// 
pub mod solution {

use crate::collections::vec_ext::inc_dec::IncDec;
use crate::graph::edges::bi_edge::BiEdge;
use crate::graph::edges::edge_trait::EdgeTrait;
use crate::graph::graph::Graph;
use crate::io::input::Input;
use crate::io::output::Output;
use std::collections::HashSet;

type PreCalc = ();

fn solve(input: &mut Input, out: &mut Output, _test_case: usize, _data: &PreCalc) {
    let n = input.read_size();
    let m = input.read_size();
    let edges = input.read_vec::<(usize, usize, usize)>(m).dec();

    let mut red = HashSet::new();
    let mut blue = HashSet::new();
    let mut next = Vec::new();
    let mut graph = Graph::new(n);
    for (u, v, c) in edges {
        if c == 0 {
            red.insert((u, v));
            red.insert((v, u));
        } else {
            blue.insert((u, v));
            blue.insert((v, u));
        }
        graph.add_edge(BiEdge::with_payload(u, v, c));
    }
    for i in 0..n {
        let mut red = Vec::new();
        let mut blue = Vec::new();
        for e in &graph[i] {
            if e.payload() == &0 {
                red.push(e.to());
            } else {
                blue.push(e.to());
            }
        }
        if red.len() == 1 {
            next.push(Some(red[0]));
        } else if blue.len() == 1 {
            next.push(Some(blue[0]));
        } else {
            next.push(None);
        }
    }
    let mut ans = HashSet::new();
    for i in 0..n {
        let mut cur = i;
        let mut to_check = vec![i];
        for sz in 1..=4 {
            to_check.sort();
            if !ans.contains(&to_check) {
                let mut in_blue = HashSet::new();
                let mut in_red = HashSet::new();
                let mut count_blue = 0;
                let mut count_red = 0;
                for &x in &to_check {
                    for &y in &to_check {
                        if x == y {
                            break;
                        }
                        if red.contains(&(x, y)) {
                            in_red.insert(x);
                            in_red.insert(y);
                            count_red += 1;
                        }
                        if blue.contains(&(x, y)) {
                            in_blue.insert(x);
                            in_blue.insert(y);
                            count_blue += 1;
                        }
                    }
                }
                if in_blue.len() == sz
                    && in_red.len() == sz
                    && count_red >= sz - 1
                    && count_blue >= sz - 1
                {
                    ans.insert(to_check.clone());
                }
            }
            if let Some(v) = next[cur] {
                if to_check.contains(&v) {
                    break;
                }
                cur = v;
                to_check.push(v);
            } else {
                break;
            }
        }
    }
    out.print_line(ans.len() + n);
}

pub(crate) fn run(mut input: Input, mut output: Output) -> bool {
    let pre_calc = ();

    #[allow(dead_code)]
    enum TestType {
        Single,
        MultiNumber,
        MultiEof,
    }
    let test_type = TestType::Single;
    match test_type {
        TestType::Single => solve(&mut input, &mut output, 1, &pre_calc),
        TestType::MultiNumber => {
            let t = input.read();
            for i in 1..=t {
                solve(&mut input, &mut output, i, &pre_calc);
            }
        }
        TestType::MultiEof => {
            let mut i = 1;
            while input.peek().is_some() {
                solve(&mut input, &mut output, i, &pre_calc);
                i += 1;
            }
        }
    }
    output.flush();
    input.skip_whitespace();
    input.peek().is_none()
}

}
pub mod collections {
pub mod dsu {
use crate::collections::iter_ext::collect::IterCollect;
use crate::collections::slice_ext::bounds::Bounds;
use crate::collections::slice_ext::legacy_fill::LegacyFill;
use std::cell::Cell;

#[derive(Clone)]
pub struct DSU {
    id: Vec<Cell<u32>>,
    size: Vec<u32>,
    count: usize,
}

impl DSU {
    pub fn new(n: usize) -> Self {
        Self {
            id: (0..n).map(|i| Cell::new(i as u32)).collect_vec(),
            size: vec![1; n],
            count: n,
        }
    }

    pub fn size(&self, i: usize) -> usize {
        self.size[self.get(i)] as usize
    }

    #[allow(clippy::len_without_is_empty)]
    pub fn len(&self) -> usize {
        self.id.len()
    }

    pub fn iter(&self) -> impl Iterator<Item = usize> + '_ {
        self.id.iter().enumerate().filter_map(|(i, id)| {
            if (i as u32) == id.get() {
                Some(i)
            } else {
                None
            }
        })
    }

    pub fn set_count(&self) -> usize {
        self.count
    }

    pub fn join(&mut self, mut a: usize, mut b: usize) -> bool {
        a = self.get(a);
        b = self.get(b);
        if a == b {
            false
        } else {
            self.size[a] += self.size[b];
            self.id[b].replace(a as u32);
            self.count -= 1;
            true
        }
    }

    pub fn get(&self, i: usize) -> usize {
        if self.id[i].get() != i as u32 {
            let res = self.get(self.id[i].get() as usize);
            self.id[i].replace(res as u32);
        }
        self.id[i].get() as usize
    }

    pub fn clear(&mut self) {
        self.count = self.id.len();
        self.size.legacy_fill(1);
        self.id.iter().enumerate().for_each(|(i, id)| {
            id.replace(i as u32);
        });
    }

    pub fn parts(&self) -> Vec<Vec<usize>> {
        let roots = self.iter().collect_vec();
        let mut res = vec![Vec::new(); roots.len()];
        for i in 0..self.id.len() {
            res[roots.as_slice().bin_search(&self.get(i)).unwrap()].push(i);
        }
        res
    }
}
}
pub mod iter_ext {
pub mod collect {
pub trait IterCollect<T>: Iterator<Item = T> + Sized {
    fn collect_vec(self) -> Vec<T> {
        self.collect()
    }
}

impl<T, I: Iterator<Item = T> + Sized> IterCollect<T> for I {}
}
}
pub mod slice_ext {
pub mod bounds {
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;
    fn less_or_eq(&self, el: &T) -> usize;
}

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 less(&self, el: &T) -> usize {
        self.lower_bound(el)
    }

    fn less_or_eq(&self, el: &T) -> usize {
        self.upper_bound(el)
    }
}
}
pub mod legacy_fill {
// 1.50
pub trait LegacyFill<T> {
    fn legacy_fill(&mut self, val: T);
}

impl<T: Clone> LegacyFill<T> for [T] {
    fn legacy_fill(&mut self, val: T) {
        for el in self.iter_mut() {
            *el = val.clone();
        }
    }
}
}
}
pub mod vec_ext {
pub mod default {
pub fn default_vec<T: Default>(len: usize) -> Vec<T> {
    let mut v = Vec::with_capacity(len);
    for _ in 0..len {
        v.push(T::default());
    }
    v
}
}
pub mod inc_dec {
use crate::numbers::num_traits::add_sub::AddSub;
use crate::numbers::num_traits::zero_one::ZeroOne;

pub trait IncDec {
    #[must_use]
    fn inc(self) -> Self;
    #[must_use]
    fn dec(self) -> Self;
}

impl<T: AddSub + ZeroOne> 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: AddSub + ZeroOne, U: AddSub + ZeroOne> 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: AddSub + ZeroOne, U: AddSub + ZeroOne, 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: AddSub + ZeroOne, U: AddSub + ZeroOne> 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 graph {
pub mod edges {
pub mod bi_edge {
use crate::graph::edges::bi_edge_trait::BiEdgeTrait;
use crate::graph::edges::edge_id::{EdgeId, NoId, WithId};
use crate::graph::edges::edge_trait::{BidirectionalEdgeTrait, EdgeTrait};

#[derive(Clone)]
pub struct BiEdgeRaw<Id: EdgeId, P> {
    to: u32,
    id: Id,
    payload: P,
}

impl<Id: EdgeId> BiEdgeRaw<Id, ()> {
    pub fn new(from: usize, to: usize) -> (usize, Self) {
        (
            from,
            Self {
                to: to as u32,
                id: Id::new(),
                payload: (),
            },
        )
    }
}

impl<Id: EdgeId, P> BiEdgeRaw<Id, P> {
    pub fn with_payload(from: usize, to: usize, payload: P) -> (usize, Self) {
        (from, Self::with_payload_impl(to, payload))
    }

    fn with_payload_impl(to: usize, payload: P) -> BiEdgeRaw<Id, P> {
        Self {
            to: to as u32,
            id: Id::new(),
            payload,
        }
    }
}

impl<Id: EdgeId, P: Clone> BidirectionalEdgeTrait for BiEdgeRaw<Id, P> {}

impl<Id: EdgeId, P: Clone> EdgeTrait for BiEdgeRaw<Id, P> {
    type Payload = P;

    const REVERSABLE: bool = true;

    fn to(&self) -> usize {
        self.to as usize
    }

    fn id(&self) -> usize {
        self.id.id()
    }

    fn set_id(&mut self, id: usize) {
        self.id.set_id(id);
    }

    fn reverse_id(&self) -> usize {
        panic!("no reverse id")
    }

    fn set_reverse_id(&mut self, _: usize) {}

    fn reverse_edge(&self, from: usize) -> Self {
        Self::with_payload_impl(from, self.payload.clone())
    }

    fn payload(&self) -> &P {
        &self.payload
    }
}

impl<Id: EdgeId, P: Clone> BiEdgeTrait for BiEdgeRaw<Id, P> {}

pub type BiEdge<P> = BiEdgeRaw<NoId, P>;
pub type BiEdgeWithId<P> = BiEdgeRaw<WithId, P>;
}
pub mod bi_edge_trait {
use crate::graph::edges::edge_trait::EdgeTrait;

pub trait BiEdgeTrait: EdgeTrait {}
}
pub mod edge {
use crate::graph::edges::edge_id::{EdgeId, NoId, WithId};
use crate::graph::edges::edge_trait::EdgeTrait;

#[derive(Clone)]
pub struct EdgeRaw<Id: EdgeId, P> {
    to: u32,
    id: Id,
    payload: P,
}

impl<Id: EdgeId> EdgeRaw<Id, ()> {
    pub fn new(from: usize, to: usize) -> (usize, Self) {
        (
            from,
            Self {
                to: to as u32,
                id: Id::new(),
                payload: (),
            },
        )
    }
}

impl<Id: EdgeId, P> EdgeRaw<Id, P> {
    pub fn with_payload(from: usize, to: usize, payload: P) -> (usize, Self) {
        (from, Self::with_payload_impl(to, payload))
    }

    fn with_payload_impl(to: usize, payload: P) -> Self {
        Self {
            to: to as u32,
            id: Id::new(),
            payload,
        }
    }
}

impl<Id: EdgeId, P: Clone> EdgeTrait for EdgeRaw<Id, P> {
    type Payload = P;

    const REVERSABLE: bool = false;

    fn to(&self) -> usize {
        self.to as usize
    }

    fn id(&self) -> usize {
        self.id.id()
    }

    fn set_id(&mut self, id: usize) {
        self.id.set_id(id);
    }

    fn reverse_id(&self) -> usize {
        panic!("no reverse")
    }

    fn set_reverse_id(&mut self, _: usize) {
        panic!("no reverse")
    }

    fn reverse_edge(&self, _: usize) -> Self {
        panic!("no reverse")
    }

    fn payload(&self) -> &P {
        &self.payload
    }
}

pub type Edge<P> = EdgeRaw<NoId, P>;
pub type EdgeWithId<P> = EdgeRaw<WithId, P>;
}
pub mod edge_id {
pub trait EdgeId: Clone {
    fn new() -> Self;
    fn id(&self) -> usize;
    fn set_id(&mut self, id: usize);
}

#[derive(Clone)]
pub struct WithId {
    id: u32,
}

impl EdgeId for WithId {
    fn new() -> Self {
        Self { id: 0 }
    }

    fn id(&self) -> usize {
        self.id as usize
    }

    fn set_id(&mut self, id: usize) {
        self.id = id as u32;
    }
}

#[derive(Clone)]
pub struct NoId {}

impl EdgeId for NoId {
    fn new() -> Self {
        Self {}
    }

    fn id(&self) -> usize {
        panic!("Id called on no id")
    }

    fn set_id(&mut self, _: usize) {}
}
}
pub mod edge_trait {
pub trait EdgeTrait: Clone {
    type Payload;
    
    const REVERSABLE: bool;

    fn to(&self) -> usize;
    fn id(&self) -> usize;
    fn set_id(&mut self, id: usize);
    fn reverse_id(&self) -> usize;
    fn set_reverse_id(&mut self, reverse_id: usize);
    #[must_use]
    fn reverse_edge(&self, from: usize) -> Self;
    fn payload(&self) -> &Self::Payload;
}

pub trait BidirectionalEdgeTrait: EdgeTrait {}
}
}
pub mod graph {
use crate::collections::dsu::DSU;
use crate::graph::edges::bi_edge::BiEdge;
use crate::graph::edges::edge::Edge;
use crate::graph::edges::edge_trait::{BidirectionalEdgeTrait, EdgeTrait};
use std::ops::{Index, IndexMut};

pub struct Graph<E: EdgeTrait> {
    pub(super) edges: Vec<Vec<E>>,
    edge_count: usize,
}

impl<E: EdgeTrait> Graph<E> {
    pub fn new(vertex_count: usize) -> Self {
        Self {
            edges: vec![Vec::new(); vertex_count],
            edge_count: 0,
        }
    }

    pub fn add_edge(&mut self, (from, mut edge): (usize, E)) -> usize {
        let to = edge.to();
        assert!(to < self.edges.len());
        let direct_id = self.edges[from].len();
        edge.set_id(self.edge_count);
        self.edges[from].push(edge);
        if E::REVERSABLE {
            let rev_id = self.edges[to].len();
            self.edges[from][direct_id].set_reverse_id(rev_id);
            let mut rev_edge = self.edges[from][direct_id].reverse_edge(from);
            rev_edge.set_id(self.edge_count);
            rev_edge.set_reverse_id(direct_id);
            self.edges[to].push(rev_edge);
        }
        self.edge_count += 1;
        direct_id
    }

    pub fn add_vertices(&mut self, cnt: usize) {
        self.edges.resize(self.edges.len() + cnt, Vec::new());
    }

    pub fn clear(&mut self) {
        self.edge_count = 0;
        for ve in self.edges.iter_mut() {
            ve.clear();
        }
    }

    pub fn vertex_count(&self) -> usize {
        self.edges.len()
    }

    pub fn edge_count(&self) -> usize {
        self.edge_count
    }

    pub fn degrees(&self) -> Vec<usize> {
        self.edges.iter().map(|v| v.len()).collect()
    }
}

impl<E: BidirectionalEdgeTrait> Graph<E> {
    pub fn is_tree(&self) -> bool {
        if self.edge_count + 1 != self.vertex_count() {
            false
        } else {
            self.is_connected()
        }
    }

    pub fn is_forest(&self) -> bool {
        let mut dsu = DSU::new(self.vertex_count());
        for i in 0..self.vertex_count() {
            for e in self[i].iter() {
                if i <= e.to() && !dsu.join(i, e.to()) {
                    return false;
                }
            }
        }
        true
    }

    pub fn is_connected(&self) -> bool {
        let mut dsu = DSU::new(self.vertex_count());
        for i in 0..self.vertex_count() {
            for e in self[i].iter() {
                dsu.join(i, e.to());
            }
        }
        dsu.set_count() == 1
    }
}

impl<E: EdgeTrait> Index<usize> for Graph<E> {
    type Output = [E];

    fn index(&self, index: usize) -> &Self::Output {
        &self.edges[index]
    }
}

impl<E: EdgeTrait> IndexMut<usize> for Graph<E> {
    fn index_mut(&mut self, index: usize) -> &mut Self::Output {
        &mut self.edges[index]
    }
}

impl Graph<Edge<()>> {
    pub fn from_edges(n: usize, edges: &[(usize, usize)]) -> Self {
        let mut graph = Self::new(n);
        for &(from, to) in edges {
            graph.add_edge(Edge::new(from, to));
        }
        graph
    }
}

impl Graph<BiEdge<()>> {
    pub fn from_biedges(n: usize, edges: &[(usize, usize)]) -> Self {
        let mut graph = Self::new(n);
        for &(from, to) in edges {
            graph.add_edge(BiEdge::new(from, to));
        }
        graph
    }
}
}
}
pub mod io {
pub mod input {
use crate::collections::vec_ext::default::default_vec;
use std::io::Read;

pub struct Input<'s> {
    input: &'s mut dyn Read,
    buf: Vec<u8>,
    at: usize,
    buf_read: usize,
}

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) -> Self {
        Self {
            input,
            buf: default_vec(Self::DEFAULT_BUF_SIZE),
            at: 0,
            buf_read: 0,
        }
    }

    pub fn new_with_size(input: &'s mut dyn Read, buf_size: usize) -> Self {
        Self {
            input,
            buf: default_vec(buf_size),
            at: 0,
            buf_read: 0,
        }
    }

    pub fn get(&mut self) -> Option<u8> {
        if self.refill_buffer() {
            let res = self.buf[self.at];
            self.at += 1;
            if res == b'\r' {
                if self.refill_buffer() && self.buf[self.at] == b'\n' {
                    self.at += 1;
                }
                return Some(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 !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()
    }

    //noinspection RsSelfConvention
    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) -> char {
        self.skip_whitespace();
        self.get().unwrap().into()
    }

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

impl Readable for char {
    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)
    }
}

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 u8 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::collections::vec_ext::default::default_vec;
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,
}

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,
        }
    }

    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,
        }
    }

    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]) {
        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);
        }
    }

    pub fn set_bool_output(&mut self, bool_output: BoolOutput) {
        self.bool_output = bool_output;
    }
}

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

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

impl<T: Writable> 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!(u8 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);
                $(
                out.put(b' ');
                self.$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}

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)
    }
}

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 numbers {
pub mod num_traits {
pub mod add_sub {
use std::ops::{Add, AddAssign, Sub, SubAssign};

pub trait Addable: Add<Output = Self> + AddAssign + Copy {}
impl<T: Add<Output = Self> + AddAssign + Copy> Addable for T {}

pub trait AddSub: Addable + Sub<Output = Self> + SubAssign {}
impl<T: Addable + Sub<Output = Self> + SubAssign> AddSub for T {}
}
pub mod zero_one {
pub trait ZeroOne {
    fn zero() -> Self;
    fn one() -> Self;
}

macro_rules! zero_one_integer_impl {
    ($($t: ident)+) => {$(
        impl ZeroOne for $t {
            fn zero() -> Self {
                0
            }

            fn one() -> Self {
                1
            }
        }
    )+};
}

zero_one_integer_impl!(i128 i64 i32 i16 i8 isize u128 u64 u32 u16 u8 usize);
}
}
}
fn main() {
    let mut sin = std::io::stdin();
    let input = if false {
        io::input::Input::new_with_size(&mut sin, 1)
    } else {
        io::input::Input::new(&mut sin)
    };

    let mut stdout = std::io::stdout();
    let output = if false {
        io::output::Output::new_with_auto_flush(&mut stdout)
    } else {
        io::output::Output::new(&mut stdout)
    };

    solution::run(input, output);
}