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

use std::cmp::Reverse;

use crate::algo_lib::graph::dfs_order::DfsOrder;
use crate::algo_lib::io::output::output;
use crate::algo_lib::io::task_io_settings::TaskIoType;
use crate::algo_lib::io::task_runner::run_task;
use crate::algo_lib::io::input::Input;
use crate::algo_lib::io::task_io_settings::TaskIoSettings;
use crate::algo_lib::misc::min_max::UpdateMinMax;
use crate::algo_lib::misc::vec_apply_delta::ApplyDelta;
use crate::algo_lib::seg_trees::hld::Hld;
use crate::algo_lib::seg_trees::seg_tree_2d::SegTree2d;
use crate::algo_lib::seg_trees::seg_tree_trait::SegTreeNode;
#[allow(unused)]
use crate::dbg;
use crate::out;
use crate::out_line;

#[derive(Clone, Copy, Debug)]
struct Color {
    min_v: usize,
    max_v: usize,
    dist: usize,
}

#[derive(Clone, Copy, Default)]
struct Node {
    value: i32,
}

impl SegTreeNode for Node {
    fn join_nodes(l: &Self, r: &Self, context: &Self::Context) -> Self {
        Self {
            value: l.value.max(r.value),
        }
    }

    fn apply_update(node: &mut Self, update: &Self::Update) {
        todo!()
    }

    fn join_updates(current: &mut Self::Update, add: &Self::Update) {
        todo!()
    }

    type Update = ();

    type Context = ();
}

fn solve(input: &mut Input, _test_case: usize) {
    let n = input.usize();
    let colors = input.vec::<usize>(n).sub_from_all(1);
    let mut g = vec![vec![]; n];
    for _ in 0..n - 1 {
        let u = input.usize() - 1;
        let v = input.usize() - 1;
        g[u].push(v);
        g[v].push(u);
    }
    let hld = Hld::new(g.clone(), 0);
    let dfs_order = DfsOrder::new(&g, 0);
    let mut by_color = vec![vec![]; n];
    for v in 0..n {
        by_color[colors[v]].push(v);
    }
    let mut pairs = vec![];
    for color in 0..colors.len() {
        if by_color[color].len() == 2 {
            let (v, u) = (by_color[color][0], by_color[color][1]);
            let lca = hld.lca(v, u);
            let dist = dfs_order.info[v].height + dfs_order.info[u].height
                - 2 * dfs_order.info[lca].height;
            let pos1 = dfs_order.info[v].pos;
            let pos2 = dfs_order.info[u].pos;
            let (min_v, max_v) = if pos1 < pos2 { (v, u) } else { (u, v) };
            pairs.push(Color { min_v, max_v, dist })
        }
    }
    let mut st_pts: Vec<_> = pairs
        .iter()
        .map(|p| (dfs_order.info[p.min_v].pos, dfs_order.info[p.max_v].pos))
        .collect();
    st_pts.push((0, 0));
    let mut st = SegTree2d::<usize, Node>::new(st_pts);
    pairs.sort_by_key(|p| Reverse(p.dist));
    let mut glob_res = 1;
    for pair in pairs.iter() {
        let (min_v, max_v) = (pair.min_v, pair.max_v);
        let mut res;
        if dfs_order.is_in_subtree_of(max_v, min_v) {
            res = st
                .query(0..dfs_order.info[min_v].pos, dfs_order.info[max_v].range())
                .value;
            res.update_max(
                st.query(
                    dfs_order.info[max_v].range(),
                    dfs_order.info[min_v].max_subtree_pos..n,
                )
                .value,
            );
            for &to in g[min_v].iter() {
                if !dfs_order.is_in_subtree_of(max_v, to) && dfs_order.info[min_v].parent != to {
                    let r1 = dfs_order.info[max_v].range();
                    let r2 = dfs_order.info[to].range();
                    if r1.start < r2.start {
                        res.update_max(st.query(r1, r2).value);
                    } else {
                        res.update_max(st.query(r2, r1).value);
                    }
                }
            }
        } else {
            res = st
                .query(dfs_order.info[min_v].range(), dfs_order.info[max_v].range())
                .value;
        }
        let mut update_res = res + 2;
        st.update(
            dfs_order.info[min_v].pos,
            dfs_order.info[max_v].pos,
            Node { value: update_res },
        );
        if dfs_order.info[max_v].parent != min_v {
            update_res += 1;
        }
        glob_res.update_max(update_res);
    }
    out_line!(glob_res);
}

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

#[allow(unused)]
pub fn submit() -> bool {
    let io = TaskIoSettings {
        is_interactive: false,
        input: TaskIoType::Std,
        output: TaskIoType::Std,
    };

    run_task(io, run)
}

}
pub mod algo_lib {
pub mod graph {
pub mod dfs_order {
use std::ops::Range;

use crate::algo_lib::misc::min_max::UpdateMinMax;
use crate::algo_lib::misc::rec_function::Callable3;
use crate::algo_lib::misc::rec_function::RecursiveFunction3;

#[derive(Clone, Copy, Default, Debug)]
pub struct VertexInfo {
    pub pos: usize,
    // range is [pos..max_subtree_pos)
    pub max_subtree_pos: usize,
    pub parent: usize,
    pub height: usize,
}

impl VertexInfo {
    pub fn range(&self) -> Range<usize> {
        self.pos..self.max_subtree_pos
    }
}

#[derive(Debug)]
pub struct DfsOrder {
    pub order: Vec<usize>,
    pub info: Vec<VertexInfo>,
}

impl DfsOrder {
    pub fn new(g: &[Vec<usize>], root: usize) -> Self {
        let n = g.len();
        let mut order = vec![];
        let mut info = vec![VertexInfo::default(); n];
        RecursiveFunction3::new(|f, v: usize, p: usize, h: usize| {
            order.push(v);
            info[v].pos = order.len() - 1;
            info[v].max_subtree_pos = order.len();
            info[v].parent = p;
            info[v].height = h;
            for &to in g[v].iter() {
                if to != p {
                    f.call(to, v, h + 1);
                    let max_subtree_pos = info[to].max_subtree_pos;
                    info[v].max_subtree_pos.update_max(max_subtree_pos);
                }
            }
        })
        .call(root, root, 0);
        assert_eq!(order.len(), n);
        Self { order, info }
    }

    pub fn is_in_subtree_of(&self, v: usize, anc: usize) -> bool {
        self.info[anc].pos <= self.info[v].pos && self.info[v].pos < self.info[anc].max_subtree_pos
    }
}
}
}
pub mod io {
pub mod input {
use std::fmt::Debug;
use std::io::Read;
use std::marker::PhantomData;
use std::path::Path;
use std::str::FromStr;

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

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

impl Input {
    const DEFAULT_BUF_SIZE: usize = 4096;

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

    fn refill_buffer(&mut self) -> bool {
        if self.at == self.buf_read {
            self.at = 0;
            self.buf_read = self.input.read(&mut self.buf).unwrap();
            self.buf_read != 0
        } else {
            true
        }
    }

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

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

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

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

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

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

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

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

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

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

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

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

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

impl Output {
    const DEFAULT_BUF_SIZE: usize = 4096;

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

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

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

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

    pub fn put(&mut self, b: u8) {
        self.buf[self.at] = b;
        self.at += 1;
        if self.at == self.buf.len() {
            self.flush();
        }
    }

    pub fn maybe_flush(&mut self) {
        if self.auto_flush {
            self.flush();
        }
    }

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

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

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

impl Write for Output {
    fn write(&mut self, buf: &[u8]) -> std::io::Result<usize> {
        let mut start = 0usize;
        let mut rem = buf.len();
        while rem > 0 {
            let len = (self.buf.len() - self.at).min(rem);
            self.buf[self.at..self.at + len].copy_from_slice(&buf[start..start + len]);
            self.at += len;
            if self.at == self.buf.len() {
                self.flush();
            }
            start += len;
            rem -= len;
        }
        if self.auto_flush {
            self.flush();
        }
        Ok(buf.len())
    }

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

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

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

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

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

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

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

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

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

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

impl<T: Writable, U: Writable, V: Writable> Writable for (T, U, V) {
    fn write(&self, output: &mut Output) {
        self.0.write(output);
        output.put(b' ');
        self.1.write(output);
        output.put(b' ');
        self.2.write(output);
    }
}

pub static mut OUTPUT: Option<Output> = None;

pub fn set_global_output_to_stdout() {
    unsafe {
        OUTPUT = Some(Output::new(Box::new(std::io::stdout())));
    }
}

pub fn set_global_output_to_file(path: &str) {
    unsafe {
        let out_file =
            std::fs::File::create(path).unwrap_or_else(|_| panic!("Can't create file {}", path));
        OUTPUT = Some(Output::new(Box::new(out_file)));
    }
}

pub fn set_global_output_to_none() {
    unsafe {
        match &mut OUTPUT {
            None => {}
            Some(output) => output.flush(),
        }
        OUTPUT = None;
    }
}

pub fn output() -> &'static mut Output {
    unsafe {
        match &mut OUTPUT {
            None => {
                panic!("Global output wasn't initialized");
            }
            Some(output) => output,
        }
    }
}

#[macro_export]
macro_rules! out {
    ($first: expr $(,$args:expr )*) => {
        output().print(&$first);
        $(output().put(b' ');
        output().print(&$args);
        )*
        output().maybe_flush();
    }
}

#[macro_export]
macro_rules! out_line {
    ($first: expr $(, $args:expr )* ) => {
        {
            out!($first $(,$args)*);
            output().put(b'\n');
            output().maybe_flush();
        }
    };
    () => {
        {
            output().put(b'\n');
            output().maybe_flush();
        }
    };
}
}
pub mod task_io_settings {
pub enum TaskIoType {
    Std,
    File(String),
}

pub struct TaskIoSettings {
    pub is_interactive: bool,
    pub input: TaskIoType,
    pub output: TaskIoType,
}
}
pub mod task_runner {
use std::io::Write;

use super::input::Input;
use super::output::Output;
use super::output::OUTPUT;
use super::task_io_settings::TaskIoSettings;
use super::task_io_settings::TaskIoType;

pub fn run_task<Res>(io: TaskIoSettings, run: impl FnOnce(Input) -> Res) -> Res {
    let output: Box<dyn Write> = match io.output {
        TaskIoType::Std => Box::new(std::io::stdout()),
        TaskIoType::File(file) => {
            let out_file = std::fs::File::create(file).unwrap();
            Box::new(out_file)
        }
    };

    unsafe {
        OUTPUT = Some(Output::new(output));
    }

    let input = match io.input {
        TaskIoType::Std => {
            let sin = std::io::stdin();
            Input::new(Box::new(sin))
        }
        TaskIoType::File(file) => Input::new_file(file),
    };

    run(input)
}
}
}
pub mod misc {
pub mod binary_search {
use crate::algo_lib::misc::num_traits::Number;
use std::ops::Range;

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

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

#[test]
fn simple_stress() {
    const N: usize = 50;
    for n in 1..N {
        for cnt_false in 0..=n {
            let mut a = vec![false; cnt_false];
            a.resize(n, true);
            let mut max_f_calls = ((n + 1) as f64).log2().ceil() as i32;
            let f_is_true = |id: usize| -> bool {
                max_f_calls -= 1;
                assert!(max_f_calls >= 0);
                a[id]
            };
            let result = binary_search_first_true(0..n, f_is_true);
            assert_eq!(result, cnt_false);
        }
    }
}
}
pub mod dbg_macro {
#[macro_export]
#[allow(unused_macros)]
macro_rules! dbg {
    ($first_val:expr, $($val:expr),+ $(,)?) => {
        eprint!("[{}:{}] {} = {:?}",
                    file!(), line!(), stringify!($first_val), &$first_val);
        ($(eprint!(", {} = {:?}", stringify!($val), &$val)),+,);
        eprintln!();
    };
    ($first_val:expr) => {
        eprintln!("[{}:{}] {} = {:?}",
                    file!(), line!(), stringify!($first_val), &$first_val)
    };
}
}
pub mod min_max {
pub trait UpdateMinMax: PartialOrd + Sized {
    #[inline(always)]
    fn update_min(&mut self, other: Self) -> bool {
        if other < *self {
            *self = other;
            true
        } else {
            false
        }
    }

    #[inline(always)]
    fn update_max(&mut self, other: Self) -> bool {
        if other > *self {
            *self = other;
            true
        } else {
            false
        }
    }
}

impl<T: PartialOrd + Sized> UpdateMinMax for T {}

pub trait FindMinMaxPos {
    fn index_of_min(&self) -> usize;
    fn index_of_max(&self) -> usize;
}

impl<T: PartialOrd> FindMinMaxPos for [T] {
    fn index_of_min(&self) -> usize {
        let mut pos_of_best = 0;
        for (idx, val) in self.iter().enumerate().skip(1) {
            if val < &self[pos_of_best] {
                pos_of_best = idx;
            }
        }
        pos_of_best
    }

    fn index_of_max(&self) -> usize {
        let mut pos_of_best = 0;
        for (idx, val) in self.iter().enumerate().skip(1) {
            if val > &self[pos_of_best] {
                pos_of_best = idx;
            }
        }
        pos_of_best
    }
}

pub fn index_of_min_by<T, F>(n: usize, f: F) -> usize
where
    T: PartialOrd,
    F: Fn(usize) -> T,
{
    assert!(n > 0);
    let mut best_idx = 0;
    let mut best_val = f(0);
    for idx in 1..n {
        let cur_val = f(idx);
        if cur_val < best_val {
            best_val = cur_val;
            best_idx = idx;
        }
    }
    best_idx
}

pub fn index_of_max_by<T, F>(n: usize, f: F) -> usize
where
    T: PartialOrd,
    F: Fn(usize) -> T,
{
    assert!(n > 0);
    let mut best_idx = 0;
    let mut best_val = f(0);
    for idx in 1..n {
        let cur_val = f(idx);
        if cur_val > best_val {
            best_val = cur_val;
            best_idx = idx;
        }
    }
    best_idx
}
}
pub mod num_traits {
use std::cmp::Ordering;
use std::fmt::Debug;
use std::ops::Add;
use std::ops::AddAssign;
use std::ops::Div;
use std::ops::DivAssign;
use std::ops::Mul;
use std::ops::MulAssign;
use std::ops::Sub;
use std::ops::SubAssign;

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

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

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

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

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

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

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

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

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

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

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

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

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

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

impl<T: Number + Ord> Signum for T {
    fn signum(&self) -> i32 {
        match self.cmp(&T::ZERO) {
            Ordering::Greater => 1,
            Ordering::Less => -1,
            Ordering::Equal => 0,
        }
    }
}
}
pub mod rec_function {
// Copied from https://github.com/EgorKulikov/rust_algo/blob/master/algo_lib/src/misc/recursive_function.rs

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: 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,
                    $($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 {
                let const_ptr = &self.f as *const F;
                let mut_ptr = const_ptr as *mut F;
                unsafe { (&mut *mut_ptr)(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 vec_apply_delta {
use crate::algo_lib::misc::num_traits::Number;

pub trait ApplyDelta<T> {
    fn add_to_all(self, delta: T) -> Self;
    fn sub_from_all(self, sub: T) -> Self;
}

impl<T> ApplyDelta<T> for Vec<T>
where
    T: Number,
{
    fn add_to_all(mut self, delta: T) -> Self {
        self.iter_mut().for_each(|val| *val += delta);
        self
    }

    fn sub_from_all(mut self, sub: T) -> Self {
        self.iter_mut().for_each(|val| *val -= sub);
        self
    }
}

impl<T> ApplyDelta<T> for Vec<(T, T)>
where
    T: Number,
{
    fn add_to_all(mut self, delta: T) -> Self {
        self.iter_mut().for_each(|(val1, val2)| {
            *val1 += delta;
            *val2 += delta
        });
        self
    }

    fn sub_from_all(mut self, sub: T) -> Self {
        self.iter_mut().for_each(|(val1, val2)| {
            *val1 -= sub;
            *val2 -= sub;
        });
        self
    }
}

pub trait ApplyDelta2<T> {
    fn add_to_all(&mut self, delta: T);
    fn sub_from_all(&mut self, sub: T);
}

impl<T> ApplyDelta2<T> for [T]
where
    T: Number,
    T: Sized,
{
    fn add_to_all(self: &mut [T], delta: T) {
        self.iter_mut().for_each(|x| *x += delta);
    }

    fn sub_from_all(&mut self, sub: T) {
        self.iter_mut().for_each(|x| *x -= sub);
    }
}
}
}
pub mod seg_trees {
pub mod hld {
use std::ops::Range;

use crate::algo_lib::misc::rec_function::Callable;
use crate::algo_lib::misc::rec_function::Callable3;
use crate::algo_lib::misc::rec_function::RecursiveFunction;
use crate::algo_lib::misc::rec_function::RecursiveFunction3;

pub struct Hld {
    parent: Vec<usize>,
    pub order: Vec<usize>,
    block_start: Vec<usize>,
    pos_in_order: Vec<usize>,
}

impl Hld {
    pub fn new(mut g: Vec<Vec<usize>>, tree_root: usize) -> Self {
        let n = g.len();
        let mut size = vec![0; n];
        let mut parent = vec![0; n];
        RecursiveFunction3::new(|f, v: usize, p: usize, h: usize| {
            parent[v] = p;
            size[v] = 1;
            for &to in g[v].iter() {
                if to != p {
                    f.call(to, v, h + 1);
                    size[v] += size[to];
                }
            }
            g[v].sort_by(|&u, &v| size[u].cmp(&size[v]).reverse());
        })
        .call(tree_root, tree_root, 0);

        let mut order = vec![];
        RecursiveFunction::new(|f, v: usize| {
            order.push(v);
            for &to in g[v].iter() {
                if to != parent[v] {
                    f.call(to);
                }
            }
        })
        .call(tree_root);
        let mut pos_in_order = vec![0; n];
        for i in 0..n {
            pos_in_order[order[i]] = i;
        }
        let mut block_start = vec![0; n];
        for i in 1..n {
            if order[i - 1] == parent[order[i]] {
                block_start[i] = block_start[i - 1];
            } else {
                block_start[i] = i;
            }
        }

        Self {
            parent,
            order,
            block_start,
            pos_in_order,
        }
    }

    pub fn find_path_segs(&self, mut u: usize, mut v: usize) -> Vec<Range<usize>> {
        let mut segs = vec![];
        while u != v {
            if self.pos_in_order[u] < self.pos_in_order[v] {
                std::mem::swap(&mut u, &mut v);
            }
            let from = std::cmp::max(
                self.block_start[self.pos_in_order[u]],
                self.pos_in_order[v] + 1,
            );
            segs.push(from..self.pos_in_order[u] + 1);
            u = self.parent[self.order[from]];
        }
        segs.push(self.pos_in_order[v]..self.pos_in_order[v] + 1);
        segs
    }

    pub fn lca(&self, mut v: usize, mut u: usize) -> usize {
        while v != u {
            if self.pos_in_order[v] < self.pos_in_order[u] {
                std::mem::swap(&mut v, &mut u);
            }
            if self.block_start[self.pos_in_order[v]] <= self.pos_in_order[u] {
                return u;
            }
            v = self.parent[self.order[self.block_start[self.pos_in_order[v]]]];
        }
        v
    }
}
}
pub mod lazy_seg_tree {
use std::ops::Range;

use crate::algo_lib::seg_trees::seg_tree_trait::SegTreeNode;

///
/// Segment Tree
///
#[allow(unused)]
#[derive(Clone)]
pub struct SegTree<T: SegTreeNode> {
    n: usize,
    tree: Vec<T>,
    updates_to_push: Vec<Option<T::Update>>,
    context: T::Context,
    right_nodes: Vec<usize>,
}

#[allow(unused)]
impl<T: SegTreeNode> SegTree<T> {
    fn pull(&mut self, v: usize, vr: usize) {
        self.tree[v] = T::join_nodes(&self.tree[v + 1], &self.tree[vr], &self.context);
    }

    fn build(&mut self, v: usize, l: usize, r: usize, init_val: &T) {
        if l + 1 == r {
            self.tree[v] = init_val.clone();
        } else {
            let m = (l + r) >> 1;
            let vr = v + ((m - l) << 1);
            self.build(v + 1, l, m, init_val);
            self.build(vr, m, r, init_val);
            self.pull(v, vr);
        }
    }

    fn push(&mut self, v: usize, l: usize, r: usize) {
        let update = self.updates_to_push[v].clone();
        self.updates_to_push[v] = None;
        match update {
            None => {}
            Some(update) => {
                let m = (l + r) >> 1;
                self.apply_update(v + 1, &update, m - l == 1);
                self.apply_update(v + ((r - l) & !1), &update, r - m == 1);
            }
        }
    }

    fn get_(&mut self, v: usize, l: usize, r: usize, ql: usize, qr: usize) -> T {
        assert!(qr >= l);
        assert!(ql < r);
        if ql <= l && r <= qr {
            return self.tree[v].clone();
        }
        let m = (l + r) >> 1;
        let vr = v + ((m - l) << 1);
        self.push(v, l, r);
        let res = if ql >= m {
            self.get_(vr, m, r, ql, qr)
        } else if qr <= m {
            self.get_(v + 1, l, m, ql, qr)
        } else {
            T::join_nodes(
                &self.get_(v + 1, l, m, ql, qr),
                &self.get_(vr, m, r, ql, qr),
                &self.context,
            )
        };
        self.pull(v, vr);
        res
    }

    fn join_updates(current: &mut Option<T::Update>, add: &T::Update) {
        match current {
            None => *current = Some(add.clone()),
            Some(current) => T::join_updates(current, add),
        };
    }

    fn apply_update(&mut self, v: usize, update: &T::Update, is_leaf: bool) {
        T::apply_update(&mut self.tree[v], update);
        if !is_leaf {
            Self::join_updates(&mut self.updates_to_push[v], update);
        }
    }

    fn modify_(&mut self, v: usize, l: usize, r: usize, ql: usize, qr: usize, update: &T::Update) {
        assert!(qr >= l);
        assert!(ql < r);
        if ql <= l && r <= qr {
            self.apply_update(v, update, r - l == 1);
            return;
        }
        let m = (l + r) >> 1;
        let vr = v + ((m - l) << 1);
        self.push(v, l, r);
        if ql >= m {
            self.modify_(vr, m, r, ql, qr, update);
        } else if qr <= m {
            self.modify_(v + 1, l, m, ql, qr, update);
        } else {
            self.modify_(v + 1, l, m, ql, qr, update);
            self.modify_(vr, m, r, ql, qr, update);
        };
        self.pull(v, vr);
    }

    pub fn update(&mut self, range: Range<usize>, update: T::Update) {
        if range.is_empty() {
            return;
        }
        assert!(!range.is_empty());
        self.modify_(0, 0, self.n, range.start, range.end, &update);
    }

    pub fn update_point(&mut self, pos: usize, new_node: T) {
        let mut l = 0;
        let mut r = self.n;
        let mut v: usize = 0;
        let mut to_pull = vec![];
        while r - l > 1 {
            let m = (l + r) >> 1;
            let vr = v + ((m - l) << 1);
            self.push(v, l, r);
            to_pull.push((v, vr));
            if pos < m {
                r = m;
                v = v + 1;
            } else {
                l = m;
                v = vr;
            }
        }
        self.tree[v] = new_node;
        for (v, vr) in to_pull.into_iter().rev() {
            self.pull(v, vr);
        }
    }

    fn find_last_true_(
        &mut self,
        v: usize,
        l: usize,
        r: usize,
        range: Range<usize>,
        f: &impl Fn(&T) -> bool,
    ) -> Option<usize> {
        if range.start >= r || l >= range.end {
            return None;
        }
        let m = (l + r) >> 1;
        let vr = v + ((m - l) << 1);
        if range.start <= l && r <= range.end {
            if !f(&self.tree[v]) {
                return None;
            }
            if r - l == 1 {
                return Some(l);
            }
        }
        self.push(v, l, r);
        if let Some(res) = self.find_last_true_(vr, m, r, range.clone(), f) {
            Some(res)
        } else {
            self.find_last_true_(v + 1, l, m, range, f)
        }
    }

    // returns position
    pub fn find_last_true(&mut self, range: Range<usize>, f: impl Fn(&T) -> bool) -> Option<usize> {
        self.find_last_true_(0, 0, self.n, range, &f)
    }

    pub fn get(&mut self, range: Range<usize>) -> T {
        if range.is_empty() {
            return T::default();
        }
        self.get_(0, 0, self.n, range.start, range.end)
    }

    pub fn new_with_context(n: usize, f: impl Fn(usize) -> T, context: T::Context) -> Self {
        assert!(n > 0);
        let tree = vec![T::default(); 2 * n - 1];
        let updates_to_push = vec![None; 2 * n - 1];
        let mut res = SegTree {
            n,
            tree,
            updates_to_push,
            context,
            right_nodes: vec![],
        };
        res.build_f(0, 0, n, &f);
        res
    }

    pub fn new(n: usize, f: impl Fn(usize) -> T) -> Self
    where
        T::Context: Default,
    {
        assert!(n > 0);
        let tree = vec![T::default(); 2 * n - 1];
        let updates_to_push = vec![None; 2 * n - 1];
        let mut res = SegTree {
            n,
            tree,
            updates_to_push,
            context: T::Context::default(),
            right_nodes: vec![],
        };
        res.build_f(0, 0, n, &f);
        res
    }

    fn build_f(&mut self, v: usize, l: usize, r: usize, f: &impl Fn(usize) -> T) {
        if l + 1 == r {
            self.tree[v] = f(l);
        } else {
            let m = (l + r) >> 1;
            let vr = v + ((m - l) << 1);
            self.build_f(v + 1, l, m, f);
            self.build_f(vr, m, r, f);
            self.pull(v, vr);
        }
    }

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

    pub fn expert_get_node(&self, node: usize) -> &T {
        &self.tree[node]
    }

    pub fn expert_get_left_node(&self, node: usize) -> usize {
        node + 1
    }

    fn build_right_nodes(&mut self, v: usize, l: usize, r: usize) {
        if l + 1 == r {
            self.right_nodes.push(0);
        } else {
            let m = (l + r) >> 1;
            let vr = v + ((m - l) << 1);
            self.right_nodes.push(vr);
            self.build_right_nodes(v + 1, l, m);
            self.build_right_nodes(vr, m, r);
        }
    }

    // TODO: shouldn't be mut
    pub fn expert_get_right_node(&mut self, node: usize) -> usize {
        if self.right_nodes.is_empty() {
            self.build_right_nodes(0, 0, self.n);
        }
        self.right_nodes[node]
    }

    // Used for Kinetic Seg Tree
    pub fn expert_rebuild_nodes(&mut self, should_rebuild: impl Fn(&T, &T::Context) -> bool) {
        self.expert_rebuild_nodes_(0, 0, self.n, &should_rebuild);
    }

    fn expert_rebuild_nodes_(
        &mut self,
        v: usize,
        l: usize,
        r: usize,
        should_rebuild: &impl Fn(&T, &T::Context) -> bool,
    ) {
        if r - l <= 1 || !should_rebuild(&self.tree[v], &self.context) {
            return;
        }
        let m = (l + r) >> 1;
        let vr = v + ((m - l) << 1);
        self.push(v, l, r);

        self.expert_rebuild_nodes_(v + 1, l, m, should_rebuild);
        self.expert_rebuild_nodes_(vr, m, r, should_rebuild);

        self.pull(v, vr);
    }

    pub fn update_context(&mut self, f: impl Fn(&mut T::Context)) {
        f(&mut self.context);
    }

    pub fn get_context(&self) -> &T::Context {
        &self.context
    }
}
}
pub mod seg_tree_2d {
use std::ops::Range;
use std::ops::RangeInclusive;

use crate::algo_lib::misc::binary_search::binary_search_first_true;
use crate::algo_lib::seg_trees::lazy_seg_tree::SegTree;
use crate::algo_lib::seg_trees::seg_tree_trait::SegTreeNode;

pub struct SegTree2d<T: Ord, U: SegTreeNode> {
    all_y: Vec<T>,
    tree_y: SegTree<U>,
    x_range: RangeInclusive<T>,
    mid_x: T,
    child: Vec<SegTree2d<T, U>>,
}

impl<T: Ord + Copy, U: SegTreeNode> SegTree2d<T, U> {
    pub fn new(pts: Vec<(T, T)>) -> Self
    where
        U::Context: Default,
    {
        assert!(!pts.is_empty());
        let mut all_x: Vec<T> = pts.iter().map(|&(x, _y)| x).collect();
        all_x.sort();
        all_x.dedup();
        let mut all_y: Vec<T> = pts.iter().map(|&(_x, y)| y).collect();
        all_y.sort();
        all_y.dedup();
        let tree_y = SegTree::new(all_y.len(), |_| U::default());
        let mid_x = all_x[all_x.len() / 2];
        let mut child = vec![];
        if all_x.len() > 1 {
            let mut left_pts = vec![];
            let mut right_pts = vec![];
            for &(x, y) in pts.iter() {
                if x < mid_x {
                    left_pts.push((x, y));
                } else {
                    right_pts.push((x, y));
                }
            }
            assert!(!left_pts.is_empty() && !right_pts.is_empty());
            let left = Self::new(left_pts);
            let right = Self::new(right_pts);
            child.push(left);
            child.push(right);
        }
        Self {
            all_y,
            tree_y,
            mid_x,
            child,
            x_range: all_x[0]..=all_x[all_x.len() - 1],
        }
    }

    pub fn update(&mut self, x: T, y: T, value: U) {
        let y_pos = self.all_y.binary_search(&y).unwrap();
        self.tree_y.update_point(y_pos, value.clone());
        if !self.child.is_empty() {
            if x < self.mid_x {
                self.child[0].update(x, y, value);
            } else {
                self.child[1].update(x, y, value);
            }
        }
    }

    pub fn query(&mut self, x_range: Range<T>, y_range: Range<T>) -> U {
        let mut res = U::default();

        if x_range.start <= *self.x_range.start() && x_range.end > *self.x_range.end() {
            let y_start =
                binary_search_first_true(0..self.all_y.len(), |p| self.all_y[p] >= y_range.start);
            let y_end =
                binary_search_first_true(0..self.all_y.len(), |p| self.all_y[p] >= y_range.end);
            res = self.tree_y.get(y_start..y_end);
        } else if !self.child.is_empty() {
            if x_range.start < self.mid_x {
                res = U::join_nodes(
                    &res,
                    &self.child[0].query(x_range.clone(), y_range.clone()),
                    self.tree_y.get_context(),
                );
            }
            if x_range.end > self.mid_x {
                res = U::join_nodes(
                    &res,
                    &self.child[1].query(x_range.clone(), y_range.clone()),
                    self.tree_y.get_context(),
                );
            }
        }
        res
    }
}
}
pub mod seg_tree_trait {
pub trait SegTreeNode: Clone + Default {
    fn join_nodes(l: &Self, r: &Self, context: &Self::Context) -> Self;

    fn apply_update(node: &mut Self, update: &Self::Update);
    fn join_updates(current: &mut Self::Update, add: &Self::Update);

    type Update: Clone;
    type Context;
}
}
}
}
fn main() {
    crate::solution::submit();
}