T: AdditionMonoid + Sub<Output = Self> + SubAssign> AdditionMonoidWithSub for T {}
pub trait AdditionGroup: AdditionMonoidWithSub + Neg<Output = Self> {}
impl<T: AdditionMonoidWithSub + Neg<Output = Self>> AdditionGroup for T {}
pub trait MultiplicationMonoid: Mul<Output = Self> + MulAssign + One + Eq + Sized {}
impl<T: Mul<Output = Self> + MulAssign + One + Eq> MultiplicationMonoid for T {}
pub trait IntegerMultiplicationMonoid: MultiplicationMonoid + Div<
        Output = Self,
    > + Rem<Output = Self> + DivAssign + RemAssign {}
impl<
    T: MultiplicationMonoid + Div<Output = Self> + Rem<Output = Self> + DivAssign
        + RemAssign,
> IntegerMultiplicationMonoid for T {}
pub trait MultiplicationGroup: MultiplicationMonoid + Div<
        Output = Self,
    > + DivAssign + Invertible<Output = Self> {}
impl<
    T: MultiplicationMonoid + Div<Output = Self> + DivAssign + Invertible<Output = Self>,
> MultiplicationGroup for T {}
pub trait SemiRing: AdditionMonoid + MultiplicationMonoid {}
impl<T: AdditionMonoid + MultiplicationMonoid> SemiRing for T {}
pub trait SemiRingWithSub: AdditionMonoidWithSub + SemiRing {}
impl<T: AdditionMonoidWithSub + SemiRing> SemiRingWithSub for T {}
pub trait Ring: SemiRing + AdditionGroup {}
impl<T: SemiRing + AdditionGroup> Ring for T {}
pub trait IntegerSemiRing: SemiRing + IntegerMultiplicationMonoid {}
impl<T: SemiRing + IntegerMultiplicationMonoid> IntegerSemiRing for T {}
pub trait IntegerSemiRingWithSub: SemiRingWithSub + IntegerSemiRing {}
impl<T: SemiRingWithSub + IntegerSemiRing> IntegerSemiRingWithSub for T {}
pub trait IntegerRing: IntegerSemiRing + Ring {}
impl<T: IntegerSemiRing + Ring> IntegerRing for T {}
pub trait Field: Ring + MultiplicationGroup {}
impl<T: Ring + MultiplicationGroup> Field for T {}
macro_rules! zero_one_integer_impl {
    ($($t:ident)+) => {
        $(impl Zero for $t { fn zero() -> Self { 0 } } impl One for $t { fn one() -> Self
        { 1 } })+
    };
}
zero_one_integer_impl!(i128 i64 i32 i16 i8 isize u128 u64 u32 u16 u8 usize);
}
pub mod invertible {
pub trait Invertible {
    type Output;
    fn inv(&self) -> Option<Self::Output>;
}
}
}
}
}