// 
pub mod solution {
//{"name":"ucup_10_k","group":"Manual","url":"","interactive":false,"timeLimit":2000,"tests":[{"input":"","output":""}],"testType":"multiNumber","input":{"type":"stdin","fileName":null,"pattern":null},"output":{"type":"stdout","fileName":null,"pattern":null},"languages":{"java":{"taskClass":"ucup_10_k"}}}

use crate::algo_lib::collections::md_arr::arr2d::Arr2d;
use crate::algo_lib::collections::min_max::MinimMaxim;
use crate::algo_lib::geometry::point::Point;
use crate::algo_lib::io::input::Input;
use crate::algo_lib::io::output::Output;
use crate::algo_lib::misc::test_type::TaskType;
use crate::algo_lib::misc::test_type::TestType;

type PreCalc = ();

fn solve(input: &mut Input, out: &mut Output, _test_case: usize, _data: &mut PreCalc) {
    let n = input.read_size();
    let f = input.read_int_vec(n);
    let pts = input.read_vec::<Point<i64>>(n);

    let area = |i1: usize, i2: usize, i3: usize| -> i64 {
        (pts[i1].x - pts[i3].x) * (pts[i2].y - pts[i1].y)
            - (pts[i1].x - pts[i2].x) * (pts[i3].y - pts[i1].y)
    };
    let mut any = Arr2d::new(n, n, 0);
    let mut same = Arr2d::new(n, n, 0);
    let mut ans = 0;
    for len in 1..n {
        for i in 0..n {
            let j = if i + len < n { i + len } else { i + len - n };
            let mut cur_any = 0;
            let mut cur_same = 0;
            for k in i..i + len {
                let k = if k < n { k } else { k - n };
                let area = area(i, k, j);
                cur_any.maxim(same[(i, k)] + area);
                if f[j] == f[k] {
                    cur_same.maxim(any[(k, j)] + area);
                }
            }
            any[(i, j)] = cur_any;
            same[(i, j)] = cur_same;
            if f[i] == f[j] {
                ans.maxim(cur_any);
            }
        }
    }
    out.print_line(ans);
}

pub static TEST_TYPE: TestType = TestType::MultiNumber;
pub static TASK_TYPE: TaskType = TaskType::Classic;

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

    match TEST_TYPE {
        TestType::Single => solve(&mut input, &mut output, 1, &mut pre_calc),
        TestType::MultiNumber => {
            let t = input.read();
            for i in 1..=t {
                solve(&mut input, &mut output, i, &mut pre_calc);
            }
        }
        TestType::MultiEof => {
            let mut i = 1;
            while input.peek().is_some() {
                solve(&mut input, &mut output, i, &mut pre_calc);
                i += 1;
            }
        }
    }
    output.flush();
    match TASK_TYPE {
        TaskType::Classic => {
            input.skip_whitespace();
            input.peek().is_none()
        }
        TaskType::Interactive => true,
    }
}

}
pub mod algo_lib {
pub mod collections {
pub mod md_arr {
pub mod arr2d {
use crate::algo_lib::collections::slice_ext::legacy_fill::LegacyFill;
use crate::algo_lib::io::input::Input;
use crate::algo_lib::io::input::Readable;
use crate::algo_lib::io::output::Output;
use crate::algo_lib::io::output::Writable;
use std::ops::Index;
use std::ops::IndexMut;
use std::ops::Range;
use std::slice::Iter;
use std::vec::IntoIter;

#[derive(Clone, Eq, PartialEq, Default)]
pub struct Arr2d<T> {
    d1: usize,
    d2: usize,
    data: Vec<T>,
}

impl<T: Clone> Arr2d<T> {
    pub fn new(d1: usize, d2: usize, value: T) -> Self {
        Self {
            d1,
            d2,
            data: vec![value; d1 * d2],
        }
    }
}

impl<T> Arr2d<T> {
    pub fn generate<F>(d1: usize, d2: usize, mut gen: F) -> Self
    where
        F: FnMut(usize, usize) -> T,
    {
        let mut data = Vec::with_capacity(d1 * d2);
        for i in 0usize..d1 {
            for j in 0usize..d2 {
                data.push(gen(i, j));
            }
        }
        Self { d1, d2, data }
    }

    pub fn d1(&self) -> usize {
        self.d1
    }

    pub fn d2(&self) -> usize {
        self.d2
    }

    pub fn iter(&self) -> Iter<'_, T> {
        self.data.iter()
    }

    pub fn iter_mut(&mut self) -> impl Iterator<Item = &mut T> {
        self.data.iter_mut()
    }

    pub fn row(&self, row: usize) -> impl Iterator<Item = &T> {
        assert!(row < self.d1);
        self.data.iter().skip(row * self.d2).take(self.d2)
    }

    pub fn row_mut(&mut self, row: usize) -> impl Iterator<Item = &mut T> {
        assert!(row < self.d1);
        self.data.iter_mut().skip(row * self.d2).take(self.d2)
    }

    pub fn column(&self, col: usize) -> impl Iterator<Item = &T> {
        assert!(col < self.d2);
        self.data.iter().skip(col).step_by(self.d2)
    }

    pub fn column_mut(&mut self, col: usize) -> impl Iterator<Item = &mut T> {
        assert!(col < self.d2);
        self.data.iter_mut().skip(col).step_by(self.d2)
    }

    pub fn swap(&mut self, r1: usize, c1: usize, r2: usize, c2: usize) {
        assert!(r1 < self.d1);
        assert!(r2 < self.d1);
        assert!(c1 < self.d2);
        assert!(c2 < self.d2);
        self.data.swap(r1 * self.d2 + c1, r2 * self.d2 + c2);
    }

    pub fn rows(&self) -> Range<usize> {
        0..self.d1
    }

    pub fn cols(&self) -> Range<usize> {
        0..self.d2
    }

    pub fn swap_rows(&mut self, r1: usize, r2: usize) {
        assert!(r1 < self.d1);
        assert!(r2 < self.d1);
        if r1 == r2 {
            return;
        }
        let (r1, r2) = (r1.min(r2), r1.max(r2));
        let (head, tail) = self.data.split_at_mut(r2 * self.d2);
        head[r1 * self.d2..(r1 + 1) * self.d2].swap_with_slice(&mut tail[..self.d2]);
    }
}

impl<T: Clone> Arr2d<T> {
    pub fn fill(&mut self, elem: T) {
        self.data.legacy_fill(elem);
    }

    pub fn transpose(&self) -> Self {
        Self::generate(self.d2, self.d1, |i, j| self[(j, i)].clone())
    }
}

impl<T> Index<(usize, usize)> for Arr2d<T> {
    type Output = T;

    fn index(&self, (row, col): (usize, usize)) -> &Self::Output {
        assert!(row < self.d1);
        assert!(col < self.d2);
        &self.data[self.d2 * row + col]
    }
}

impl<T> Index<usize> for Arr2d<T> {
    type Output = [T];

    fn index(&self, index: usize) -> &Self::Output {
        &self.data[self.d2 * index..self.d2 * (index + 1)]
    }
}

impl<T> IndexMut<(usize, usize)> for Arr2d<T> {
    fn index_mut(&mut self, (row, col): (usize, usize)) -> &mut T {
        assert!(row < self.d1);
        assert!(col < self.d2);
        &mut self.data[self.d2 * row + col]
    }
}

impl<T> IndexMut<usize> for Arr2d<T> {
    fn index_mut(&mut self, index: usize) -> &mut [T] {
        &mut self.data[self.d2 * index..self.d2 * (index + 1)]
    }
}

impl<T> AsRef<Vec<T>> for Arr2d<T> {
    fn as_ref(&self) -> &Vec<T> {
        &self.data
    }
}

impl<T> AsMut<Vec<T>> for Arr2d<T> {
    fn as_mut(&mut self) -> &mut Vec<T> {
        &mut self.data
    }
}

impl<T: Writable> Writable for Arr2d<T> {
    fn write(&self, output: &mut Output) {
        let mut at = 0usize;
        for i in 0usize..self.d1 {
            if i != 0 {
                output.put(b'\n');
            }
            for j in 0usize..self.d2 {
                if j != 0 {
                    output.put(b' ');
                }
                self.data[at].write(output);
                at += 1;
            }
        }
    }
}

impl<T> IntoIterator for Arr2d<T> {
    type Item = T;
    type IntoIter = IntoIter<T>;

    fn into_iter(self) -> Self::IntoIter {
        self.data.into_iter()
    }
}

impl<'a, T> IntoIterator for &'a Arr2d<T> {
    type Item = &'a T;
    type IntoIter = Iter<'a, T>;

    fn into_iter(self) -> Self::IntoIter {
        self.iter()
    }
}

pub trait Arr2dRead {
    fn read_table<T: Readable>(&mut self, d1: usize, d2: usize) -> Arr2d<T>;
    fn read_int_table(&mut self, d1: usize, d2: usize) -> Arr2d<i32>;
    fn read_long_table(&mut self, d1: usize, d2: usize) -> Arr2d<i64>;
    fn read_size_table(&mut self, d1: usize, d2: usize) -> Arr2d<usize>;
    fn read_char_table(&mut self, d1: usize, d2: usize) -> Arr2d<char>;
}

impl Arr2dRead for Input<'_> {
    fn read_table<T: Readable>(&mut self, d1: usize, d2: usize) -> Arr2d<T> {
        Arr2d::generate(d1, d2, |_, _| self.read())
    }

    fn read_int_table(&mut self, d1: usize, d2: usize) -> Arr2d<i32> {
        self.read_table(d1, d2)
    }

    fn read_long_table(&mut self, d1: usize, d2: usize) -> Arr2d<i64> {
        self.read_table(d1, d2)
    }

    fn read_size_table(&mut self, d1: usize, d2: usize) -> Arr2d<usize> {
        self.read_table(d1, d2)
    }

    fn read_char_table(&mut self, d1: usize, d2: usize) -> Arr2d<char> {
        self.read_table(d1, d2)
    }
}

pub trait Arr2dCharWrite {
    fn print_table(&mut self, table: &Arr2d<char>);
}

impl Arr2dCharWrite for Output<'_> {
    fn print_table(&mut self, table: &Arr2d<char>) {
        let mut at = 0usize;
        for _ in 0..table.d1 {
            for _ in 0..table.d2 {
                self.print(table.data[at]);
                at += 1;
            }
            self.put(b'\n');
        }
    }
}

impl<T: Readable> Readable for Arr2d<T> {
    fn read(input: &mut Input) -> Self {
        let d1 = input.read();
        let d2 = input.read();
        input.read_table(d1, d2)
    }
}
}
}
pub mod 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 slice_ext {
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 geometry {
pub mod geometry_utils {
use crate::algo_lib::numbers::real::RealTrait;

pub fn canonize_angle<T: RealTrait + Copy>(angle: T) -> T {
    canonize_angle_base(angle, T::zero() - T::PI)
}

pub fn canonize_angle_base<T: RealTrait + Copy>(angle: T, base: T) -> T {
    let two = T::one() + T::one();
    let mut angle = angle;
    while angle < base - T::epsilon() {
        angle += T::PI * two;
    }
    while angle > base + T::PI * two - T::epsilon() {
        angle -= T::PI * two;
    }
    angle
}
}
pub mod line {
use crate::algo_lib::geometry::point::Point;
use crate::algo_lib::numbers::num_traits::algebra::Field;
use crate::algo_lib::numbers::num_traits::algebra::Ring;
use crate::algo_lib::numbers::real::RealTrait;

#[derive(Copy, Clone, Ord, PartialOrd, Eq, PartialEq, Hash)]
pub struct Line<T> {
    pub a: T,
    pub b: T,
    pub c: T,
}

impl<T> Line<T> {
    pub fn new(a: T, b: T, c: T) -> Self {
        Self { a, b, c }
    }
}

impl<T: Ring + Copy> Line<T> {
    pub fn value(&self, p: Point<T>) -> T {
        self.a * p.x + self.b * p.y + self.c
    }

    pub fn parallel(&self, p: Point<T>) -> Line<T> {
        Line::new(self.a, self.b, T::zero() - self.a * p.x - self.b * p.y)
    }

    pub fn perpendicular(&self, p: Point<T>) -> Line<T> {
        Line::new(
            T::zero() - self.b,
            self.a,
            T::zero() + self.b * p.x - self.a * p.y,
        )
    }
}

impl<T: Ring + Copy> Line<T> {
    pub fn is_parallel(&self, other: Line<T>) -> bool {
        self.a * other.b == self.b * other.a
    }

    pub fn is_perpendicular(&self, other: Line<T>) -> bool {
        self.a * other.a + self.b * other.b == T::zero()
    }
}

impl<T: Field + Copy> Line<T> {
    pub fn intersect(&self, other: Line<T>) -> Point<T> {
        let det = self.a * other.b - other.a * self.b;
        let x = (self.b * other.c - other.b * self.c) / det;
        let y = (other.a * self.c - self.a * other.c) / det;
        Point::new(x, y)
    }

    pub fn square_dist_point(&self, p: Point<T>) -> T {
        let val = self.value(p);
        val * val / (self.a * self.a + self.b * self.b)
    }
}

impl<T: Ring + Copy + PartialEq> Line<T> {
    pub fn contains(&self, p: Point<T>) -> bool {
        self.value(p) == T::zero()
    }
}

impl<T: RealTrait + Copy> Line<T> {
    pub fn new_real(a: T, b: T, c: T) -> Self {
        let h = T::hypot(a, b);
        Self {
            a: a / h,
            b: b / h,
            c: c / h,
        }
    }

    pub fn dist_point(&self, p: Point<T>) -> T {
        self.square_dist_point(p).sqrt()
    }

    pub fn contains_real(&self, p: Point<T>) -> bool {
        self.dist_point(p) < T::epsilon()
    }

    pub fn is_parallel_real(&self, other: Line<T>) -> bool {
        (self.a * other.b - self.b * other.a).abs() < T::epsilon()
    }

    pub fn is_perpendicular_real(&self, other: Line<T>) -> bool {
        (self.a * other.a + self.b * other.b).abs() < T::epsilon()
    }

    pub fn canonize(&mut self) {
        let h = T::hypot(self.a, self.b);
        self.a /= h;
        self.b /= h;
        self.c /= h;
    }
}
}
pub mod point {
use crate::algo_lib::geometry::geometry_utils::canonize_angle;
use crate::algo_lib::geometry::line::Line;
use crate::algo_lib::io::input::Input;
use crate::algo_lib::io::input::Readable;
use crate::algo_lib::io::output::Output;
use crate::algo_lib::io::output::Writable;
use crate::algo_lib::numbers::num_traits::algebra::Ring;
use crate::algo_lib::numbers::num_traits::algebra::Zero;
use crate::algo_lib::numbers::real::RealTrait;
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;

#[derive(Copy, Clone, Hash, Ord, PartialOrd, Eq, PartialEq)]
pub struct Point<T> {
    pub x: T,
    pub y: T,
}

impl<T> Point<T> {
    pub fn new(x: T, y: T) -> Self {
        Self { x, y }
    }
}

impl<T: Zero> Point<T> {
    pub fn origin() -> Self {
        Self::new(T::zero(), T::zero())
    }
}

impl<T: Ring + Copy> Point<T> {
    pub fn square_dist_point(&self, p: Self) -> T {
        let delta = *self - p;
        delta * delta
    }

    pub fn line(&self, p: Self) -> Line<T> {
        let a = self.y - p.y;
        let b = p.x - self.x;
        Line::new(a, b, T::zero() - a * self.x - b * self.y)
    }
}

impl<T: RealTrait + Copy> Point<T> {
    pub fn from_polar(r: T, alpha: T) -> Self {
        Self::new(r * alpha.cos(), r * alpha.sin())
    }

    pub fn dist_point(&self, p: Self) -> T {
        self.square_dist_point(p).sqrt()
    }

    pub fn same(&self, p: Self) -> bool {
        (self.x - p.x).abs() < T::epsilon() && (self.y - p.y).abs() < T::epsilon()
    }

    pub fn angle(&self) -> T {
        T::atan2(self.y, self.x)
    }

    pub fn angle_to(&self, p: Self) -> T {
        canonize_angle(p.angle() - self.angle()).abs()
    }
}

impl<T: AddAssign> Add for Point<T> {
    type Output = Point<T>;

    fn add(mut self, rhs: Self) -> Self::Output {
        self += rhs;
        self
    }
}

impl<T: AddAssign> AddAssign for Point<T> {
    fn add_assign(&mut self, rhs: Self) {
        self.x += rhs.x;
        self.y += rhs.y;
    }
}

impl<T: SubAssign> Sub for Point<T> {
    type Output = Point<T>;

    fn sub(mut self, rhs: Self) -> Self::Output {
        self -= rhs;
        self
    }
}

impl<T: SubAssign> SubAssign for Point<T> {
    fn sub_assign(&mut self, rhs: Self) {
        self.x -= rhs.x;
        self.y -= rhs.y;
    }
}

impl<T: MulAssign + Copy> MulAssign<T> for Point<T> {
    fn mul_assign(&mut self, rhs: T) {
        self.x *= rhs;
        self.y *= rhs;
    }
}

impl<T: MulAssign + Copy> Mul<T> for Point<T> {
    type Output = Point<T>;

    fn mul(mut self, rhs: T) -> Self::Output {
        self *= rhs;
        self
    }
}

impl<T: DivAssign + Copy> DivAssign<T> for Point<T> {
    fn div_assign(&mut self, rhs: T) {
        self.x /= rhs;
        self.y /= rhs;
    }
}

impl<T: DivAssign + Copy> Div<T> for Point<T> {
    type Output = Point<T>;

    fn div(mut self, rhs: T) -> Self::Output {
        self /= rhs;
        self
    }
}

impl<T: Mul<Output = U>, U: Add> Mul for Point<T> {
    type Output = U::Output;

    fn mul(self, rhs: Self) -> Self::Output {
        self.x * rhs.x + self.y * rhs.y
    }
}

impl<T: Writable> Writable for Point<T> {
    fn write(&self, output: &mut Output) {
        self.x.write(output);
        ' '.write(output);
        self.y.write(output);
    }
}

impl<T: Readable> Readable for Point<T> {
    fn read(input: &mut Input) -> Self {
        let x = input.read();
        let y = input.read();
        Self::new(x, y)
    }
}
}
}
pub mod io {
pub mod input {
use crate::algo_lib::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 !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)
        }
    }

    //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::algo_lib::collections::vec_ext::default::default_vec;
use std::cmp::Reverse;
use std::io::stderr;
use std::io::Stderr;
use std::io::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]) {
        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(b' ');
            }
            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;
    }
}

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(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!(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}
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;
use std::ops::AddAssign;
use std::ops::Div;
use std::ops::DivAssign;
use std::ops::Mul;
use std::ops::MulAssign;
use std::ops::Neg;
use std::ops::Rem;
use std::ops::RemAssign;
use std::ops::Sub;
use std::ops::SubAssign;

pub trait Zero {
    fn zero() -> Self;
}

pub trait One {
    fn one() -> Self;
}

pub trait AdditionMonoid: Add<Output = Self> + AddAssign + Zero + Eq + Sized {}

impl<T: Add<Output = Self> + AddAssign + Zero + Eq> AdditionMonoid for T {}

pub trait AdditionMonoidWithSub: AdditionMonoid + Sub<Output = Self> + SubAssign {}

impl<T: AdditionMonoid + Sub<Output = Self> + SubAssign> AdditionMonoidWithSub for T {}

pub trait AdditionGroup: AdditionMonoidWithSub + Neg<Output = Self> {}

impl<T: AdditionMonoidWithSub + Neg<Output = Self>> AdditionGroup for T {}

pub trait MultiplicationMonoid: Mul<Output = Self> + MulAssign + One + Eq + Sized {}

impl<T: Mul<Output = Self> + MulAssign + One + Eq> MultiplicationMonoid for T {}

pub trait IntegerMultiplicationMonoid:
    MultiplicationMonoid + Div<Output = Self> + Rem<Output = Self> + DivAssign + RemAssign
{
}

impl<T: MultiplicationMonoid + Div<Output = Self> + Rem<Output = Self> + DivAssign + RemAssign>
    IntegerMultiplicationMonoid for T
{
}

pub trait MultiplicationGroup:
    MultiplicationMonoid + Div<Output = Self> + DivAssign + Invertible<Output = Self>
{
}

impl<T: MultiplicationMonoid + Div<Output = Self> + DivAssign + Invertible<Output = Self>>
    MultiplicationGroup for T
{
}

pub trait SemiRing: AdditionMonoid + MultiplicationMonoid {}

impl<T: AdditionMonoid + MultiplicationMonoid> SemiRing for T {}

pub trait SemiRingWithSub: AdditionMonoidWithSub + SemiRing {}

impl<T: AdditionMonoidWithSub + SemiRing> SemiRingWithSub for T {}

pub trait Ring: SemiRing + AdditionGroup {}

impl<T: SemiRing + AdditionGroup> Ring for T {}

pub trait IntegerSemiRing: SemiRing + IntegerMultiplicationMonoid {}

impl<T: SemiRing + IntegerMultiplicationMonoid> IntegerSemiRing for T {}

pub trait IntegerSemiRingWithSub: SemiRingWithSub + IntegerSemiRing {}

impl<T: SemiRingWithSub + IntegerSemiRing> IntegerSemiRingWithSub for T {}

pub trait IntegerRing: IntegerSemiRing + Ring {}

impl<T: IntegerSemiRing + Ring> IntegerRing for T {}

pub trait Field: Ring + MultiplicationGroup {}

impl<T: Ring + MultiplicationGroup> Field for T {}

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

        impl One for $t {
            fn one() -> Self {
                1
            }
        }
    )+};
}

zero_one_integer_impl!(i128 i64 i32 i16 i8 isize u128 u64 u32 u16 u8 usize);
}
pub mod invertible {
pub trait Invertible {
    type Output;

    fn inv(&self) -> Option<Self::Output>;
}
}
}
pub mod real {
use crate::algo_lib::io::input::Input;
use crate::algo_lib::io::input::Readable;
use crate::algo_lib::io::output::Output;
use crate::algo_lib::io::output::Writable;
use crate::algo_lib::numbers::num_traits::algebra::Field;
use crate::algo_lib::numbers::num_traits::algebra::One;
use crate::algo_lib::numbers::num_traits::algebra::Zero;
use crate::algo_lib::numbers::num_traits::invertible::Invertible;
use std::cmp::Ordering;
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::Neg;
use std::ops::Sub;
use std::ops::SubAssign;

pub trait RealTrait: Ord + Field {
    const PI: Self;

    fn abs(&self) -> Self;
    fn sqrt(&self) -> Self;
    fn sin(&self) -> Self;
    fn cos(&self) -> Self;
    fn tan(&self) -> Self;
    fn hypot(x: Self, y: Self) -> Self;
    fn atan2(y: Self, x: Self) -> Self;

    fn epsilon() -> Self;
    fn set_epsilon(eps: Self);
}

#[derive(Copy, Clone, PartialOrd, PartialEq, Debug, Default)]
pub struct Real(pub f64);

impl Real {
    pub fn round(&self) -> i64 {
        self.0.round() as i64
    }
}

impl Eq for Real {}

#[allow(clippy::derive_ord_xor_partial_ord)]
impl Ord for Real {
    fn cmp(&self, other: &Self) -> Ordering {
        self.partial_cmp(other).unwrap()
    }
}

impl AddAssign for Real {
    fn add_assign(&mut self, rhs: Self) {
        self.0 += rhs.0;
    }
}

impl Add for Real {
    type Output = Self;

    fn add(mut self, rhs: Self) -> Self::Output {
        self += rhs;
        self
    }
}

impl SubAssign for Real {
    fn sub_assign(&mut self, rhs: Self) {
        self.0 -= rhs.0;
    }
}

impl Sub for Real {
    type Output = Self;

    fn sub(mut self, rhs: Self) -> Self::Output {
        self -= rhs;
        self
    }
}

impl MulAssign for Real {
    fn mul_assign(&mut self, rhs: Self) {
        self.0 *= rhs.0;
    }
}

impl Mul for Real {
    type Output = Self;

    fn mul(mut self, rhs: Self) -> Self::Output {
        self.0 *= rhs.0;
        self
    }
}

impl DivAssign for Real {
    fn div_assign(&mut self, rhs: Self) {
        self.0 /= rhs.0;
    }
}

impl Div for Real {
    type Output = Self;

    fn div(mut self, rhs: Self) -> Self::Output {
        self /= rhs;
        self
    }
}

impl Neg for Real {
    type Output = Self;

    fn neg(self) -> Self::Output {
        Self(-self.0)
    }
}

impl Zero for Real {
    fn zero() -> Self {
        Self(0.0)
    }
}

impl One for Real {
    fn one() -> Self {
        Self(1.0)
    }
}

static mut EPSILON: Real = Real(1e-9);

impl RealTrait for Real {
    const PI: Self = Self(std::f64::consts::PI);

    fn abs(&self) -> Self {
        Self(self.0.abs())
    }

    fn sqrt(&self) -> Self {
        Self(self.0.sqrt())
    }

    fn sin(&self) -> Self {
        Self(self.0.sin())
    }

    fn cos(&self) -> Self {
        Self(self.0.cos())
    }

    fn tan(&self) -> Self {
        Self(self.0.tan())
    }

    fn hypot(x: Self, y: Self) -> Self {
        Self(f64::hypot(x.0, y.0))
    }

    fn atan2(y: Self, x: Self) -> Self {
        Self(f64::atan2(y.0, x.0))
    }

    fn epsilon() -> Self {
        unsafe { EPSILON }
    }

    fn set_epsilon(eps: Self) {
        unsafe {
            EPSILON = eps;
        }
    }
}

impl Invertible for Real {
    type Output = Self;

    fn inv(&self) -> Option<Self::Output> {
        if self == &Self::zero() {
            None
        } else {
            Some(Self(1.0 / self.0))
        }
    }
}

impl Readable for Real {
    fn read(input: &mut Input) -> Self {
        Self(
            String::from_utf8(input.next_token().unwrap())
                .unwrap()
                .parse()
                .unwrap(),
        )
    }
}

impl Writable for Real {
    fn write(&self, output: &mut Output) {
        self.0.to_string().write(output);
    }
}

pub trait RealReader {
    fn read_real(&mut self) -> Real;
    fn read_real_vec(&mut self, n: usize) -> Vec<Real>;
}

impl RealReader for Input<'_> {
    fn read_real(&mut self) -> Real {
        self.read()
    }

    fn read_real_vec(&mut self, n: usize) -> Vec<Real> {
        self.read_vec(n)
    }
}

pub trait IntoReal {
    fn into_real(self) -> Real;
}

macro_rules! into_real {
    ($($t: ident)+) => {$(
        impl IntoReal for $t {
            fn into_real(self) -> Real {
                Real(self as f64)
            }
        }
    )+};
}

into_real!(u8 u16 u32 u64 u128 usize i8 i16 i32 i64 i128 isize f64);
}
}
}
fn main() {
    let mut sin = std::io::stdin();
    let input = algo_lib::io::input::Input::new(&mut sin);
    let mut stdout = std::io::stdout();
    let output = algo_lib::io::output::Output::new(&mut stdout);
    solution::run(input, output);
}