pub mod solution {
//{"name":"c","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":"c"}}}

use std::cmp::min;
use std::time::Instant;

use crate::algo_lib::collections::array_2d::Array2D;
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::math::modulo::Mod7;
use crate::algo_lib::misc::gen_vector::gen_vec;
use crate::algo_lib::misc::rand::Random;
#[allow(unused)]
use crate::dbg;
use crate::out;
use crate::out_line;

type Mod = Mod7;

fn solve_g(g: &Array2D<bool>) -> Mod {
    let n = g.len();
    let mut deg: Vec<usize> = gen_vec(n, |id| (0..n).map(|to| if g[id][to] { 1 } else { 0 }).sum());
    let mut seen = vec![false; n];
    let mut res = Mod::ZERO;
    for _ in 0..n {
        let v = (0..n)
            .filter(|&v| !seen[v])
            .min_by_key(|&v| deg[v])
            .unwrap();
        seen[v] = true;
        let mut neigh = vec![];
        for to in 0..n {
            if g[v][to] && !seen[to] {
                deg[to] -= 1;
                neigh.push(to);
            }
        }
        assert!(neigh.len() <= 44);
        let first_part = min((neigh.len() + 3) / 2, neigh.len());
        let (first, second) = neigh.split_at(first_part);
        let mut first_mask = vec![0; neigh.len()];
        let mut second_mask = vec![0; neigh.len()];
        for i in 0..neigh.len() {
            let v = neigh[i];
            for j in 0..first.len() {
                if g[v][first[j]] {
                    first_mask[i] |= 1 << j;
                }
            }
            for j in 0..second.len() {
                if g[v][second[j]] {
                    second_mask[i] |= 1 << j;
                }
            }
        }
        let mut dp = vec![Mod::ZERO; 1 << second.len()];
        let mut ok_first_mask = vec![(1 << first.len()) - 1; 1 << first.len()];
        let mut ok_second_mask = vec![(1 << second.len()) - 1; 1 << first.len()];
        for mask in 0usize..(1 << first.len()) {
            if mask != 0 {
                let first_bit = mask.trailing_zeros() as usize;
                ok_first_mask[mask] &= first_mask[first_bit];
                ok_second_mask[mask] &= second_mask[first_bit];
            }
            if mask & ok_first_mask[mask] != mask {
                continue;
            }
            dp[ok_second_mask[mask]] += Mod::ONE;
        }
        for i in 0..second.len() {
            for mask in 0..(1 << second.len()) {
                if (1 << i) & mask != 0 {
                    let dp_mask = dp[mask];
                    dp[mask ^ (1 << i)] += dp_mask;
                }
            }
        }
        for mask in 0..(1 << second.len()) {
            let mut ok_second_mask = (1 << second.len()) - 1;
            for i in 0..second.len() {
                if (1 << i) & mask != 0 {
                    ok_second_mask &= second_mask[i + first.len()];
                }
            }
            if mask & ok_second_mask != mask {
                continue;
            }
            res += dp[mask];
        }
    }
    dbg!(res);
    res
}

fn stress() {
    for it in 1.. {
        let start = Instant::now();
        dbg!(it);
        let mut rnd = Random::new(it);
        let n = 45; //rnd.gen(1..2);
        dbg!(n * (n - 1) / 2);
        let mut m = rnd.gen(0..n * (n - 1) / 2 + 1);
        if m > 1000 {
            m = 1000;
        }
        let mut g = Array2D::new_f(n, n, |i, j| true);
        for _ in 0..m {
            let fr = rnd.gen(0..n);
            let to = rnd.gen(0..n);
            g[fr][to] = true;
            g[to][fr] = true;
        }
        let res = solve_g(&g);
        dbg!(start.elapsed());
    }
}

fn solve(input: &mut Input, _test_case: usize) {
    let n = input.usize();
    let mut g = Array2D::new_f(n, n, |i, j| i == j);
    let m = input.usize();
    for _ in 0..m {
        let fr = input.usize() - 1;
        let to = input.usize() - 1;
        g[fr][to] = true;
        g[to][fr] = true;
    }
    let res = solve_g(&g);
    out_line!(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 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)]
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 last_exn {
use std::collections::BTreeSet;

pub trait LastExn<T> {
    fn last_exn(&self) -> &T;
}

impl<T> LastExn<T> for &[T] {
    fn last_exn(&self) -> &T {
        self.last().unwrap()
    }
}

impl<T> LastExn<T> for Vec<T> {
    fn last_exn(&self) -> &T {
        self.last().unwrap()
    }
}

impl<T> LastExn<T> for BTreeSet<T> {
    fn last_exn(&self) -> &T {
        self.iter().next_back().unwrap()
    }
}
}
}
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 math {
pub mod modulo {
use crate::algo_lib::collections::last_exn::LastExn;
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::misc::num_traits::ConvSimple;
use crate::algo_lib::misc::num_traits::HasConstants;
use crate::algo_lib::misc::num_traits::Number;
use std::io::Write;
use std::marker::PhantomData;

pub trait Value: Clone + Copy + Eq + Default + Ord {
    fn val() -> i32;
}

#[derive(Copy, Clone, Eq, PartialEq, Default, Ord, PartialOrd, Hash)]
pub struct ModWithValue<M>(i32, PhantomData<M>)
where
    M: Value;

impl<M> ModWithValue<M>
where
    M: Value,
{
    #[allow(unused)]
    pub const ZERO: Self = Self(0, PhantomData);

    #[allow(unused)]
    pub const ONE: Self = Self(1, PhantomData);

    #[allow(unused)]
    pub const TWO: Self = Self(2, PhantomData);

    fn rev_rec(a: i32, m: i32) -> i32 {
        if a == 1 {
            return a;
        }
        ((1 - Self::rev_rec(m % a, a) as i64 * m as i64) / a as i64 + m as i64) as i32
    }

    #[allow(dead_code)]
    pub fn inv(self) -> Self {
        ModWithValue(Self::rev_rec(self.0, M::val()), PhantomData)
    }

    pub fn value(&self) -> i32 {
        self.0
    }

    #[allow(dead_code)]
    pub fn new<T: Number>(x: T) -> Self {
        let mut x = x.to_i32();
        if x < 0 {
            x += M::val();
            if x < 0 {
                x %= M::val();
                x += M::val();
            }
        } else if x >= M::val() {
            x -= M::val();
            if x >= M::val() {
                x %= M::val();
            }
        }
        assert!(0 <= x && x < M::val());
        Self(x, PhantomData)
    }

    pub fn pown(self, pw: usize) -> Self {
        if pw == 0 {
            Self::ONE
        } else if pw == 1 {
            self
        } else {
            let half = self.pown(pw / 2);
            let res = half * half;
            if pw % 2 == 0 {
                res
            } else {
                res * self
            }
        }
    }

    pub fn gen_powers(base: Self, n: usize) -> Vec<Self> {
        let mut res = Vec::with_capacity(n);
        res.push(Self::ONE);
        for _ in 1..n {
            res.push(*res.last_exn() * base);
        }
        res
    }
}

impl<M> std::fmt::Display for ModWithValue<M>
where
    M: Value,
{
    fn fmt(&self, f: &mut std::fmt::Formatter) -> std::fmt::Result {
        write!(f, "{}", self.0)
    }
}

impl<M> std::fmt::Debug for ModWithValue<M>
where
    M: Value + Copy + Eq,
{
    fn fmt(&self, f: &mut std::fmt::Formatter) -> std::fmt::Result {
        const MAX: i32 = 100;

        if self.0 <= MAX {
            write!(f, "{}", self.0)
        } else if self.0 >= M::val() - MAX {
            write!(f, "-{}", M::val() - self.0)
        } else {
            for denom in 1..MAX {
                let num = *self * Self(denom, PhantomData);
                if num.0 <= MAX {
                    return write!(f, "{}/{}", num.0, denom);
                } else if num.0 >= M::val() - MAX {
                    return write!(f, "-{}/{}", M::val() - num.0, denom);
                }
            }
            write!(f, "(?? {} ??)", self.0)
        }
    }
}

impl<M> std::ops::Add for ModWithValue<M>
where
    M: Value,
{
    type Output = Self;

    fn add(self, rhs: Self) -> Self::Output {
        let res = self.0 + rhs.0;
        if res >= M::val() {
            ModWithValue(res - M::val(), PhantomData)
        } else {
            ModWithValue(res, PhantomData)
        }
    }
}

impl<M> std::ops::AddAssign for ModWithValue<M>
where
    M: Value,
{
    fn add_assign(&mut self, rhs: Self) {
        self.0 += rhs.0;
        if self.0 >= M::val() {
            self.0 -= M::val();
        }
    }
}

impl<M> std::ops::Sub for ModWithValue<M>
where
    M: Value,
{
    type Output = Self;

    fn sub(self, rhs: Self) -> Self::Output {
        let res = self.0 - rhs.0;
        if res < 0 {
            ModWithValue(res + M::val(), PhantomData)
        } else {
            ModWithValue(res, PhantomData)
        }
    }
}

impl<M> std::ops::SubAssign for ModWithValue<M>
where
    M: Value,
{
    fn sub_assign(&mut self, rhs: Self) {
        self.0 -= rhs.0;
        if self.0 < 0 {
            self.0 += M::val();
        }
    }
}

impl<M> std::ops::Mul for ModWithValue<M>
where
    M: Value,
{
    type Output = Self;

    fn mul(self, rhs: Self) -> Self::Output {
        let res = (self.0 as i64) * (rhs.0 as i64) % (M::val() as i64);
        ModWithValue(res as i32, PhantomData)
    }
}

impl<M> std::ops::MulAssign for ModWithValue<M>
where
    M: Value,
{
    fn mul_assign(&mut self, rhs: Self) {
        self.0 = ((self.0 as i64) * (rhs.0 as i64) % (M::val() as i64)) as i32;
    }
}

impl<M> std::ops::Div for ModWithValue<M>
where
    M: Value,
{
    type Output = Self;

    #[allow(clippy::suspicious_arithmetic_impl)]
    fn div(self, rhs: Self) -> Self::Output {
        let rhs_inv = rhs.inv();
        self * rhs_inv
    }
}

impl<M> std::ops::DivAssign for ModWithValue<M>
where
    M: Value,
{
    #[allow(clippy::suspicious_op_assign_impl)]
    fn div_assign(&mut self, rhs: Self) {
        *self *= rhs.inv();
    }
}

impl<M> Writable for ModWithValue<M>
where
    M: Value,
{
    fn write(&self, output: &mut Output) {
        output.write_fmt(format_args!("{}", self.0)).unwrap();
    }
}

impl<M> Readable for ModWithValue<M>
where
    M: Value,
{
    fn read(input: &mut Input) -> Self {
        let i32 = input.i32();
        Self::new(i32)
    }
}

impl<M> HasConstants<ModWithValue<M>> for ModWithValue<M>
where
    M: Value,
{
    // This doesn't make much sense, but hope we never use
    const MAX: ModWithValue<M> = ModWithValue::ZERO;
    const MIN: ModWithValue<M> = ModWithValue::ZERO;
    const ZERO: ModWithValue<M> = ModWithValue::ZERO;
    const ONE: ModWithValue<M> = ModWithValue::ONE;
    const TWO: ModWithValue<M> = ModWithValue::TWO;
}

impl<M> ConvSimple<ModWithValue<M>> for ModWithValue<M>
where
    M: Value,
{
    fn from_i32(val: i32) -> ModWithValue<M> {
        ModWithValue::new(val)
    }

    fn to_i32(self) -> i32 {
        self.0
    }

    fn to_f64(self) -> f64 {
        self.0 as f64
    }
}

pub trait ConstValue: Value + Copy {
    const VAL: i32;
}

impl<V: ConstValue> Value for V {
    fn val() -> i32 {
        Self::VAL
    }
}

#[derive(Copy, Clone, Eq, PartialEq, Default, Ord, PartialOrd, Hash)]
pub struct Value7();
impl ConstValue for Value7 {
    const VAL: i32 = 1_000_000_007;
}
pub type Mod7 = ModWithValue<Value7>;

#[derive(Copy, Clone, Eq, PartialEq, Default, Ord, PartialOrd, Hash)]
pub struct Value9();
impl ConstValue for Value9 {
    const VAL: i32 = 1_000_000_009;
}
pub type Mod9 = ModWithValue<Value9>;

#[derive(Copy, Clone, Eq, PartialEq, Default, Ord, PartialOrd, Hash)]
#[allow(non_camel_case_types)]
pub struct Value_998_244_353();
impl ConstValue for Value_998_244_353 {
    const VAL: i32 = 998_244_353;
}
#[allow(non_camel_case_types)]
pub type Mod_998_244_353 = ModWithValue<Value_998_244_353>;

pub trait ModuloTrait: Number {
    fn mod_value() -> i32;
    fn pown(self, n: usize) -> Self;
}

impl<V: Value> ModuloTrait for ModWithValue<V> {
    fn mod_value() -> i32 {
        V::val()
    }

    fn pown(self, n: usize) -> Self {
        self.pown(n)
    }
}
}
}
pub mod misc {
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
    }
}
}
}
}
fn main() {
    crate::solution::submit();
}