// https://contest.ucup.ac/contest/1893/problem/9731
pub mod solution {
//{"name":"F. Fuzzy Ranking","group":"Universal Cup - The 3rd Universal Cup. Stage 25: Hangzhou","url":"https://contest.ucup.ac/contest/1893/problem/9731","interactive":false,"timeLimit":1000,"tests":[{"input":"2\n5 2 2\n1 2 3 4 5\n5 4 3 2 1\n1 0 2\n1 2 1\n5 3 3\n1 2 3 4 5\n1 3 2 4 5\n1 2 3 5 4\n0 0 2\n0 2 3\n1 0 3\n","output":"3\n10\n1\n1\n2\n"}],"testType":"single","input":{"type":"stdin","fileName":null,"pattern":null},"output":{"type":"stdout","fileName":null,"pattern":null},"languages":{"java":{"taskClass":"FFuzzyRanking"}}}

use std::collections::VecDeque;

use crate::algo_lib::collections::array_2d::Array2D;
#[allow(unused)]
use crate::dbg;
use crate::algo_lib::io::input::Input;
use crate::algo_lib::io::output::Output;
use crate::algo_lib::misc::binary_search::binary_search_first_true;
use crate::algo_lib::misc::rand::Random;
use crate::algo_lib::misc::vec_apply_delta::ApplyDelta;

#[derive(Clone, Copy, Debug)]
struct Segment {
    l: usize,
    r: usize,
}

impl Segment {
    fn new(l: usize, r: usize) -> Self {
        Self { l, r }
    }
}

struct Solver {
    segs: Vec<Vec<Segment>>,
    dp: Vec<Vec<i64>>,
}

impl Solver {
    fn new(perms: &[Vec<usize>]) -> Self {
        let k = perms.len();
        let n = perms[0].len();
        let mut g = vec![vec![]; n];
        for i in 0..k {
            for j in 0..n - 1 {
                g[perms[i][j + 1]].push(perms[i][j]);
            }
        }
        let mut segs: Vec<Vec<Segment>> = vec![vec![]; k];
        let mut dp = vec![vec![0i64; n + 1]; k];
        for i in 0..k {
            let mut seen = vec![false; n];
            let mut perm_inv = vec![0; n];
            for pos in 0..n {
                perm_inv[perms[i][pos]] = pos;
            }
            for pos in 0..n {
                let v = perms[i][pos];
                if seen[v] {
                    continue;
                }
                let mut max_pos = pos;
                let mut q = VecDeque::new();
                q.push_back(v);
                while let Some(v) = q.pop_front() {
                    seen[v] = true;
                    for &u in &g[v] {
                        if !seen[u] {
                            seen[u] = true;
                            q.push_back(u);
                            max_pos = max_pos.max(perm_inv[u]);
                        }
                    }
                }
                segs[i].push(Segment::new(pos, max_pos + 1));
            }
            {
                let mut sum_len = 0;
                for s in segs[i].iter() {
                    // dbg!(s);
                    sum_len += s.r - s.l;
                    for pos in s.l..s.r {
                        dp[i][pos + 1] = dp[i][pos];
                        dp[i][pos + 1] += (pos - s.l) as i64;
                    }
                }
                assert_eq!(sum_len, n);
            }
        }
        Self { segs, dp }
    }

    fn calc(&self, id: usize, mut l: usize, r: usize) -> i64 {
        let segs = &self.segs[id];
        let first_seg = binary_search_first_true(0..segs.len(), |i| segs[i].r > l);
        let mut v = 0;
        let first_seg_end = segs[first_seg].r.min(r);
        v += calc(l, first_seg_end);
        l = first_seg_end;
        if l != r {
            v += self.dp[id][r] - self.dp[id][l];
        }
        v
    }
}

fn solve(input: &mut Input, out: &mut Output, _test_case: usize) {
    let tc = input.usize();
    for _ in 0..tc {
        let n = input.usize();
        let k = input.usize();
        let q = input.usize();
        let mut perms = vec![];
        for _ in 0..k {
            let p = input.vec::<usize>(n).sub_from_all(1);
            perms.push(p);
        }
        let mut solver = Solver::new(&perms);

        let mut prev_v = 0;
        for _ in 0..q {
            let id = (input.i64() + prev_v) % k as i64;
            let l = (input.i64() + prev_v) % n as i64;
            let r = (input.i64() + prev_v) % n as i64;
            let id = id as usize;
            let mut l = l as usize;
            let r = r as usize + 1;
            assert!(l < r);
            let v = solver.calc(id, l, r);
            out.println(v);
            prev_v = v;
        }
    }
}

fn calc(l: usize, r: usize) -> i64 {
    let r = r - 1;
    assert!(l <= r);
    let n = (r - l) as i64;
    n * (n + 1) / 2
}

fn stress() {
    const MX: usize = 10;
    for it in 418.. {
        dbg!(it);

        let mut rnd = Random::new(it);
        let k = rnd.gen(1..MX);
        let n = rnd.gen(1..MX);
        let mut perms = vec![];
        let mut g = Array2D::new(false, n, n);
        for _ in 0..k {
            let p = rnd.gen_permutation(n);
            dbg!(p);
            perms.push(p);
        }
        for i in 0..k {
            for j in 0..n - 1 {
                g[perms[i][j]][perms[i][j + 1]] = true;
            }
        }
        for i in 0..n {
            for j in 0..n {
                for k in 0..n {
                    if g[j][i] && g[i][k] {
                        g[j][k] = true;
                    }
                }
            }
        }
        let solver = Solver::new(&perms);
        for _ in 0..100 {
            let id = rnd.gen(0..k);
            let l = rnd.gen(0..n);
            let r = rnd.gen(l + 1..n + 1);
            let mut real_ans = 0;
            for p1 in l..r {
                for p2 in p1 + 1..r {
                    if g[perms[id][p1]][perms[id][p2]] && g[perms[id][p2]][perms[id][p1]] {
                        real_ans += 1;
                    }
                }
            }
            let my_ans = solver.calc(id, l, r);
            dbg!(id, l, r);
            dbg!(real_ans, my_ans);
            assert_eq!(real_ans, my_ans);
        }
    }
}

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

}
pub mod algo_lib {
#![feature(test)]
#![allow(clippy::too_many_arguments)]
#![allow(clippy::type_complexity)]

pub mod collections {
pub mod array_2d {
use crate::algo_lib::io::output::Output;
use crate::algo_lib::io::output::Writable;
use crate::algo_lib::misc::num_traits::Number;
use std::io::Write;
use std::ops::Index;
use std::ops::IndexMut;
use std::ops::Mul;

// TODO: implement good Debug
#[derive(Clone, Debug, PartialEq, Eq, PartialOrd, Ord, Hash)]
pub struct Array2D<T> {
    rows: usize,
    cols: usize,
    v: Vec<T>,
}

pub struct Iter<'a, T> {
    array: &'a Array2D<T>,
    row: usize,
    col: usize,
}

impl<T> Array2D<T>
where
    T: Clone,
{
    #[allow(unused)]
    pub fn new(empty: T, rows: usize, cols: usize) -> Self {
        Self {
            rows,
            cols,
            v: vec![empty; rows * cols],
        }
    }

    pub fn new_f(rows: usize, cols: usize, mut f: impl FnMut(usize, usize) -> T) -> Self {
        let mut v = Vec::with_capacity(rows * cols);
        for r in 0..rows {
            for c in 0..cols {
                v.push(f(r, c));
            }
        }
        Self { rows, cols, v }
    }

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

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

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

    pub fn swap(&mut self, row1: usize, row2: usize) {
        assert!(row1 < self.rows);
        assert!(row2 < self.rows);
        if row1 != row2 {
            for col in 0..self.cols {
                self.v.swap(row1 * self.cols + col, row2 * self.cols + col);
            }
        }
    }

    pub fn transpose(&self) -> Self {
        Self::new_f(self.cols, self.rows, |r, c| self[c][r].clone())
    }

    pub fn iter(&self) -> Iter<T> {
        Iter {
            array: self,
            row: 0,
            col: 0,
        }
    }

    pub fn pref_sum(&self) -> Self
    where
        T: Number,
    {
        let mut res = Self::new(T::ZERO, self.rows + 1, self.cols + 1);
        for i in 0..self.rows {
            for j in 0..self.cols {
                let value = self[i][j] + res[i][j + 1] + res[i + 1][j] - res[i][j];
                res[i + 1][j + 1] = value;
            }
        }
        res
    }
}

impl<T> Writable for Array2D<T>
where
    T: Writable,
{
    fn write(&self, output: &mut Output) {
        for r in 0..self.rows {
            self[r].write(output);
            output.write_all(&[b'\n']).unwrap();
        }
    }
}

impl<T> Index<usize> for Array2D<T> {
    type Output = [T];

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

impl<T> IndexMut<usize> for Array2D<T> {
    fn index_mut(&mut self, index: usize) -> &mut Self::Output {
        &mut self.v[(index) * self.cols..(index + 1) * self.cols]
    }
}

impl<T> Mul for &Array2D<T>
where
    T: Number,
{
    type Output = Array2D<T>;

    fn mul(self, rhs: Self) -> Self::Output {
        let n = self.rows;
        let m = self.cols;
        assert_eq!(m, rhs.rows);
        let k2 = rhs.cols;
        let mut res = Array2D::new(T::ZERO, n, k2);
        for i in 0..n {
            for j in 0..m {
                for k in 0..k2 {
                    res[i][k] += self[i][j] * rhs[j][k];
                }
            }
        }
        res
    }
}

impl<T> Array2D<T>
where
    T: Number,
{
    pub fn pown(&self, pw: usize) -> Self {
        assert_eq!(self.rows, self.cols);
        let n = self.rows;
        if pw == 0 {
            Self::new_f(n, n, |r, c| if r == c { T::ONE } else { T::ZERO })
        } else if pw == 1 {
            self.clone()
        } else {
            let half = self.pown(pw / 2);
            let half2 = &half * &half;
            if pw & 1 == 0 {
                half2
            } else {
                &half2 * self
            }
        }
    }
}

impl<'a, T> Iterator for Iter<'a, T> {
    type Item = &'a T;

    fn next(&mut self) -> Option<Self::Item> {
        if self.col == self.array.cols {
            self.col = 0;
            self.row += 1;
        }
        if self.row >= self.array.rows {
            return None;
        }
        let elem = &self.array[self.row][self.col];
        self.col += 1;
        Some(elem)
    }
}
}
}
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_stdin() -> Self {
        let stdin = std::io::stdin();
        Self::new(Box::new(stdin))
    }

    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 + Debug>(&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_stdout() -> Self {
        let stdout = std::io::stdout();
        Self::new(Box::new(stdout))
    }

    pub fn new_file(path: impl AsRef<std::path::Path>) -> Self {
        let file = std::fs::File::create(path).unwrap();
        Self::new(Box::new(file))
    }

    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 println<T: Writable>(&mut self, s: T) {
        s.write(self);
        self.put(b'\n');
    }

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

    pub fn 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 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 gen_vector {
pub fn gen_vec<T>(n: usize, f: impl FnMut(usize) -> T) -> Vec<T> {
    (0..n).map(f).collect()
}
}
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 rand {
use crate::algo_lib::misc::gen_vector::gen_vec;
use crate::algo_lib::misc::num_traits::Number;
use std::ops::Range;
use std::time::SystemTime;
use std::time::UNIX_EPOCH;

#[allow(dead_code)]
pub struct Random {
    state: u64,
}

impl Random {
    pub fn gen_u64(&mut self) -> u64 {
        let mut x = self.state;
        x ^= x << 13;
        x ^= x >> 7;
        x ^= x << 17;
        self.state = x;
        x
    }

    #[allow(dead_code)]
    pub fn next_in_range(&mut self, from: usize, to: usize) -> usize {
        assert!(from < to);
        (from as u64 + self.gen_u64() % ((to - from) as u64)) as usize
    }

    pub fn gen_index<T>(&mut self, a: &[T]) -> usize {
        self.gen(0..a.len())
    }

    #[allow(dead_code)]
    #[inline(always)]
    pub fn gen_double(&mut self) -> f64 {
        (self.gen_u64() as f64) / (std::usize::MAX as f64)
    }

    #[allow(dead_code)]
    pub fn new(seed: u64) -> Self {
        let state = if seed == 0 { 787788 } else { seed };
        Self { state }
    }

    pub fn new_time_seed() -> Self {
        let time = SystemTime::now();
        let seed = (time.duration_since(UNIX_EPOCH).unwrap().as_nanos() % 1_000_000_000) as u64;
        if seed == 0 {
            Self::new(787788)
        } else {
            Self::new(seed)
        }
    }

    #[allow(dead_code)]
    pub fn gen_permutation(&mut self, n: usize) -> Vec<usize> {
        let mut result: Vec<_> = (0..n).collect();
        for i in 0..n {
            let idx = self.next_in_range(0, i + 1);
            result.swap(i, idx);
        }
        result
    }

    pub fn shuffle<T>(&mut self, a: &mut [T]) {
        for i in 1..a.len() {
            a.swap(i, self.gen(0..i + 1));
        }
    }

    pub fn gen<T>(&mut self, range: Range<T>) -> T
    where
        T: Number,
    {
        let from = T::to_i32(range.start);
        let to = T::to_i32(range.end);
        assert!(from < to);
        let len = (to - from) as usize;
        T::from_i32(self.next_in_range(0, len) as i32 + from)
    }

    pub fn gen_vec<T>(&mut self, n: usize, range: Range<T>) -> Vec<T>
    where
        T: Number,
    {
        gen_vec(n, |_| self.gen(range.clone()))
    }

    pub fn gen_nonempty_range(&mut self, n: usize) -> Range<usize> {
        let x = self.gen(0..n);
        let y = self.gen(0..n);
        if x <= y {
            x..y + 1
        } else {
            y..x + 1
        }
    }

    pub fn gen_bool(&mut self) -> bool {
        self.gen(0..2) == 0
    }
}
}
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);
    }
}
}
}
}
fn main() {
    let input = algo_lib::io::input::Input::new_stdin();
    let mut output = algo_lib::io::output::Output::new_stdout();
    crate::solution::run(input, output);
}