pub trait IterScan: Sized {
    type Output;
    fn scan<'a, I: Iterator<Item = &'a str>>(iter: &mut I) -> Option<Self::Output>;
}
pub trait MarkedIterScan: Sized {
    type Output;
    fn mscan<'a, I: Iterator<Item = &'a str>>(self, iter: &mut I) -> Option<Self::Output>;
}
#[derive(Debug)]
pub struct Scanner<'a> {
    iter: std::str::SplitAsciiWhitespace<'a>,
}
impl<'a> Scanner<'a> {
    #[inline]
    pub fn new(s: &'a str) -> Self {
        let iter = s.split_ascii_whitespace();
        Self { iter }
    }
    #[inline]
    pub fn scan<T: IterScan>(&mut self) -> <T as IterScan>::Output {
        T::scan(&mut self.iter).unwrap()
    }
    #[inline]
    pub fn mscan<T: MarkedIterScan>(&mut self, marker: T) -> <T as MarkedIterScan>::Output {
        marker.mscan(&mut self.iter).unwrap()
    }
    #[inline]
    pub fn scan_vec<T: IterScan>(&mut self, size: usize) -> Vec<<T as IterScan>::Output> {
        (0..size)
            .map(|_| T::scan(&mut self.iter).unwrap())
            .collect()
    }
    #[inline]
    pub fn scan_chars(&mut self) -> Vec<char> {
        self.iter.next().unwrap().chars().collect::<Vec<char>>()
    }
}
mod scanner_impls {
    use super::*;
    macro_rules !iter_scan_impls {($($t :ty ) *) =>{$(impl IterScan for $t {type Output =Self ;#[inline ] fn scan <'a ,I :Iterator <Item =&'a str >>(iter :&mut I ) ->Option <Self >{iter .next () ?.parse ::<$t >() .ok () } } ) *} ;}
    iter_scan_impls !(char u8 u16 u32 u64 usize i8 i16 i32 i64 isize f32 f64 u128 i128 String ) ;
    macro_rules !iter_scan_tuple_impl {($($T :ident ) *) =>{impl <$($T :IterScan ) ,*>IterScan for ($($T ,) *) {type Output =($(<$T as IterScan >::Output ,) *) ;#[inline ] fn scan <'a ,It :Iterator <Item =&'a str >>(_iter :&mut It ) ->Option <Self ::Output >{Some (($($T ::scan (_iter ) ?,) *) ) } } } ;}
    iter_scan_tuple_impl!();
    iter_scan_tuple_impl!(A);
    iter_scan_tuple_impl !(A B ) ;
    iter_scan_tuple_impl !(A B C ) ;
    iter_scan_tuple_impl !(A B C D ) ;
    iter_scan_tuple_impl !(A B C D E ) ;
    iter_scan_tuple_impl !(A B C D E F ) ;
    iter_scan_tuple_impl !(A B C D E F G ) ;
    iter_scan_tuple_impl !(A B C D E F G H ) ;
    iter_scan_tuple_impl !(A B C D E F G H I ) ;
    iter_scan_tuple_impl !(A B C D E F G H I J ) ;
    iter_scan_tuple_impl !(A B C D E F G H I J K ) ;
    pub struct ScannerIter<'a, 'b, T> {
        inner: &'b mut Scanner<'a>,
        _marker: std::marker::PhantomData<fn() -> T>,
    }
    impl<'a, 'b, T: IterScan> Iterator for ScannerIter<'a, 'b, T> {
        type Item = <T as IterScan>::Output;
        fn next(&mut self) -> Option<Self::Item> {
            T::scan(&mut self.inner.iter)
        }
    }
    impl<'a> Scanner<'a> {
        #[inline]
        pub fn iter<'b, T: IterScan>(&'b mut self) -> ScannerIter<'a, 'b, T> {
            ScannerIter {
                inner: self,
                _marker: std::marker::PhantomData,
            }
        }
    }
}
mod marker {
    use super::*;
    pub struct Usize1;
    impl IterScan for Usize1 {
        type Output = usize;
        #[inline]
        fn scan<'a, I: Iterator<Item = &'a str>>(iter: &mut I) -> Option<Self::Output> {
            usize::scan(iter).map(|x| x.wrapping_sub(1))
        }
    }
    pub struct Isize1;
    impl IterScan for Isize1 {
        type Output = isize;
        #[inline]
        fn scan<'a, I: Iterator<Item = &'a str>>(iter: &mut I) -> Option<Self::Output> {
            isize::scan(iter).map(|x| x.wrapping_sub(1))
        }
    }
}
#[macro_export]
macro_rules !min {($e :expr ) =>{$e } ;($e :expr ,$($es :expr ) ,+) =>{std ::cmp ::min ($e ,min !($($es ) ,+) ) } ;}
#[macro_export]
macro_rules !chmin {($dst :expr ,$($src :expr ) ,+) =>{{let x =std ::cmp ::min ($dst ,min !($($src ) ,+) ) ;$dst =x ;} } ;}
#[macro_export]
macro_rules !max {($e :expr ) =>{$e } ;($e :expr ,$($es :expr ) ,+) =>{std ::cmp ::max ($e ,max !($($es ) ,+) ) } ;}
#[macro_export]
macro_rules !chmax {($dst :expr ,$($src :expr ) ,+) =>{{let x =std ::cmp ::max ($dst ,max !($($src ) ,+) ) ;$dst =x ;} } ;}
pub trait Modulus {
    fn get_modulus() -> u32;
    #[inline]
    fn modulo(x: u32) -> u32 {
        x % Self::get_modulus()
    }
}
#[allow(unused_macros)]
macro_rules! make_modulus {
    ($t :ident ,$e :expr ) => {
        pub struct $t {}
        impl Modulus for $t {
            #[inline]
            fn get_modulus() -> u32 {
                const MODULUS: u32 = $e;
                MODULUS
            }
        }
    };
}
#[allow(unused_macros)]
macro_rules! make_dynamic_modulus {
    ($t :ident ,$m :ident ,$e :expr ) => {
        pub struct $t {}
        static mut $m: u32 = $e;
        impl Modulus for $t {
            #[inline]
            fn get_modulus() -> u32 {
                unsafe { $m }
            }
        }
    };
}
pub mod modulus {
    use super::*;
    pub struct Modulo1000000007 {}
    impl Modulus for Modulo1000000007 {
        #[inline]
        fn get_modulus() -> u32 {
            const MODULUS: u32 = 1_000_000_007;
            MODULUS
        }
    }
    pub struct Modulo1000000009 {}
    impl Modulus for Modulo1000000009 {
        #[inline]
        fn get_modulus() -> u32 {
            const MODULUS: u32 = 1_000_000_009;
            MODULUS
        }
    }
    pub struct Modulo998244353 {}
    impl Modulus for Modulo998244353 {
        #[inline]
        fn get_modulus() -> u32 {
            const MODULUS: u32 = 998_244_353;
            MODULUS
        }
    }
    pub struct DynModulo {}
    static mut DYN_MODULUS: u32 = 1_000_000_007;
    impl Modulus for DynModulo {
        #[inline]
        fn get_modulus() -> u32 {
            unsafe { DYN_MODULUS }
        }
    }
    pub fn set_dyn_modulus(m: u32) {
        unsafe {
            DYN_MODULUS = m;
        }
    }
}
pub struct MInt<M>
where
    M: Modulus,
{
    x: u32,
    _marker: std::marker::PhantomData<fn() -> M>,
}
impl<M: Modulus> MInt<M> {
    #[inline]
    pub fn new(x: u32) -> Self {
        Self {
            x: M::modulo(x),
            _marker: std::marker::PhantomData,
        }
    }
    #[inline]
    pub fn new_unchecked(x: u32) -> Self {
        Self {
            x,
            _marker: std::marker::PhantomData,
        }
    }
    #[inline]
    pub fn inner(self) -> u32 {
        self.x
    }
    #[inline]
    pub fn one() -> Self {
        Self::new_unchecked(1)
    }
    #[inline]
    pub fn zero() -> Self {
        Self::new_unchecked(0)
    }
    #[inline]
    pub fn get_mod() -> u32 {
        M::get_modulus()
    }
    #[inline]
    pub fn pow(mut self, mut y: usize) -> Self {
        let mut x = Self::one();
        while y > 0 {
            if y & 1 == 1 {
                x *= self;
            }
            self *= self;
            y >>= 1;
        }
        x
    }
    #[inline]
    /// only prime modulus
    pub fn inv(self) -> Self {
        let mut a = self.x;
        let (mut b, mut u, mut s) = (M::get_modulus(), 1, 0);
        let k = a.trailing_zeros();
        a >>= k;
        for _ in 0..k {
            if u & 1 == 1 {
                u += M::get_modulus();
            }
            u /= 2;
        }
        while a != b {
            if b < a {
                std::mem::swap(&mut a, &mut b);
                std::mem::swap(&mut u, &mut s);
            }
            b -= a;
            if s < u {
                s += M::get_modulus();
            }
            s -= u;
            let k = b.trailing_zeros();
            b >>= k;
            for _ in 0..k {
                if s & 1 == 1 {
                    s += M::get_modulus();
                }
                s /= 2;
            }
        }
        Self::new_unchecked(s)
    }
}
mod mint_impls {
    use super::*;
    use std::{
        cmp::Ordering,
        fmt::{self, Debug},
        hash::{Hash, Hasher},
        iter::{Product, Sum},
        marker::PhantomData,
        num::ParseIntError,
        ops::{Add, AddAssign, Div, DivAssign, Mul, MulAssign, Neg, Sub, SubAssign},
        str::FromStr,
    };
    impl<M: Modulus> Clone for MInt<M> {
        #[inline]
        fn clone(&self) -> Self {
            Self {
                x: Clone::clone(&self.x),
                _marker: PhantomData,
            }
        }
    }
    impl<M: Modulus> Copy for MInt<M> {}
    impl<M: Modulus> Debug for MInt<M> {
        fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result {
            Debug::fmt(&self.x, f)
        }
    }
    impl<M: Modulus> Default for MInt<M> {
        #[inline]
        fn default() -> Self {
            Self::zero()
        }
    }
    impl<M: Modulus> PartialEq for MInt<M> {
        #[inline]
        fn eq(&self, other: &Self) -> bool {
            PartialEq::eq(&self.x, &other.x)
        }
    }
    impl<M: Modulus> PartialOrd for MInt<M> {
        #[inline]
        fn partial_cmp(&self, other: &Self) -> Option<Ordering> {
            PartialOrd::partial_cmp(&self.x, &other.x)
        }
    }
    impl<M: Modulus> Eq for MInt<M> {}
    impl<M: Modulus> Ord for MInt<M> {
        #[inline]
        fn cmp(&self, other: &Self) -> Ordering {
            Ord::cmp(&self.x, &other.x)
        }
    }
    impl<M: Modulus> Hash for MInt<M> {
        #[inline]
        fn hash<H: Hasher>(&self, state: &mut H) {
            Hash::hash(&self.x, state)
        }
    }
    impl<M: Modulus> From<u32> for MInt<M> {
        #[inline]
        fn from(x: u32) -> Self {
            Self::new(x)
        }
    }
    impl<M: Modulus> From<u64> for MInt<M> {
        #[inline]
        fn from(x: u64) -> Self {
            Self::new_unchecked((x % M::get_modulus() as u64) as u32)
        }
    }
    impl<M: Modulus> From<i32> for MInt<M> {
        #[inline]
        fn from(x: i32) -> Self {
            let x = x % M::get_modulus() as i32;
            if x < 0 {
                Self::new_unchecked((x + M::get_modulus() as i32) as u32)
            } else {
                Self::new_unchecked(x as u32)
            }
        }
    }
    impl<M: Modulus> From<i64> for MInt<M> {
        #[inline]
        fn from(x: i64) -> Self {
            let x = x % M::get_modulus() as i64;
            if x < 0 {
                Self::new_unchecked((x + M::get_modulus() as i64) as u32)
            } else {
                Self::new_unchecked(x as u32)
            }
        }
    }
    impl<M: Modulus> Add for MInt<M> {
        type Output = Self;
        #[inline]
        fn add(self, rhs: Self) -> Self::Output {
            let mut x = self.x + rhs.x;
            if x >= M::get_modulus() {
                x -= M::get_modulus();
            }
            Self::new_unchecked(x)
        }
    }
    impl<M: Modulus> Sub for MInt<M> {
        type Output = Self;
        #[inline]
        fn sub(self, rhs: Self) -> Self::Output {
            if self.x < rhs.x {
                Self::new_unchecked(self.x + M::get_modulus() - rhs.x)
            } else {
                Self::new_unchecked(self.x - rhs.x)
            }
        }
    }
    impl<M: Modulus> Mul for MInt<M> {
        type Output = Self;
        #[inline]
        fn mul(self, rhs: Self) -> Self::Output {
            Self::new_unchecked((self.x as u64 * rhs.x as u64 % M::get_modulus() as u64) as u32)
        }
    }
    impl<M: Modulus> Div for MInt<M> {
        type Output = Self;
        #[inline]
        fn div(self, rhs: Self) -> Self::Output {
            self * rhs.inv()
        }
    }
    impl<M: Modulus> Neg for MInt<M> {
        type Output = Self;
        #[inline]
        fn neg(self) -> Self::Output {
            if self.x == 0 {
                Self::zero()
            } else {
                Self::new_unchecked(M::get_modulus() - self.x)
            }
        }
    }
    impl<M: Modulus> Sum for MInt<M> {
        #[inline]
        fn sum<I: Iterator<Item = Self>>(iter: I) -> Self {
            iter.fold(Self::zero(), Add::add)
        }
    }
    impl<M: Modulus> Product for MInt<M> {
        #[inline]
        fn product<I: Iterator<Item = Self>>(iter: I) -> Self {
            iter.fold(Self::one(), Mul::mul)
        }
    }
    impl<'a, M: Modulus + 'a> Sum<&'a MInt<M>> for MInt<M> {
        #[inline]
        fn sum<I: Iterator<Item = &'a Self>>(iter: I) -> Self {
            iter.fold(Self::zero(), Add::add)
        }
    }
    impl<'a, M: Modulus + 'a> Product<&'a MInt<M>> for MInt<M> {
        #[inline]
        fn product<I: Iterator<Item = &'a Self>>(iter: I) -> Self {
            iter.fold(Self::one(), Mul::mul)
        }
    }
    impl<M: Modulus> fmt::Display for MInt<M> {
        fn fmt<'a>(&self, f: &mut fmt::Formatter<'a>) -> Result<(), fmt::Error> {
            write!(f, "{}", self.x)
        }
    }
    impl<M: Modulus> FromStr for MInt<M> {
        type Err = ParseIntError;
        #[inline]
        fn from_str(s: &str) -> Result<Self, Self::Err> {
            s.parse::<u32>().map(Self::new)
        }
    }
    macro_rules! mint_ref_binop {
        ($imp :ident ,$method :ident ,$t :ty ) => {
            impl<M: Modulus> $imp<$t> for &$t {
                type Output = <$t as $imp<$t>>::Output;
                #[inline]
                fn $method(self, other: $t) -> <$t as $imp<$t>>::Output {
                    $imp::$method(*self, other)
                }
            }
            impl<M: Modulus> $imp<&$t> for $t {
                type Output = <$t as $imp<$t>>::Output;
                #[inline]
                fn $method(self, other: &$t) -> <$t as $imp<$t>>::Output {
                    $imp::$method(self, *other)
                }
            }
            impl<M: Modulus> $imp<&$t> for &$t {
                type Output = <$t as $imp<$t>>::Output;
                #[inline]
                fn $method(self, other: &$t) -> <$t as $imp<$t>>::Output {
                    $imp::$method(*self, *other)
                }
            }
        };
    }
    mint_ref_binop!(Add, add, MInt<M>);
    mint_ref_binop!(Sub, sub, MInt<M>);
    mint_ref_binop!(Mul, mul, MInt<M>);
    mint_ref_binop!(Div, div, MInt<M>);
    macro_rules! mint_ref_unop {
        ($imp :ident ,$method :ident ,$t :ty ) => {
            impl<M: Modulus> $imp for &$t {
                type Output = <$t as $imp>::Output;
                #[inline]
                fn $method(self) -> <$t as $imp>::Output {
                    $imp::$method(*self)
                }
            }
        };
    }
    mint_ref_unop!(Neg, neg, MInt<M>);
    macro_rules! mint_ref_op_assign {
        ($imp :ident ,$method :ident ,$t :ty ,$fromimp :ident ,$frommethod :ident ) => {
            impl<M: Modulus> $imp<$t> for $t {
                #[inline]
                fn $method(&mut self, rhs: $t) {
                    *self = $fromimp::$frommethod(*self, rhs);
                }
            }
            impl<M: Modulus> $imp<&$t> for $t {
                #[inline]
                fn $method(&mut self, other: &$t) {
                    $imp::$method(self, *other);
                }
            }
        };
    }
    mint_ref_op_assign!(AddAssign, add_assign, MInt<M>, Add, add);
    mint_ref_op_assign!(SubAssign, sub_assign, MInt<M>, Sub, sub);
    mint_ref_op_assign!(MulAssign, mul_assign, MInt<M>, Mul, mul);
    mint_ref_op_assign!(DivAssign, div_assign, MInt<M>, Div, div);
}
impl<M: Modulus> IterScan for MInt<M> {
    type Output = Self;
    #[inline]
    fn scan<'a, I: Iterator<Item = &'a str>>(iter: &mut I) -> Option<Self::Output> {
        iter.next()?.parse::<MInt<M>>().ok()
    }
}
#[derive(Clone, Debug)]
pub struct BinaryIndexedTree<M: Monoid> {
    n: usize,
    bit: Vec<M::T>,
    m: M,
}
impl<M: Monoid> BinaryIndexedTree<M> {
    #[inline]
    pub fn new(n: usize, m: M) -> Self {
        let bit = vec![m.unit(); n + 1];
        Self { n, bit, m }
    }
    #[inline]
    /// fold [0, k)
    pub fn accumulate0(&self, mut k: usize) -> M::T {
        debug_assert!(k <= self.n);
        let mut res = self.m.unit();
        while k > 0 {
            res = self.m.operate(&res, &self.bit[k]);
            k -= k & !k + 1;
        }
        res
    }
    #[inline]
    /// fold [0, k]
    pub fn accumulate(&self, k: usize) -> M::T {
        self.accumulate0(k + 1)
    }
    #[inline]
    pub fn update(&mut self, k: usize, x: M::T) {
        debug_assert!(k < self.n);
        let mut k = k + 1;
        while k <= self.n {
            self.bit[k] = self.m.operate(&self.bit[k], &x);
            k += k & !k + 1;
        }
    }
}
impl<G: Group> BinaryIndexedTree<G> {
    #[inline]
    pub fn fold(&self, l: usize, r: usize) -> G::T {
        debug_assert!(l < self.n && 0 < r && r <= self.n);
        self.m
            .operate(&self.m.inverse(&self.accumulate0(l)), &self.accumulate0(r))
    }
    #[inline]
    pub fn get(&self, k: usize) -> G::T {
        self.fold(k, k + 1)
    }
    #[inline]
    pub fn set(&mut self, k: usize, x: G::T) {
        let y = self.m.inverse(&self.get(k));
        self.update(k, self.m.operate(&y, &x));
    }
}
impl<M: Monoid> BinaryIndexedTree<M>
where
    M::T: Ord,
{
    #[inline]
    pub fn lower_bound(&self, x: M::T) -> usize {
        let n = self.n;
        let mut acc = self.m.unit();
        let mut pos = 0;
        let mut k = 1 << format!("{:b}", n).len();
        while k > 0 {
            if k + pos <= n && self.m.operate(&acc, &self.bit[k + pos]) < x {
                pos += k;
                acc = self.m.operate(&acc, &self.bit[pos]);
            }
            k >>= 1;
        }
        pos
    }
}
/// binary operaion: $T \circ T \to T$
pub trait Magma {
    /// type of operands: $T$
    type T: Clone + PartialEq;
    /// binary operaion: $\circ$
    fn operate(&self, x: &Self::T, y: &Self::T) -> Self::T;
    #[inline]
    fn reverse_operate(&self, x: &Self::T, y: &Self::T) -> Self::T {
        self.operate(x, y)
    }
}
/// $\forall a,\forall b,\forall c \in T, (a \circ b) \circ c = a \circ (b \circ c)$
pub trait Associative {}
/// associative binary operation
pub trait SemiGroup: Magma + Associative {}
impl<S: Magma + Associative> SemiGroup for S {}
/// $\exists e \in T, \forall a \in T, e \circ a = a \circ e = e$
pub trait Unital: Magma {
    /// identity element: $e$
    fn unit(&self) -> Self::T;
}
/// associative binary operation and an identity element
pub trait Monoid: SemiGroup + Unital {
    /// binary exponentiation: $x^n = x\circ\ddots\circ x$
    fn pow(&self, x: Self::T, n: usize) -> Self::T {
        let mut n = n;
        let mut res = self.unit();
        let mut base = x;
        while n > 0 {
            if n & 1 == 1 {
                res = self.operate(&res, &base);
            }
            base = self.operate(&base, &base);
            n = n >> 1;
        }
        res
    }
}
impl<M: SemiGroup + Unital> Monoid for M {}
/// $\exists e \in T, \forall a \in T, \exists b,c \in T, b \circ a = a \circ c = e$
pub trait Invertible: Magma {
    /// $a$ where $a \circ x = e$
    fn inverse(&self, x: &Self::T) -> Self::T;
}
/// short cut of right inverse binary operation
pub trait RightInvertibleMagma: Magma {
    /// right inverse binary operation: $\cdot \circ (\cdot^{-1})$
    fn rinv_operation(&self, x: &Self::T, y: &Self::T) -> Self::T;
}
/// associative binary operation and an identity element and inverse elements
pub trait Group: Monoid + Invertible {}
impl<G: Monoid + Invertible> Group for G {}
/// $\forall a,\forall b \in T, a \circ b = b \circ a$
pub trait Commutative {}
/// commutative monoid
pub trait AbelianMonoid: Monoid + Commutative {}
impl<M: Monoid + Commutative> AbelianMonoid for M {}
/// commutative group
pub trait AbelianGroup: Group + Commutative {}
impl<G: Group + Commutative> AbelianGroup for G {}
/// $\forall a \in T, a \circ a = a$
pub trait Idempotent {}
/// idempotent monoid
pub trait IdempotentMonoid: Monoid + Idempotent {}
impl<M: Monoid + Idempotent> IdempotentMonoid for M {}
/// $+$
#[derive(Clone, Copy, Debug, Default, Eq, Hash, Ord, PartialEq, PartialOrd)]
pub struct AdditiveOperation<T: Copy + PartialEq + AdditiveIdentity> {
    _marker: std::marker::PhantomData<fn() -> T>,
}
pub trait AdditiveIdentity: Sized + std::ops::Add<Output = Self> {
    fn zero() -> Self;
}
#[macro_use]
mod additive_operation_impl {
    use super::*;
    #[macro_export(local_inner_macros)]
    macro_rules !impl_additive_identity {([$($wh :tt ) *] ,$t :ty ,$zero :expr ) =>{impl <$($wh ) *>AdditiveIdentity for $t {#[inline ] fn zero () ->Self {$zero } } } ;($t :ty ,$zero :expr ) =>{impl AdditiveIdentity for $t {#[inline ] fn zero () ->Self {$zero } } } ;}
    impl_additive_identity!(usize, 0usize);
    impl_additive_identity!(u8, 0u8);
    impl_additive_identity!(u16, 0u16);
    impl_additive_identity!(u32, 0u32);
    impl_additive_identity!(u64, 0u64);
    impl_additive_identity!(isize, 0isize);
    impl_additive_identity!(i8, 0i8);
    impl_additive_identity!(i16, 0i16);
    impl_additive_identity!(i32, 0i32);
    impl_additive_identity!(i64, 0i64);
    impl_additive_identity!(f32, 0.0f32);
    impl_additive_identity!(f64, 0.0f64);
    impl<T: Copy + PartialEq + AdditiveIdentity> AdditiveOperation<T> {
        pub fn new() -> Self {
            Self {
                _marker: std::marker::PhantomData,
            }
        }
    }
    impl<T: Copy + PartialEq + AdditiveIdentity> Magma for AdditiveOperation<T> {
        type T = T;
        #[inline]
        fn operate(&self, x: &Self::T, y: &Self::T) -> Self::T {
            *x + *y
        }
    }
    impl<T: Copy + PartialEq + AdditiveIdentity> Unital for AdditiveOperation<T> {
        #[inline]
        fn unit(&self) -> Self::T {
            AdditiveIdentity::zero()
        }
    }
    impl<T: Copy + PartialEq + AdditiveIdentity> Associative for AdditiveOperation<T> {}
    impl<T: Copy + PartialEq + AdditiveIdentity> Commutative for AdditiveOperation<T> {}
    impl<T: Copy + PartialEq + AdditiveIdentity + std::ops::Neg<Output = T>> Invertible
        for AdditiveOperation<T>
    {
        #[inline]
        fn inverse(&self, x: &Self::T) -> Self::T {
            -*x
        }
    }
    impl<T: Copy + PartialEq + AdditiveIdentity + std::ops::Sub<Output = T>> RightInvertibleMagma
        for AdditiveOperation<T>
    {
        #[inline]
        fn rinv_operation(&self, x: &Self::T, y: &Self::T) -> Self::T {
            *x - *y
        }
    }
}
/// binary search helper
pub trait Bisect: Copy {
    /// return between two elements
    fn halve(self, other: Self) -> Self;
    /// the end condition of binary search
    fn section_end(self, other: Self) -> bool;
}
mod bisect_impl {
    use super::*;
    macro_rules !impl_bisect_unsigned {($($t :ty ) *) =>{$(impl Bisect for $t {fn halve (self ,other :Self ) ->Self {if self >other {other +(self -other ) /2 } else {self +(other -self ) /2 } } fn section_end (self ,other :Self ) ->bool {(if self >other {self -other } else {other -self } ) <=1 } } ) *} ;}
    macro_rules !impl_bisect_signed {($($t :ty ) *) =>{$(impl Bisect for $t {fn halve (self ,other :Self ) ->Self {(self +other ) /2 } fn section_end (self ,other :Self ) ->bool {(self -other ) .abs () <=1 } } ) *} ;}
    macro_rules !impl_bisect_float {($($t :ty ) *) =>{$(impl Bisect for $t {fn halve (self ,other :Self ) ->Self {(self +other ) /2. } fn section_end (self ,other :Self ) ->bool {(self -other ) .abs () <=1e-8 } } ) *} ;}
    impl_bisect_unsigned !(u8 u16 u32 u64 usize ) ;
    impl_bisect_signed !(i8 i16 i32 i64 isize ) ;
    impl_bisect_float !(f32 f64 ) ;
}
pub fn binary_search<T: Bisect, F: Fn(T) -> bool>(f: F, ok: T, err: T) -> T {
    let mut ok = ok;
    let mut err = err;
    while !ok.section_end(err) {
        let m = ok.halve(err);
        if f(m) {
            ok = m;
        } else {
            err = m;
        }
    }
    ok
}
pub fn lower_bound<T: Bisect + Ord>(v: &[T], x: T) -> usize {
    binary_search(|i| v[i as usize] >= x, v.len() as i64, -1) as usize
}
pub fn upper_bound<T: Bisect + Ord>(v: &[T], x: T) -> usize {
    binary_search(|i| v[i as usize] > x, v.len() as i64, -1) as usize
}
#[derive(Clone, Debug)]
pub struct Compress<T> {
    v: Vec<T>,
}
impl<T: Ord> Compress<T> {
    pub fn get(&self, x: &T) -> usize {
        self.v.binary_search(&x).unwrap()
    }
}
impl<T> Compress<T> {
    pub fn len(&self) -> usize {
        self.v.len()
    }
}
impl<T> std::ops::Index<usize> for Compress<T> {
    type Output = T;
    fn index(&self, index: usize) -> &Self::Output {
        &self.v[index]
    }
}
impl<T: Ord> std::iter::FromIterator<T> for Compress<T> {
    fn from_iter<I: IntoIterator<Item = T>>(iter: I) -> Self {
        use std::collections::BTreeSet;
        let v = iter
            .into_iter()
            .collect::<BTreeSet<T>>()
            .into_iter()
            .collect::<Vec<T>>();
        Self { v }
    }
}
fn main() {
    #[allow(unused_imports)]
    use std::io::{Read as _, Write as _};
    let __out = std::io::stdout();
    let mut __in_buf = String::new();
    std::io::stdin().read_to_string(&mut __in_buf).unwrap();
    let mut __scanner = Scanner::new(&__in_buf);
    #[allow(unused_macros)]
    macro_rules !scan {() =>{scan !(usize ) } ;(($($t :tt ) ,*) ) =>{($(scan !($t ) ) ,*) } ;([$t :tt ;$len :expr ] ) =>{(0 ..$len ) .map (|_ |scan !($t ) ) .collect ::<Vec <_ >>() } ;({$t :tt =>$f :expr } ) =>{$f (scan !($t ) ) } ;(chars ) =>{__scanner .scan_chars () } ;($t :ty ) =>{__scanner .scan ::<$t >() } ;}
    let mut __out = std::io::BufWriter::new(__out.lock());
    #[allow(unused_macros)]
    macro_rules !print {($($arg :tt ) *) =>(::std ::write !(__out ,$($arg ) *) .unwrap () ) }
    #[allow(unused_macros)]
    macro_rules !println {($($arg :tt ) *) =>(::std ::writeln !(__out ,$($arg ) *) .unwrap () ) }
    #[allow(unused_macros)]
    macro_rules! echo {
        ($iter :expr ) => {
            echo!($iter, "\n")
        };
        ($iter :expr ,$sep :expr ) => {
            let mut iter = $iter;
            if let Some(item) = iter.next() {
                print!("{}", item);
            }
            for item in iter {
                print!("{}{}", $sep, item);
            }
            println!();
        };
    }
    let n = scan!();
    let mut xy = scan!([(i64, i64); n]);
    let mut ans = (M::new(2).pow(n) - M::one()) * M::new(n as u32);
    xy.sort();
    let c: Compress<_> = xy.iter().map(|t| t.1).collect();
    let mut l = BinaryIndexedTree::new(n, AdditiveOperation::new());
    let mut r = BinaryIndexedTree::new(n, AdditiveOperation::new());
    for i in 0..n {
        r.update(c.get(&xy[i].1), 1i64);
    }
    for (i, (_x, y)) in xy.iter().cloned().enumerate() {
        r.update(c.get(&y), -1i64);
        let p = l.accumulate(c.get(&y)) as usize;
        let q = r.accumulate(c.get(&y)) as usize;
        let v = vec![p, i - p, n - i - 1 - q, q];
        for i in 0..4 {
            ans += M::new(2).pow(v[i]) - M::one();
            ans -= M::new(2).pow(v[i] + v[(i + 1) % 4]) - M::one();
        }
        l.update(c.get(&y), 1i64);
    }
    println!("{}", ans);
}
type M = MInt<modulus::Modulo998244353>;

Measured memory_bytes: 17108