// 
pub mod solution {

use crate::io::input::Input;
use crate::io::output::Output;
use crate::misc::memo::memoization_2d::Memoization2d;
use crate::misc::recursive_function::Callable2;
use crate::numbers::mod_int::ModIntF;
use crate::numbers::num_traits::zero_one::ZeroOne;

type PreCalc = ();

fn solve(input: &mut Input, out: &mut Output, _test_case: usize, _data: &PreCalc) {
    let n = input.read_size();
    let a = input.read_size_vec(n);

    let mut v = Vec::new();
    let mut start = Vec::with_capacity(n);
    for (i, &a) in a.iter().enumerate() {
        start.push(v.len());
        for _ in 0..a {
            v.push(i);
        }
    }
    start.push(v.len());
    v.push(n);
    type Mod = ModIntF;
    let mut mem = Memoization2d::new(v.len(), v.len(), |mem, at, free| {
        if at == 0 && free == 0 {
            return Mod::one();
        }
        let mut res = Mod::zero();
        if free > 0 {
            res += mem.call(at, free - 1);
        }
        if at > 0 && v[at - 1] == v[at] {
            res += mem.call(at - 1, free);
        }
        for i in 0..v[at] {
            if a[i] == 0 {
                continue;
            }
            res += mem.call(start[i + 1] - 1, free + at - start[i + 1]);
        }
        res
    });
    out.print_line(mem.call(v.len() - 1, 0))
}

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

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

}
pub mod collections {
pub mod md_arr {
pub mod arr2d {
use crate::collections::slice_ext::legacy_fill::LegacyFill;
use crate::io::input::{Input, Readable};
use crate::io::output::{Output, Writable};
use std::ops::{Index, IndexMut, 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
    }
}

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 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 io {
pub mod input {
use crate::collections::vec_ext::default::default_vec;
use std::io::Read;

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

macro_rules! read_impl {
    ($t: ty, $read_name: ident, $read_vec_name: ident) => {
        pub fn $read_name(&mut self) -> $t {
            self.read()
        }

        pub fn $read_vec_name(&mut self, len: usize) -> Vec<$t> {
            self.read_vec(len)
        }
    };

    ($t: ty, $read_name: ident, $read_vec_name: ident, $read_pair_vec_name: ident) => {
        read_impl!($t, $read_name, $read_vec_name);

        pub fn $read_pair_vec_name(&mut self, len: usize) -> Vec<($t, $t)> {
            self.read_vec(len)
        }
    };
}

impl<'s> Input<'s> {
    const DEFAULT_BUF_SIZE: usize = 4096;

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

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

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

    pub fn peek(&mut self) -> Option<u8> {
        if self.refill_buffer() {
            let res = self.buf[self.at];
            Some(if res == b'\r' { b'\n' } else { res })
        } else {
            None
        }
    }

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

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

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

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

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

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

    read_impl!(u32, read_unsigned, read_unsigned_vec);
    read_impl!(u64, read_u64, read_u64_vec);
    read_impl!(usize, read_size, read_size_vec, read_size_pair_vec);
    read_impl!(i32, read_int, read_int_vec, read_int_pair_vec);
    read_impl!(i64, read_long, read_long_vec, read_long_pair_vec);
    read_impl!(i128, read_i128, read_i128_vec);

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

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

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

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

macro_rules! read_integer {
    ($($t:ident)+) => {$(
        impl Readable for $t {
            fn read(input: &mut Input) -> Self {
                input.skip_whitespace();
                let mut c = input.get().unwrap();
                let sgn = match c {
                    b'-' => {
                        c = input.get().unwrap();
                        true
                    }
                    b'+' => {
                        c = input.get().unwrap();
                        false
                    }
                    _ => false,
                };
                let mut res = 0;
                loop {
                    assert!(c.is_ascii_digit());
                    res *= 10;
                    let d = (c - b'0') as $t;
                    if sgn {
                        res -= d;
                    } else {
                        res += d;
                    }
                    match input.get() {
                        None => break,
                        Some(ch) => {
                            if ch.is_ascii_whitespace() {
                                break;
                            } else {
                                c = ch;
                            }
                        }
                    }
                }
                res
            }
        }
    )+};
}

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

macro_rules! tuple_readable {
    ($($name:ident)+) => {
        impl<$($name: Readable), +> Readable for ($($name,)+) {
            fn read(input: &mut Input) -> Self {
                ($($name::read(input),)+)
            }
        }
    }
}

tuple_readable! {T}
tuple_readable! {T U}
tuple_readable! {T U V}
tuple_readable! {T U V X}
tuple_readable! {T U V X Y}
tuple_readable! {T U V X Y Z}
tuple_readable! {T U V X Y Z A}
tuple_readable! {T U V X Y Z A B}
tuple_readable! {T U V X Y Z A B C}
tuple_readable! {T U V X Y Z A B C D}
tuple_readable! {T U V X Y Z A B C D E}
tuple_readable! {T U V X Y Z A B C D E F}

impl Read for Input<'_> {
    fn read(&mut self, buf: &mut [u8]) -> std::io::Result<usize> {
        if self.at == self.buf_read {
            self.input.read(buf)
        } else {
            let mut i = 0;
            while i < buf.len() && self.at < self.buf_read {
                buf[i] = self.buf[self.at];
                i += 1;
                self.at += 1;
            }
            Ok(i)
        }
    }
}
}
pub mod output {
use crate::collections::vec_ext::default::default_vec;
use std::io::{stderr, Stderr, Write};

#[derive(Copy, Clone)]
pub enum BoolOutput {
    YesNo,
    YesNoCaps,
    PossibleImpossible,
    Custom(&'static str, &'static str),
}

impl BoolOutput {
    pub fn output(&self, output: &mut Output, val: bool) {
        (if val { self.yes() } else { self.no() }).write(output);
    }

    fn yes(&self) -> &str {
        match self {
            BoolOutput::YesNo => "Yes",
            BoolOutput::YesNoCaps => "YES",
            BoolOutput::PossibleImpossible => "Possible",
            BoolOutput::Custom(yes, _) => yes,
        }
    }

    fn no(&self) -> &str {
        match self {
            BoolOutput::YesNo => "No",
            BoolOutput::YesNoCaps => "NO",
            BoolOutput::PossibleImpossible => "Impossible",
            BoolOutput::Custom(_, no) => no,
        }
    }
}

pub struct Output<'s> {
    output: &'s mut dyn Write,
    buf: Vec<u8>,
    at: usize,
    auto_flush: bool,
    bool_output: BoolOutput,
}

impl<'s> Output<'s> {
    const DEFAULT_BUF_SIZE: usize = 4096;

    pub fn new(output: &'s mut dyn Write) -> Self {
        Self {
            output,
            buf: default_vec(Self::DEFAULT_BUF_SIZE),
            at: 0,
            auto_flush: false,
            bool_output: BoolOutput::YesNoCaps,
        }
    }

    pub fn new_with_auto_flush(output: &'s mut dyn Write) -> Self {
        Self {
            output,
            buf: default_vec(Self::DEFAULT_BUF_SIZE),
            at: 0,
            auto_flush: true,
            bool_output: BoolOutput::YesNoCaps,
        }
    }

    pub fn flush(&mut self) {
        if self.at != 0 {
            self.output.write_all(&self.buf[..self.at]).unwrap();
            self.output.flush().unwrap();
            self.at = 0;
        }
    }

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

    pub fn print_line<T: Writable>(&mut self, s: T) {
        self.print(s);
        self.put(b'\n');
        self.maybe_flush();
    }

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

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

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

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

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

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

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

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

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

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

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

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

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

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

impl<T: Writable> Writable for &T {
    fn write(&self, output: &mut Output) {
        T::write(self, output)
    }
}

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

impl Writable for () {
    fn write(&self, _output: &mut Output) {}
}

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

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

macro_rules! tuple_writable {
    ($name0:ident $($name:ident: $id:tt )*) => {
        impl<$name0: Writable, $($name: Writable,)*> Writable for ($name0, $($name,)*) {
            fn write(&self, out: &mut Output) {
                self.0.write(out);
                $(
                out.put(b' ');
                self.$id.write(out);
                )*
            }
        }
    }
}

tuple_writable! {T}
tuple_writable! {T U:1}
tuple_writable! {T U:1 V:2}
tuple_writable! {T U:1 V:2 X:3}
tuple_writable! {T U:1 V:2 X:3 Y:4}
tuple_writable! {T U:1 V:2 X:3 Y:4 Z:5}
tuple_writable! {T U:1 V:2 X:3 Y:4 Z:5 A:6}
tuple_writable! {T U:1 V:2 X:3 Y:4 Z:5 A:6 B:7}

impl<T: Writable> Writable for Option<T> {
    fn write(&self, output: &mut Output) {
        match self {
            None => (-1).write(output),
            Some(t) => t.write(output),
        }
    }
}

impl Writable for bool {
    fn write(&self, output: &mut Output) {
        let bool_output = output.bool_output;
        bool_output.output(output, *self)
    }
}

static mut ERR: Option<Stderr> = None;
pub fn err() -> Output<'static> {
    unsafe {
        if ERR.is_none() {
            ERR = Some(stderr());
        }
        Output::new_with_auto_flush(ERR.as_mut().unwrap())
    }
}
}
}
pub mod misc {
pub mod memo {
pub mod memoization_2d {
use crate::collections::md_arr::arr2d::Arr2d;
use crate::misc::recursive_function::Callable2;

pub struct Memoization2d<F, Output>
where
    F: FnMut(&mut dyn Callable2<usize, usize, Output>, usize, usize) -> Output,
{
    f: std::cell::UnsafeCell<F>,
    res: Arr2d<Option<Output>>,
}

impl<F, Output: Clone> Memoization2d<F, Output>
where
    F: FnMut(&mut dyn Callable2<usize, usize, Output>, usize, usize) -> Output,
{
    pub fn new(d1: usize, d2: usize, f: F) -> Self {
        Self {
            f: std::cell::UnsafeCell::new(f),
            res: Arr2d::new(d1, d2, None),
        }
    }
}

impl<F, Output: Clone> Callable2<usize, usize, Output> for Memoization2d<F, Output>
where
    F: FnMut(&mut dyn Callable2<usize, usize, Output>, usize, usize) -> Output,
{
    fn call(&mut self, n: usize, m: usize) -> Output {
        match self.res[(n, m)].as_ref() {
            None => {
                let res = unsafe { (*self.f.get())(self, n, m) };
                self.res[(n, m)] = Some(res.clone());
                res
            }
            Some(res) => res.clone(),
        }
    }
}
}
}
pub mod recursive_function {
use std::marker::PhantomData;

macro_rules! recursive_function {
    ($name: ident, $trait: ident, ($($type: ident $arg: ident,)*)) => {
        pub trait $trait<$($type, )*Output> {
            fn call(&mut self, $($arg: $type,)*) -> Output;
        }

        pub struct $name<F, $($type, )*Output>
        where
            F: FnMut(&mut dyn $trait<$($type, )*Output>, $($type, )*) -> Output,
        {
            f: std::cell::UnsafeCell<F>,
            $($arg: PhantomData<$type>,
            )*
            phantom_output: PhantomData<Output>,
        }

        impl<F, $($type, )*Output> $name<F, $($type, )*Output>
        where
            F: FnMut(&mut dyn $trait<$($type, )*Output>, $($type, )*) -> Output,
        {
            pub fn new(f: F) -> Self {
                Self {
                    f: std::cell::UnsafeCell::new(f),
                    $($arg: Default::default(),
                    )*
                    phantom_output: Default::default(),
                }
            }
        }

        impl<F, $($type, )*Output> $trait<$($type, )*Output> for $name<F, $($type, )*Output>
        where
            F: FnMut(&mut dyn $trait<$($type, )*Output>, $($type, )*) -> Output,
        {
            fn call(&mut self, $($arg: $type,)*) -> Output {
                unsafe { (*self.f.get())(self, $($arg, )*) }
            }
        }
    }
}

recursive_function!(RecursiveFunction0, Callable0, ());
recursive_function!(RecursiveFunction, Callable, (Arg arg,));
recursive_function!(RecursiveFunction2, Callable2, (Arg1 arg1, Arg2 arg2,));
recursive_function!(RecursiveFunction3, Callable3, (Arg1 arg1, Arg2 arg2, Arg3 arg3,));
recursive_function!(RecursiveFunction4, Callable4, (Arg1 arg1, Arg2 arg2, Arg3 arg3, Arg4 arg4,));
recursive_function!(RecursiveFunction5, Callable5, (Arg1 arg1, Arg2 arg2, Arg3 arg3, Arg4 arg4, Arg5 arg5,));
recursive_function!(RecursiveFunction6, Callable6, (Arg1 arg1, Arg2 arg2, Arg3 arg3, Arg4 arg4, Arg5 arg5, Arg6 arg6,));
recursive_function!(RecursiveFunction7, Callable7, (Arg1 arg1, Arg2 arg2, Arg3 arg3, Arg4 arg4, Arg5 arg5, Arg6 arg6, Arg7 arg7,));
recursive_function!(RecursiveFunction8, Callable8, (Arg1 arg1, Arg2 arg2, Arg3 arg3, Arg4 arg4, Arg5 arg5, Arg6 arg6, Arg7 arg7, Arg8 arg8,));
recursive_function!(RecursiveFunction9, Callable9, (Arg1 arg1, Arg2 arg2, Arg3 arg3, Arg4 arg4, Arg5 arg5, Arg6 arg6, Arg7 arg7, Arg8 arg8, Arg9 arg9,));
}
pub mod value {
use std::hash::Hash;

pub trait Value<T>: Copy + Eq + Hash {
    fn val() -> T;
}

pub trait ConstValue<T>: Value<T> {
    const VAL: T;
}

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

#[macro_export]
macro_rules! value {
    ($name: ident: $t: ty = $val: expr) => {
        #[derive(Copy, Clone, Eq, PartialEq, Hash, Ord, PartialOrd, Default)]
        pub struct $name {}

        impl $crate::misc::value::ConstValue<$t> for $name {
            const VAL: $t = $val;
        }
    };
}

pub trait DynamicValue<T>: Value<T> {
    //noinspection RsSelfConvention
    fn set_val(t: T);
}

#[macro_export]
macro_rules! dynamic_value {
    ($name: ident: $t: ty) => {
        static mut VAL: Option<$t> = None;

        #[derive(Copy, Clone, Eq, PartialEq, Hash, Default)]
        struct $name {}

        impl $crate::misc::value::DynamicValue<$t> for $name {
            fn set_val(t: $t) {
                unsafe {
                    VAL = Some(t);
                }
            }
        }

        impl $crate::misc::value::Value<$t> for $name {
            fn val() -> $t {
                unsafe { VAL.unwrap() }
            }
        }
    };
    ($name: ident: $t: ty = $val: expr) => {
        dynamic_value!($name: $t);

        $name::set_val($val);
    };
}
}
pub mod when {
#[macro_export]
macro_rules! when {
    {$($cond: expr => $then: expr,)*} => {
        match () {
            $(_ if $cond => $then,)*
            _ => unreachable!(),
        }
    };
    {$($cond: expr => $then: expr,)* else $(=>)? $else: expr,} => {
        match () {
            $(_ if $cond => $then,)*
            _ => $else,
        }
    };
}
}
}
pub mod numbers {
pub mod gcd {
use crate::numbers::num_traits::add_sub::AddSub;
use crate::numbers::num_traits::mul_div_rem::{MulDivRem, Multable};
use crate::numbers::num_traits::wideable::Wideable;
use crate::numbers::num_traits::zero_one::ZeroOne;
use std::mem::swap;

pub fn extended_gcd<T: Copy + ZeroOne + AddSub + MulDivRem + Wideable + PartialEq>(
    a: T,
    b: T,
) -> (T, T::W, T::W)
where
    T::W: Copy + ZeroOne + AddSub + Multable,
{
    if a == T::zero() {
        (b, T::W::zero(), T::W::one())
    } else {
        let (d, y, mut x) = extended_gcd(b % a, a);
        x -= T::W::from(b / a) * y;
        (d, x, y)
    }
}

pub fn gcd<T: Copy + ZeroOne + MulDivRem + PartialEq>(mut a: T, mut b: T) -> T {
    while b != T::zero() {
        a %= b;
        swap(&mut a, &mut b);
    }
    a
}

pub fn lcm<T: Copy + ZeroOne + MulDivRem + PartialEq>(a: T, b: T) -> T {
    (a / gcd(a, b)) * b
}
}
pub mod mod_int {
use crate::io::input::{Input, Readable};
use crate::io::output::{Output, Writable};
use crate::misc::value::Value;
use crate::numbers::gcd::extended_gcd;
use crate::numbers::num_traits::add_sub::AddSub;
use crate::numbers::num_traits::as_index::AsIndex;
use crate::numbers::num_traits::from_u8::FromU8;
use crate::numbers::num_traits::invertable::Invertable;
use crate::numbers::num_traits::mul_div_rem::{MulDiv, MulDivRem};
use crate::numbers::num_traits::wideable::Wideable;
use crate::numbers::num_traits::zero_one::ZeroOne;
use crate::{value, when};
use std::collections::HashMap;
use std::fmt::{Display, Formatter};
use std::hash::Hash;
use std::marker::PhantomData;
use std::ops::{Add, AddAssign, Div, DivAssign, Mul, MulAssign, Neg, Sub, SubAssign};

pub trait BaseModInt:
    AddSub + MulDiv + Neg<Output = Self> + Copy + ZeroOne + PartialEq + Invertable<Output = Self>
{
    type W: AddSub + MulDivRem + Copy + ZeroOne + From<Self::T>;
    type T: AddSub + MulDivRem + Copy + PartialEq + ZeroOne + Wideable<W = Self::W> + Ord;

    fn from(v: Self::T) -> Self;
    fn module() -> Self::T;
}

#[derive(Copy, Clone, Eq, PartialEq, Hash, Default)]
pub struct ModInt<T, V: Value<T>> {
    n: T,
    phantom: PhantomData<V>,
}

impl<T: Copy, V: Value<T>> ModInt<T, V> {
    pub fn val(&self) -> T {
        self.n
    }
}

impl<T: AddSub + Copy + ZeroOne + Ord, V: Value<T>> ModInt<T, V> {
    unsafe fn unchecked_new(n: T) -> Self {
        debug_assert!(n >= T::zero() && n < V::val());
        Self {
            n,
            phantom: Default::default(),
        }
    }

    unsafe fn maybe_subtract_mod(mut n: T) -> T {
        debug_assert!(n < V::val() + V::val() && n >= T::zero());
        if n >= V::val() {
            n -= V::val();
        }
        n
    }
}

impl<T: AddSub + Copy + ZeroOne + Ord + MulDivRem, V: Value<T>> ModInt<T, V> {
    pub fn new(n: T) -> Self {
        unsafe { Self::unchecked_new(Self::maybe_subtract_mod(n % (V::val()) + V::val())) }
    }
}

impl<T: Copy + ZeroOne + AddSub + MulDivRem + Wideable + PartialEq + Ord + Hash, V: Value<T>>
    ModInt<T, V>
where
    T::W: Copy + ZeroOne + AddSub + MulDivRem,
{
    pub fn log(&self, alpha: Self) -> T {
        let mut base = HashMap::new();
        let mut exp = T::zero();
        let mut pow = Self::one();
        let mut inv = *self;
        let alpha_inv = alpha.inv().unwrap();
        while exp * exp < Self::module() {
            if inv == Self::one() {
                return exp;
            }
            base.insert(inv, exp);
            exp += T::one();
            pow *= alpha;
            inv *= alpha_inv;
        }
        let step = pow;
        let mut i = T::one();
        loop {
            if let Some(b) = base.get(&pow) {
                break exp * i + *b;
            }
            pow *= step;
            i += T::one();
        }
    }
}

impl<T: Wideable + AddSub + Copy + ZeroOne + Ord, V: Value<T>> ModInt<T, V>
where
    T::W: MulDivRem,
{
    pub fn new_from_wide(n: T::W) -> Self {
        unsafe {
            Self::unchecked_new(Self::maybe_subtract_mod(
                T::downcast(n % (V::val()).into()) + V::val(),
            ))
        }
    }
}

impl<T: Copy + ZeroOne + AddSub + MulDivRem + Wideable + PartialEq + Ord, V: Value<T>> Invertable
    for ModInt<T, V>
where
    T::W: Copy + ZeroOne + AddSub + MulDivRem,
{
    type Output = Self;

    fn inv(&self) -> Option<Self> {
        let (g, x, _) = extended_gcd(self.n, V::val());
        if g != T::one() {
            None
        } else {
            Some(Self::new_from_wide(x))
        }
    }
}

impl<T: AddSub + MulDivRem + Copy + PartialEq + Wideable + ZeroOne + Ord, V: Value<T>> BaseModInt
    for ModInt<T, V>
where
    T::W: AddSub + MulDivRem + Copy + ZeroOne,
{
    type W = T::W;
    type T = T;

    fn from(v: Self::T) -> Self {
        Self::new(v)
    }

    fn module() -> T {
        V::val()
    }
}

impl<T: AddSub + Copy + ZeroOne + Ord + MulDivRem, V: Value<T>> From<T> for ModInt<T, V> {
    fn from(n: T) -> Self {
        Self::new(n)
    }
}

impl<T: AddSub + Copy + ZeroOne + Ord, V: Value<T>> AddAssign for ModInt<T, V> {
    fn add_assign(&mut self, rhs: Self) {
        self.n = unsafe { Self::maybe_subtract_mod(self.n + rhs.n) };
    }
}

impl<T: AddSub + Copy + ZeroOne + Ord, V: Value<T>> Add for ModInt<T, V> {
    type Output = Self;

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

impl<T: AddSub + Copy + ZeroOne + Ord, V: Value<T>> SubAssign for ModInt<T, V> {
    fn sub_assign(&mut self, rhs: Self) {
        self.n = unsafe { Self::maybe_subtract_mod(self.n + V::val() - rhs.n) };
    }
}

impl<T: AddSub + Copy + ZeroOne + Ord, V: Value<T>> Sub for ModInt<T, V> {
    type Output = Self;

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

impl<T: AddSub + MulDivRem + Copy + Wideable + ZeroOne + Ord, V: Value<T>> MulAssign
    for ModInt<T, V>
where
    T::W: MulDivRem + Copy,
{
    fn mul_assign(&mut self, rhs: Self) {
        self.n = T::downcast(T::W::from(self.n) * T::W::from(rhs.n) % T::W::from(V::val()));
    }
}

impl<T: AddSub + MulDivRem + Copy + Wideable + ZeroOne + Ord, V: Value<T>> Mul for ModInt<T, V>
where
    T::W: MulDivRem + Copy,
{
    type Output = Self;

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

impl<T: AddSub + MulDivRem + Copy + PartialEq + Wideable + ZeroOne + Ord, V: Value<T>> DivAssign
    for ModInt<T, V>
where
    T::W: AddSub + MulDivRem + Copy + ZeroOne,
{
    #[allow(clippy::suspicious_op_assign_impl)]
    fn div_assign(&mut self, rhs: Self) {
        *self *= rhs.inv().unwrap();
    }
}

impl<T: AddSub + MulDivRem + Copy + PartialEq + Wideable + ZeroOne + Ord, V: Value<T>> Div
    for ModInt<T, V>
where
    T::W: AddSub + MulDivRem + Copy + ZeroOne,
{
    type Output = Self;

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

impl<T: AddSub + Copy + ZeroOne + Ord, V: Value<T>> Neg for ModInt<T, V> {
    type Output = Self;

    fn neg(mut self) -> Self::Output {
        self.n = unsafe { Self::maybe_subtract_mod(V::val() - self.n) };
        self
    }
}

impl<T: Display, V: Value<T>> Display for ModInt<T, V> {
    fn fmt(&self, f: &mut Formatter<'_>) -> std::fmt::Result {
        <T as Display>::fmt(&self.n, f)
    }
}

impl<T: AddSub + Copy + ZeroOne + Ord + MulDivRem + Readable, V: Value<T>> Readable
    for ModInt<T, V>
{
    fn read(input: &mut Input) -> Self {
        Self::new(T::read(input))
    }
}

impl<T: Writable, V: Value<T>> Writable for ModInt<T, V> {
    fn write(&self, output: &mut Output) {
        self.n.write(output);
    }
}

impl<T: ZeroOne + MulDivRem + AddSub + Copy + Ord, V: Value<T>> ZeroOne for ModInt<T, V> {
    fn zero() -> Self {
        unsafe { Self::unchecked_new(T::zero()) }
    }

    fn one() -> Self {
        Self::new(T::one())
    }
}

impl<T, V: Value<T>> Wideable for ModInt<T, V> {
    type W = Self;

    fn downcast(w: Self::W) -> Self {
        w
    }
}

impl<T: AddSub + Copy + ZeroOne + Ord + MulDivRem + FromU8, V: Value<T>> FromU8 for ModInt<T, V> {
    fn from_u8(n: u8) -> Self {
        Self::new(T::from_u8(n))
    }
}

impl<
        T: AddSub + MulDivRem + Copy + PartialEq + Wideable + ZeroOne + Ord + Display + FromU8,
        V: Value<T>,
    > std::fmt::Debug for ModInt<T, V>
where
    T::W: AddSub + MulDivRem + Copy + ZeroOne,
{
    fn fmt(&self, f: &mut std::fmt::Formatter) -> std::fmt::Result {
        let max = T::from_u8(100);
        when! {
            self.n <= max => write!(f, "{}", self.n),
            self.n >= V::val() - max => write!(f, "{}", self.n - V::val()),
            else => {
                let mut denominator = T::one();
                while denominator < max {
                    let mut num = T::one();
                    while num < max {
                        if Self::new(num) / Self::new(denominator) == *self {
                            return write!(f, "{}/{}", num, denominator);
                        }
                        if -Self::new(num) / Self::new(denominator) == *self {
                            return write!(f, "-{}/{}", num, denominator);
                        }
                        num += T::one();
                    }
                    denominator += T::one();
                }
                write!(f, "(?? {} ??)", self.n)
            },
        }
    }
}

impl<T: AddSub + Copy + ZeroOne + Ord + MulDivRem + AsIndex, V: Value<T>> AsIndex for ModInt<T, V> {
    fn from_index(idx: usize) -> Self {
        Self::new(T::from_index(idx))
    }

    fn to_index(self) -> usize {
        self.n.to_index()
    }
}

value!(Val7: i32 = 1_000_000_007);
pub type ModInt7 = ModInt<i32, Val7>;

value!(Val9: i32 = 1_000_000_009);
pub type ModInt9 = ModInt<i32, Val9>;

value!(ValF: i32 = 998_244_353);
pub type ModIntF = ModInt<i32, ValF>;
}
pub mod num_traits {
pub mod add_sub {
use std::ops::{Add, AddAssign, Sub, SubAssign};

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

pub trait AddSub: Addable + Sub<Output = Self> + SubAssign {}
impl<T: Addable + Sub<Output = Self> + SubAssign> AddSub for T {}
}
pub mod as_index {
pub trait AsIndex {
    fn from_index(idx: usize) -> Self;
    fn to_index(self) -> usize;
}

macro_rules! from_index_impl {
    ($($t: ident)+) => {$(
        impl AsIndex for $t {
            fn from_index(idx: usize) -> Self {
                idx as $t
            }

            fn to_index(self) -> usize {
                self as usize
            }
        }
    )+};
}

from_index_impl!(i128 i64 i32 i16 i8 isize u128 u64 u32 u16 u8 usize);
}
pub mod from_u8 {
pub trait FromU8 {
    fn from_u8(val: u8) -> Self;
}

macro_rules! from_u8_impl {
    ($($t: ident)+) => {$(
        impl FromU8 for $t {
            fn from_u8(val: u8) -> Self {
                val as $t
            }
        }
    )+};
}

from_u8_impl!(i128 i64 i32 i16 i8 isize u128 u64 u32 u16 u8 usize);
}
pub mod invertable {
pub trait Invertable: Sized {
    type Output;

    fn inv(&self) -> Option<Self>;
}
}
pub mod mul_div_rem {
use std::ops::{Div, DivAssign, Mul, MulAssign, Rem, RemAssign};

pub trait Multable: Mul<Output = Self> + MulAssign + Copy {}
impl<T: Mul<Output = Self> + MulAssign + Copy> Multable for T {}

pub trait MulDiv: Multable + Div<Output = Self> + DivAssign {}
impl<T: Multable + Div<Output = Self> + DivAssign> MulDiv for T {}

pub trait MulDivRem: MulDiv + Rem<Output = Self> + RemAssign {}
impl<T: MulDiv + Rem<Output = Self> + RemAssign> MulDivRem for T {}
}
pub mod wideable {
use std::convert::From;

pub trait Wideable: Sized {
    type W: From<Self>;

    fn downcast(w: Self::W) -> Self;
}

macro_rules! wideable_impl {
    ($($t: ident $w: ident),+) => {$(
        impl Wideable for $t {
            type W = $w;

            fn downcast(w: Self::W) -> Self {
                w as $t
            }
        }
    )+};
}

wideable_impl!(i128 i128, i64 i128, i32 i64, i16 i32, i8 i16, isize isize, u128 u128, u64 u128, u32 u64, u16 u32, u8 u16, usize usize);
}
pub mod zero_one {
pub trait ZeroOne {
    fn zero() -> Self;
    fn one() -> Self;
}

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

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

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

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

    solution::run(input, output);
}