// https://judge.eluminatis-of-lu.com/contest/676ffd92569fb90008aac7da/1158
use crate::algo_lib::collections::iter_ext::iter_copied::ItersCopied;
use crate::algo_lib::collections::min_max::MinimMaxim;
use crate::algo_lib::io::input::Input;
use crate::algo_lib::io::output::Output;
use crate::algo_lib::misc::test_type::TaskType;
use std::cmp::Reverse;
use crate::algo_lib::misc::test_type::TestType;
use crate::algo_lib::numbers::primes::sieve::primes;
use crate::algo_lib::string::str::StrReader;
type PreCalc = ();
fn solve(input: &mut Input, out: &mut Output, _test_case: usize, _data: &mut PreCalc) {
    let p: Vec<usize> = primes(2000);
    let mut reps = vec![Vec::new(); 2001];
    for i in p.copy_iter() {
        reps[i].push((i, 0, 0));
        for j in p.copy_iter() {
            if i + j > 2000 {
                break;
            }
            reps[i + j].push((i, j, 0));
            for k in p.copy_iter() {
                if i + j + k > 2000 {
                    break;
                }
                reps[i + j + k].push((i, j, k));
                if j == k {
                    break;
                }
            }
            if i == j {
                break;
            }
        }
    }
    let t = input.read_size();
    for _ in 0..t {
        let n = input.read_size();
        let s = input.read_str();
        let mut q = Vec::with_capacity(3);
        for c in b'a'..=b'c' {
            q.push(s.copy_count(c));
        }
        q.sort_by_key(|x| Reverse(*x));
        let mut ans = None;
        for (i, j, k) in reps[n].copy_iter() {
            ans.minim((i.abs_diff(q[0]) + j.abs_diff(q[1]) + k.abs_diff(q[2])) / 2);
        }
        out.print_line(ans);
    }
}
pub static TEST_TYPE: TestType = TestType::Single;
pub static TASK_TYPE: TaskType = TaskType::Classic;
pub(crate) fn run(mut input: Input, mut output: Output) -> bool {
    let mut pre_calc = ();
    match TEST_TYPE {
        TestType::Single => solve(&mut input, &mut output, 1, &mut pre_calc),
        TestType::MultiNumber => {
            let t = input.read();
            for i in 1..=t {
                solve(&mut input, &mut output, i, &mut pre_calc);
            }
        }
        TestType::MultiEof => {
            let mut i = 1;
            while input.peek().is_some() {
                solve(&mut input, &mut output, i, &mut pre_calc);
                i += 1;
            }
        }
    }
    output.flush();
    match TASK_TYPE {
        TaskType::Classic => input.is_empty(),
        TaskType::Interactive => true,
    }
}


fn main() {
    let 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 bit_set {
use crate::algo_lib::collections::iter_ext::iter_copied::ItersCopied;
use crate::algo_lib::numbers::num_traits::bit_ops::BitOps;
use std::ops::{BitAndAssign, BitOrAssign, BitXorAssign, Index, ShlAssign, ShrAssign};
const TRUE: bool = true;
const FALSE: bool = false;
#[derive(Clone, Eq, PartialEq, Hash)]
pub struct BitSet {
    data: Vec<u64>,
    len: usize,
}
impl BitSet {
    pub fn new(len: usize) -> Self {
        let data_len = if len == 0 { 0 } else { Self::index(len - 1) + 1 };
        Self {
            data: vec![0; data_len],
            len,
        }
    }
    pub fn from_slice(len: usize, set: &[usize]) -> Self {
        let mut res = Self::new(len);
        for &i in set {
            res.set(i);
        }
        res
    }
    pub fn set(&mut self, at: usize) {
        assert!(at < self.len);
        self.data[Self::index(at)].set_bit(at & 63);
    }
    pub fn unset(&mut self, at: usize) {
        assert!(at < self.len);
        self.data[Self::index(at)].unset_bit(at & 63);
    }
    pub fn change(&mut self, at: usize, value: bool) {
        if value {
            self.set(at);
        } else {
            self.unset(at);
        }
    }
    pub fn flip(&mut self, at: usize) {
        self.change(at, !self[at]);
    }
    #[allow(clippy::len_without_is_empty)]
    pub fn len(&self) -> usize {
        self.len
    }
    pub fn fill(&mut self, value: bool) {
        self.data.fill(if value { std::u64::MAX } else { 0 });
        if value {
            self.fix_last();
        }
    }
    pub fn is_superset(&self, other: &Self) -> bool {
        assert_eq!(self.len, other.len);
        for (we, them) in self.data.copy_zip(&other.data) {
            if (we & them) != them {
                return false;
            }
        }
        true
    }
    pub fn is_subset(&self, other: &Self) -> bool {
        other.is_superset(self)
    }
    pub fn iter(&self) -> BitSetIter<'_> {
        self.into_iter()
    }
    fn index(at: usize) -> usize {
        at >> 6
    }
    pub fn count_ones(&self) -> usize {
        self.data.iter().map(|x| x.count_ones() as usize).sum()
    }
    fn fix_last(&mut self) {
        if self.len & 63 != 0 {
            let mask = (1 << (self.len & 63)) - 1;
            *self.data.last_mut().unwrap() &= mask;
        }
    }
}
pub struct BitSetIter<'s> {
    at: usize,
    inside: usize,
    set: &'s BitSet,
}
impl<'s> Iterator for BitSetIter<'s> {
    type Item = usize;
    fn next(&mut self) -> Option<Self::Item> {
        while self.at < self.set.data.len()
            && (self.inside == 64 || (self.set.data[self.at] >> self.inside) == 0)
        {
            self.at += 1;
            self.inside = 0;
        }
        if self.at == self.set.data.len() {
            None
        } else {
            self.inside
                += (self.set.data[self.at] >> self.inside).trailing_zeros() as usize;
            let res = self.at * 64 + self.inside;
            self.inside += 1;
            Some(res)
        }
    }
}
impl<'a> IntoIterator for &'a BitSet {
    type Item = usize;
    type IntoIter = BitSetIter<'a>;
    fn into_iter(self) -> Self::IntoIter {
        BitSetIter {
            at: 0,
            inside: 0,
            set: self,
        }
    }
}
impl BitOrAssign<&BitSet> for BitSet {
    fn bitor_assign(&mut self, rhs: &BitSet) {
        assert_eq!(self.len, rhs.len);
        for (i, &j) in self.data.iter_mut().zip(rhs.data.iter()) {
            *i |= j;
        }
    }
}
impl BitAndAssign<&BitSet> for BitSet {
    fn bitand_assign(&mut self, rhs: &BitSet) {
        assert_eq!(self.len, rhs.len);
        for (i, &j) in self.data.iter_mut().zip(rhs.data.iter()) {
            *i &= j;
        }
    }
}
impl BitXorAssign<&BitSet> for BitSet {
    fn bitxor_assign(&mut self, rhs: &BitSet) {
        assert_eq!(self.len, rhs.len);
        for (i, &j) in self.data.iter_mut().zip(rhs.data.iter()) {
            *i ^= j;
        }
    }
}
impl ShlAssign<usize> for BitSet {
    fn shl_assign(&mut self, rhs: usize) {
        if rhs == 0 {
            return;
        }
        if rhs >= self.len {
            self.fill(false);
            return;
        }
        let small_shift = rhs & 63;
        if small_shift != 0 {
            let mut carry = 0;
            for data in self.data.iter_mut() {
                let new_carry = (*data) >> (64 - small_shift);
                *data <<= small_shift;
                *data |= carry;
                carry = new_carry;
            }
        }
        let big_shift = rhs >> 6;
        if big_shift != 0 {
            self.data.rotate_right(big_shift);
            self.data[..big_shift].fill(0);
        }
        self.fix_last();
    }
}
impl ShrAssign<usize> for BitSet {
    fn shr_assign(&mut self, rhs: usize) {
        if rhs == 0 {
            return;
        }
        if rhs >= self.len {
            self.fill(false);
            return;
        }
        let small_shift = rhs & 63;
        if small_shift != 0 {
            let mut carry = 0;
            for data in self.data.iter_mut().rev() {
                let new_carry = (*data) << (64 - small_shift);
                *data >>= small_shift;
                *data |= carry;
                carry = new_carry;
            }
        }
        let big_shift = rhs >> 6;
        if big_shift != 0 {
            self.data.rotate_left(big_shift);
            let from = self.data.len() - big_shift;
            self.data[from..].fill(0);
        }
    }
}
impl Index<usize> for BitSet {
    type Output = bool;
    fn index(&self, at: usize) -> &Self::Output {
        assert!(at < self.len);
        if self.data[Self::index(at)].is_set(at & 63) { &TRUE } else { &FALSE }
    }
}
impl From<Vec<bool>> for BitSet {
    fn from(data: Vec<bool>) -> Self {
        let mut res = Self::new(data.len());
        for (i, &value) in data.iter().enumerate() {
            res.change(i, value);
        }
        res
    }
}
}
pub mod iter_ext {
pub mod iter_copied {
use std::iter::{
    Chain, Copied, Enumerate, Filter, Map, Rev, Skip, StepBy, Sum, Take, Zip,
};
pub trait ItersCopied<'a, T: 'a + Copy>: Sized + 'a
where
    &'a Self: IntoIterator<Item = &'a T>,
{
    fn copy_iter(&'a self) -> Copied<<&'a Self as IntoIterator>::IntoIter> {
        self.into_iter().copied()
    }
    fn copy_enumerate(
        &'a self,
    ) -> Enumerate<Copied<<&'a Self as IntoIterator>::IntoIter>> {
        self.copy_iter().enumerate()
    }
    fn copy_rev(&'a self) -> Rev<Copied<<&'a Self as IntoIterator>::IntoIter>>
    where
        Copied<<&'a Self as IntoIterator>::IntoIter>: DoubleEndedIterator,
    {
        self.copy_iter().rev()
    }
    fn copy_skip(
        &'a self,
        n: usize,
    ) -> Skip<Copied<<&'a Self as IntoIterator>::IntoIter>> {
        self.copy_iter().skip(n)
    }
    fn copy_take(
        &'a self,
        n: usize,
    ) -> Take<Copied<<&'a Self as IntoIterator>::IntoIter>> {
        self.copy_iter().take(n)
    }
    fn copy_chain<V>(
        &'a self,
        chained: &'a V,
    ) -> Chain<
        Copied<<&'a Self as IntoIterator>::IntoIter>,
        Copied<<&'a V as IntoIterator>::IntoIter>,
    >
    where
        &'a V: IntoIterator<Item = &'a T>,
    {
        self.copy_iter().chain(chained.into_iter().copied())
    }
    fn copy_zip<V>(
        &'a self,
        other: &'a V,
    ) -> Zip<
        Copied<<&'a Self as IntoIterator>::IntoIter>,
        Copied<<&'a V as IntoIterator>::IntoIter>,
    >
    where
        &'a V: IntoIterator<Item = &'a T>,
    {
        self.copy_iter().zip(other.into_iter().copied())
    }
    fn copy_max(&'a self) -> T
    where
        T: Ord,
    {
        self.copy_iter().max().unwrap()
    }
    fn copy_max_by_key<B, F>(&'a self, f: F) -> T
    where
        F: FnMut(&T) -> B,
        B: Ord,
    {
        self.copy_iter().max_by_key(f).unwrap()
    }
    fn copy_min(&'a self) -> T
    where
        T: Ord,
    {
        self.copy_iter().min().unwrap()
    }
    fn copy_min_by_key<B, F>(&'a self, f: F) -> T
    where
        F: FnMut(&T) -> B,
        B: Ord,
    {
        self.copy_iter().min_by_key(f).unwrap()
    }
    fn copy_sum(&'a self) -> T
    where
        T: Sum<T>,
    {
        self.copy_iter().sum()
    }
    fn copy_map<F, U>(
        &'a self,
        f: F,
    ) -> Map<Copied<<&'a Self as IntoIterator>::IntoIter>, F>
    where
        F: FnMut(T) -> U,
    {
        self.copy_iter().map(f)
    }
    fn copy_all(&'a self, f: impl FnMut(T) -> bool) -> bool {
        self.copy_iter().all(f)
    }
    fn copy_any(&'a self, f: impl FnMut(T) -> bool) -> bool {
        self.copy_iter().any(f)
    }
    fn copy_step_by(
        &'a self,
        step: usize,
    ) -> StepBy<Copied<<&'a Self as IntoIterator>::IntoIter>> {
        self.copy_iter().step_by(step)
    }
    fn copy_filter<F: FnMut(&T) -> bool>(
        &'a self,
        f: F,
    ) -> Filter<Copied<<&'a Self as IntoIterator>::IntoIter>, F> {
        self.copy_iter().filter(f)
    }
    fn copy_fold<Acc, F>(&'a self, init: Acc, f: F) -> Acc
    where
        F: FnMut(Acc, T) -> Acc,
    {
        self.copy_iter().fold(init, f)
    }
    fn copy_reduce<F>(&'a self, f: F) -> Option<T>
    where
        F: FnMut(T, T) -> T,
    {
        self.copy_iter().reduce(f)
    }
    fn copy_position<P>(&'a self, predicate: P) -> Option<usize>
    where
        P: FnMut(T) -> bool,
    {
        self.copy_iter().position(predicate)
    }
    fn copy_find(&'a self, val: T) -> Option<usize>
    where
        T: PartialEq,
    {
        self.copy_iter().position(|x| x == val)
    }
    fn copy_count(&'a self, val: T) -> usize
    where
        T: PartialEq,
    {
        self.copy_iter().filter(|&x| x == val).count()
    }
}
impl<'a, U: 'a, T: 'a + Copy> ItersCopied<'a, T> for U
where
    &'a U: IntoIterator<Item = &'a T>,
{}
}
}
pub mod min_max {
pub trait MinimMaxim<Rhs = Self>: PartialOrd + Sized {
    fn minim(&mut self, other: Rhs) -> bool;
    fn maxim(&mut self, other: Rhs) -> bool;
}
impl<T: PartialOrd> MinimMaxim for T {
    fn minim(&mut self, other: Self) -> bool {
        if other < *self {
            *self = other;
            true
        } else {
            false
        }
    }
    fn maxim(&mut self, other: Self) -> bool {
        if other > *self {
            *self = other;
            true
        } else {
            false
        }
    }
}
impl<T: PartialOrd> MinimMaxim<T> for Option<T> {
    fn minim(&mut self, other: T) -> bool {
        match self {
            None => {
                *self = Some(other);
                true
            }
            Some(v) => v.minim(other),
        }
    }
    fn maxim(&mut self, other: T) -> bool {
        match self {
            None => {
                *self = Some(other);
                true
            }
            Some(v) => v.maxim(other),
        }
    }
}
}
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 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 $t { fn one() -> Self
        { 1 } })+
    };
}
zero_one_integer_impl!(i128 i64 i32 i16 i8 isize u128 u64 u32 u16 u8 usize);
}
pub mod as_index {
pub trait AsIndex {
    fn from_index(idx: usize) -> Self;
    fn to_index(self) -> usize;
}
macro_rules! from_index_impl {
    ($($t:ident)+) => {
        $(impl AsIndex for $t { fn from_index(idx : usize) -> Self { idx as $t } fn
        to_index(self) -> usize { self as usize } })+
    };
}
from_index_impl!(i128 i64 i32 i16 i8 isize u128 u64 u32 u16 u8 usize);
}
pub mod bit_ops {
use crate::algo_lib::numbers::num_traits::algebra::{One, Zero};
use std::ops::{
    BitAnd, BitAndAssign, BitOr, BitOrAssign, BitXor, BitXorAssign, Not, RangeInclusive,
    Shl, Sub,
};
use std::ops::{ShlAssign, Shr, ShrAssign};
pub trait BitOps: Copy + BitAnd<
        Output = Self,
    > + BitAndAssign + BitOr<
        Output = Self,
    > + BitOrAssign + BitXor<
        Output = Self,
    > + BitXorAssign + Not<
        Output = Self,
    > + Shl<
        usize,
        Output = Self,
    > + ShlAssign<
        usize,
    > + Shr<usize, Output = Self> + ShrAssign<usize> + Zero + One + PartialEq {
    #[inline]
    fn bit(at: usize) -> Self {
        Self::one() << at
    }
    #[inline]
    fn is_set(&self, at: usize) -> bool {
        (*self >> at & Self::one()) == Self::one()
    }
    #[inline]
    fn set_bit(&mut self, at: usize) {
        *self |= Self::bit(at);
    }
    #[inline]
    fn unset_bit(&mut self, at: usize) {
        *self &= !Self::bit(at);
    }
    #[must_use]
    #[inline]
    fn with_bit(mut self, at: usize) -> Self {
        self.set_bit(at);
        self
    }
    #[must_use]
    #[inline]
    fn without_bit(mut self, at: usize) -> Self {
        self.unset_bit(at);
        self
    }
    #[inline]
    fn flip_bit(&mut self, at: usize) {
        *self ^= Self::bit(at);
    }
    #[must_use]
    #[inline]
    fn flipped_bit(mut self, at: usize) -> Self {
        self.flip_bit(at);
        self
    }
    fn all_bits(n: usize) -> Self {
        let mut res = Self::zero();
        for i in 0..n {
            res.set_bit(i);
        }
        res
    }
    fn iter_all(n: usize) -> RangeInclusive<Self> {
        Self::zero()..=Self::all_bits(n)
    }
}
pub struct BitIter<T> {
    cur: T,
    all: T,
    ended: bool,
}
impl<T: Copy> BitIter<T> {
    pub fn new(all: T) -> Self {
        Self {
            cur: all,
            all,
            ended: false,
        }
    }
}
impl<T: BitOps + Sub<Output = T>> Iterator for BitIter<T> {
    type Item = T;
    fn next(&mut self) -> Option<Self::Item> {
        if self.ended {
            return None;
        }
        let res = self.cur;
        if self.cur == T::zero() {
            self.ended = true;
        } else {
            self.cur = (self.cur - T::one()) & self.all;
        }
        Some(res)
    }
}
impl<
    T: Copy + BitAnd<Output = Self> + BitAndAssign + BitOr<Output = Self> + BitOrAssign
        + BitXor<Output = Self> + BitXorAssign + Not<Output = Self>
        + Shl<usize, Output = Self> + ShlAssign<usize> + Shr<usize, Output = Self>
        + ShrAssign<usize> + One + Zero + PartialEq,
> BitOps for T {}
pub trait Bits: BitOps {
    fn bits() -> u32;
}
macro_rules! bits_integer_impl {
    ($($t:ident $bits:expr),+) => {
        $(impl Bits for $t { fn bits() -> u32 { $bits } })+
    };
}
bits_integer_impl!(
    i128 128, i64 64, i32 32, i16 16, i8 8, isize 64, u128 128, u64 64, u32 32, u16 16,
    u8 8, usize 64
);
}
pub mod invertible {
pub trait Invertible {
    type Output;
    fn inv(&self) -> Option<Self::Output>;
}
}
}
pub mod primes {
pub mod sieve {
use crate::algo_lib::collections::bit_set::BitSet;
use crate::algo_lib::numbers::num_traits::as_index::AsIndex;
pub fn primality_table(n: usize) -> BitSet {
    let mut res = BitSet::new(n);
    res.fill(true);
    if n > 0 {
        res.unset(0);
    }
    if n > 1 {
        res.unset(1);
    }
    let mut i = 2;
    while i * i < n {
        if res[i] {
            for j in ((i * i)..n).step_by(i) {
                res.unset(j);
            }
        }
        i += 1;
    }
    res
}
pub fn primes<T: AsIndex>(n: usize) -> Vec<T> {
    primality_table(n).into_iter().map(|i| T::from_index(i)).collect()
}
pub fn divisor_table<T: AsIndex + PartialEq>(n: usize) -> Vec<T> {
    let mut res: Vec<_> = (0..n).map(|i| T::from_index(i)).collect();
    let mut i = 2;
    while i * i < n {
        if res[i] == T::from_index(i) {
            for j in ((i * i)..n).step_by(i) {
                res[j] = T::from_index(i);
            }
        }
        i += 1;
    }
    res
}
}
}
}
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
    }
}
}
}
}