pub fn main() {
    crate::prepare!();
    sc!(n, a: [u32; n]);
    let ps = primes(1_000_000);
    let m = ps.len();
    let pt = PrimeTable::new(1_000_000);
    let mut rng = Xorshift::default();
    let hash: Vec<_> = (0..m).map(|_| rng.rand64()).collect();
    let id: HashMap<_, _> = ps.iter().enumerate().map(|(i, &p)| (p as u32, i)).collect();
    let mut c = HashCounter::<u64>::new();
    let mut b = 0u64;
    c.add(b);
    for a in a {
        for (p, c) in pt.prime_factors(a) {
            if c % 2 == 1 {
                b ^= hash[id[&p]];
            }
        }
        c.add(b);
    }
    let ans: usize = c.values().map(|c| c * c.saturating_sub(1) / 2).sum();
    pp!(ans);
}
#[allow(unused_imports)]use std::{cmp::{Ordering,Reverse},collections::{BTreeMap,BTreeSet,BinaryHeap,HashMap,HashSet,VecDeque}};
mod main_macros{#[doc=" Prepare useful macros."]#[doc=" - `prepare!();`: default (all input scanner (`sc!`, `sv!`) + buf print (`pp!`))"]#[doc=" - `prepare!(?);`: interactive (line scanner (`scln!`) + buf print (`pp!`))"]#[macro_export]macro_rules!prepare{(@normal($dol:tt))=>{#[allow(unused_imports)]use std::io::Write as _;let __out=std::io::stdout();#[allow(unused_mut,unused_variables)]let mut __out=std::io::BufWriter::new(__out.lock());#[allow(unused_macros)]macro_rules!pp{($dol($dol t:tt)*)=>{$dol crate::iter_print!(__out,$dol($dol t)*)}}let __in_buf=read_stdin_all_unchecked();#[allow(unused_mut,unused_variables)]let mut __scanner=Scanner::new(&__in_buf);#[allow(unused_macros)]macro_rules!sc{($dol($dol t:tt)*)=>{$dol crate::scan!(__scanner,$dol($dol t)*)}}#[allow(unused_macros)]macro_rules!sv{($dol($dol t:tt)*)=>{$dol crate::scan_value!(__scanner,$dol($dol t)*)}}};(@interactive($dol:tt))=>{#[allow(unused_imports)]use std::io::Write as _;let __out=std::io::stdout();#[allow(unused_mut,unused_variables)]let mut __out=std::io::BufWriter::new(__out.lock());#[allow(unused_macros)]#[doc=" - to flush: `pp!(@flush);`"]macro_rules!pp{($dol($dol t:tt)*)=>{$dol crate::iter_print!(__out,$dol($dol t)*)}}#[allow(unused_macros)]#[doc=" Scan a line, and previous line will be truncated in the next call."]macro_rules!scln{($dol($dol t:tt)*)=>{let __in_buf=read_stdin_line();#[allow(unused_mut,unused_variables)]let mut __scanner=Scanner::new(&__in_buf);$dol crate::scan!(__scanner,$dol($dol t)*)}}};()=>{$crate::prepare!(@normal($))};(?)=>{$crate::prepare!(@interactive($))};}}
mod iter_print{use std::{fmt::Display,io::{Error,Write}};pub trait IterPrint{fn iter_print<W,S>(self,writer:&mut W,sep:S,is_head:bool)->Result<(),Error>where W:Write,S:Display;}macro_rules!iter_print_tuple_impl{(@impl$($A:ident$a:ident)?,$($B:ident$b:ident)*)=>{impl<$($A,)?$($B),*>IterPrint for($($A,)?$($B),*)where$($A:Display,)?$($B:Display),*{#[allow(unused_variables)]fn iter_print<W,S>(self,writer:&mut W,sep:S,is_head:bool)->Result<(),Error>where W:Write,S:Display{let($($a,)?$($b,)*)=self;$(if is_head{::std::write!(writer,"{}",$a)?;}else{::std::write!(writer,"{}{}",sep,$a)?;})?$(::std::write!(writer,"{}{}",sep,$b)?;)*Ok(())}}};(@inc,,$C:ident$c:ident$($D:ident$d:ident)*)=>{iter_print_tuple_impl!(@impl,);iter_print_tuple_impl!(@inc$C$c,,$($D$d)*);};(@inc$A:ident$a:ident,$($B:ident$b:ident)*,$C:ident$c:ident$($D:ident$d:ident)*)=>{iter_print_tuple_impl!(@impl$A$a,$($B$b)*);iter_print_tuple_impl!(@inc$A$a,$($B$b)*$C$c,$($D$d)*);};(@inc$A:ident$a:ident,$($B:ident$b:ident)*,)=>{iter_print_tuple_impl!(@impl$A$a,$($B$b)*);};($($t:tt)*)=>{iter_print_tuple_impl!(@inc,,$($t)*);};}iter_print_tuple_impl!(A a B b C c D d E e F f G g H h I i J j K k);#[doc=" Print expressions with a separator."]#[doc=" - `iter_print!(writer, args...)`"]#[doc=" - `@sep $expr`: set separator (default: `' '`)"]#[doc=" - `@fmt $lit => {$($expr),*}`: print `format!($lit, $($expr),*)`"]#[doc=" - `@flush`: flush writer (auto insert `!`)"]#[doc=" - `@iter $expr`: print iterator"]#[doc=" - `@iterns $expr`: print iterator with no separators"]#[doc=" - `@iterln $expr`: print iterator with separator `'\\n'`"]#[doc=" - `@iter2d $expr`: print 2d-iterator"]#[doc=" - `@tuple $expr`: print tuple (need to import [`IterPrint`], each elements impls `Display`)"]#[doc=" - `$expr`: print expr"]#[doc=" - `;`: print `'\\n'`"]#[doc=" - `!`: not print `'\\n'` at the end"]#[macro_export]macro_rules!iter_print{(@@fmt$writer:expr,$sep:expr,$is_head:expr,$lit:literal,$($e:expr),*)=>{if!$is_head{::std::write!($writer,"{}",$sep).expect("io error");}::std::write!($writer,$lit,$($e),*).expect("io error");};(@@item$writer:expr,$sep:expr,$is_head:expr,$e:expr)=>{$crate::iter_print!(@@fmt$writer,$sep,$is_head,"{}",$e);};(@@line_feed$writer:expr$(,)?)=>{::std::writeln!($writer).expect("io error");};(@@iter$writer:expr,$sep:expr,$is_head:expr,$iter:expr)=>{{let mut iter=$iter.into_iter();if let Some(item)=iter.next(){$crate::iter_print!(@@item$writer,$sep,$is_head,item);}for item in iter{$crate::iter_print!(@@item$writer,$sep,false,item);}}};(@@iterns$writer:expr,$sep:expr,$is_head:expr,$iter:expr)=>{{let mut iter=$iter.into_iter();if let Some(item)=iter.next(){$crate::iter_print!(@@item$writer,$sep,$is_head,item);}for item in iter{$crate::iter_print!(@@item$writer,$sep,true,item);}}};(@@iterln$writer:expr,$sep:expr,$is_head:expr,$iter:expr)=>{{let mut iter=$iter.into_iter();if let Some(item)=iter.next(){$crate::iter_print!(@@item$writer,'\n',$is_head,item);}for item in iter{$crate::iter_print!(@@item$writer,'\n',false,item);}}};(@@iter2d$writer:expr,$sep:expr,$is_head:expr,$iter:expr)=>{let mut iter=$iter.into_iter();if let Some(item)=iter.next(){$crate::iter_print!(@@iter$writer,$sep,$is_head,item);}for item in iter{$crate::iter_print!(@@line_feed$writer);$crate::iter_print!(@@iter$writer,$sep,true,item);}};(@@tuple$writer:expr,$sep:expr,$is_head:expr,$tuple:expr)=>{IterPrint::iter_print($tuple,&mut$writer,$sep,$is_head).expect("io error");};(@@assert_tag item)=>{};(@@assert_tag iter)=>{};(@@assert_tag iterns)=>{};(@@assert_tag iterln)=>{};(@@assert_tag iter2d)=>{};(@@assert_tag tuple)=>{};(@@assert_tag$tag:ident)=>{::std::compile_error!(::std::concat!("invalid tag in `iter_print!`: `",std::stringify!($tag),"`"));};(@@inner$writer:expr,$sep:expr,$is_head:expr,@sep$e:expr,$($t:tt)*)=>{$crate::iter_print!(@@inner$writer,$e,$is_head,$($t)*);};(@@inner$writer:expr,$sep:expr,$is_head:expr,@flush$($t:tt)*)=>{$writer.flush().expect("io error");$crate::iter_print!(@@inner$writer,$sep,$is_head,!$($t)*);};(@@inner$writer:expr,$sep:expr,$is_head:expr,@fmt$lit:literal=>{$($e:expr),*$(,)?}$($t:tt)*)=>{$crate::iter_print!(@@fmt$writer,$sep,$is_head,$lit,$($e),*);$crate::iter_print!(@@inner$writer,$sep,$is_head,$($t)*);};(@@inner$writer:expr,$sep:expr,$is_head:expr,@$tag:ident$e:expr,$($t:tt)*)=>{$crate::iter_print!(@@assert_tag$tag);$crate::iter_print!(@@$tag$writer,$sep,$is_head,$e);$crate::iter_print!(@@inner$writer,$sep,false,$($t)*);};(@@inner$writer:expr,$sep:expr,$is_head:expr,@$tag:ident$e:expr;$($t:tt)*)=>{$crate::iter_print!(@@assert_tag$tag);$crate::iter_print!(@@$tag$writer,$sep,$is_head,$e);$crate::iter_print!(@@line_feed$writer);$crate::iter_print!(@@inner$writer,$sep,true,$($t)*);};(@@inner$writer:expr,$sep:expr,$is_head:expr,@$tag:ident$e:expr)=>{$crate::iter_print!(@@assert_tag$tag);$crate::iter_print!(@@$tag$writer,$sep,$is_head,$e);$crate::iter_print!(@@inner$writer,$sep,false,);};(@@inner$writer:expr,$sep:expr,$is_head:expr,@$tag:ident$($t:tt)*)=>{::std::compile_error!(::std::concat!("invalid expr in `iter_print!`: `",std::stringify!($($t)*),"`"));};(@@inner$writer:expr,$sep:expr,$is_head:expr,,$($t:tt)*)=>{$crate::iter_print!(@@inner$writer,$sep,$is_head,$($t)*);};(@@inner$writer:expr,$sep:expr,$is_head:expr,;$($t:tt)*)=>{$crate::iter_print!(@@line_feed$writer);$crate::iter_print!(@@inner$writer,$sep,$is_head,$($t)*);};(@@inner$writer:expr,$sep:expr,$is_head:expr,!$($t:tt)*)=>{$crate::iter_print!(@@inner$writer,$sep,$is_head,$($t)*);};(@@inner$writer:expr,$sep:expr,$is_head:expr,!)=>{};(@@inner$writer:expr,$sep:expr,$is_head:expr,)=>{$crate::iter_print!(@@line_feed$writer);};(@@inner$writer:expr,$sep:expr,$is_head:expr,$($t:tt)*)=>{$crate::iter_print!(@@inner$writer,$sep,$is_head,@item$($t)*);};($writer:expr,$($t:tt)*)=>{{$crate::iter_print!(@@inner$writer,' ',true,$($t)*);}};}}
pub use self::scanner::*;
mod scanner{use std::{iter::{repeat_with,FromIterator},marker::PhantomData};pub fn read_stdin_all()->String{use std::io::Read as _;let mut s=String::new();std::io::stdin().read_to_string(&mut s).expect("io error");s}pub fn read_stdin_all_unchecked()->String{use std::io::Read as _;let mut buf=Vec::new();std::io::stdin().read_to_end(&mut buf).expect("io error");unsafe{String::from_utf8_unchecked(buf)}}pub fn read_all(mut reader:impl std::io::Read)->String{let mut s=String::new();reader.read_to_string(&mut s).expect("io error");s}pub fn read_all_unchecked(mut reader:impl std::io::Read)->String{let mut buf=Vec::new();reader.read_to_end(&mut buf).expect("io error");unsafe{String::from_utf8_unchecked(buf)}}pub fn read_stdin_line()->String{let mut s=String::new();std::io::stdin().read_line(&mut s).expect("io error");s}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(Clone,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>(&mut self)-><T as IterScan>::Output where T:IterScan{<T as IterScan>::scan(&mut self.iter).expect("scan error")}#[inline]pub fn mscan<T>(&mut self,marker:T)-><T as MarkedIterScan>::Output where T:MarkedIterScan{marker.mscan(&mut self.iter).expect("scan error")}#[inline]pub fn scan_vec<T>(&mut self,size:usize)->Vec<<T as IterScan>::Output>where T:IterScan{(0..size).map(|_|<T as IterScan>::scan(&mut self.iter).expect("scan error")).collect()}#[inline]pub fn iter<'b,T>(&'b mut self)->ScannerIter<'a,'b,T>where T:IterScan{ScannerIter{inner:self,_marker:std::marker::PhantomData}}}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::<$t>().ok()}})*};}iter_scan_impls!(char u8 u16 u32 u64 usize i8 i16 i32 i64 isize f32 f64 u128 i128 String);macro_rules!iter_scan_tuple_impl{(@impl$($T:ident)*)=>{impl<$($T:IterScan),*>IterScan for($($T,)*){type Output=($(<$T as IterScan>::Output,)*);#[inline]fn scan<'a,It:Iterator<Item=&'a str>>(_iter:&mut It)->Option<Self::Output>{Some(($(<$T as IterScan>::scan(_iter)?,)*))}}};(@inner$($T:ident)*,)=>{iter_scan_tuple_impl!(@impl$($T)*);};(@inner$($T:ident)*,$U:ident$($Rest:ident)*)=>{iter_scan_tuple_impl!(@impl$($T)*);iter_scan_tuple_impl!(@inner$($T)*$U,$($Rest)*);};($($T:ident)*)=>{iter_scan_tuple_impl!(@inner,$($T)*);};}iter_scan_tuple_impl!(A B C D E F G H I J K);pub struct ScannerIter<'a,'b,T>{inner:&'b mut Scanner<'a>,_marker:std::marker::PhantomData<fn()->T>}impl<'a,'b,T>Iterator for ScannerIter<'a,'b,T>where T:IterScan{type Item=<T as IterScan>::Output;#[inline]fn next(&mut self)->Option<Self::Item>{<T as IterScan>::scan(&mut self.inner.iter)}}#[doc=" - `scan_value!(scanner, ELEMENT)`"]#[doc=""]#[doc=" ELEMENT :="]#[doc=" - `$ty`: IterScan"]#[doc=" - `@$expr`: MarkedIterScan"]#[doc=" - `[ELEMENT; $expr]`: vector"]#[doc=" - `[ELEMENT]`: iterator"]#[doc=" - `($(ELEMENT)*,)`: tuple"]#[macro_export]macro_rules!scan_value{(@repeat$scanner:expr,[$($t:tt)*]$($len:expr)?)=>{::std::iter::repeat_with(||$crate::scan_value!(@inner$scanner,[]$($t)*))$(.take($len).collect::<Vec<_>>())?};(@tuple$scanner:expr,[$([$($args:tt)*])*])=>{($($($args)*,)*)};(@$tag:ident$scanner:expr,[[$($args:tt)*]])=>{$($args)*};(@$tag:ident$scanner:expr,[$($args:tt)*]@$e:expr)=>{$crate::scan_value!(@$tag$scanner,[$($args)*[$scanner.mscan($e)]])};(@$tag:ident$scanner:expr,[$($args:tt)*]@$e:expr,$($t:tt)*)=>{$crate::scan_value!(@$tag$scanner,[$($args)*[$scanner.mscan($e)]]$($t)*)};(@$tag:ident$scanner:expr,[$($args:tt)*]($($tuple:tt)*)$($t:tt)*)=>{$crate::scan_value!(@$tag$scanner,[$($args)*[$crate::scan_value!(@tuple$scanner,[]$($tuple)*)]]$($t)*)};(@$tag:ident$scanner:expr,[$($args:tt)*][@$e:expr;$len:expr]$($t:tt)*)=>{$crate::scan_value!(@$tag$scanner,[$($args)*[$crate::scan_value!(@repeat$scanner,[@$e]$len)]]$($t)*)};(@$tag:ident$scanner:expr,[$($args:tt)*][[$($tt:tt)*];$len:expr]$($t:tt)*)=>{$crate::scan_value!(@$tag$scanner,[$($args)*[$crate::scan_value!(@repeat$scanner,[[$($tt)*]]$len)]]$($t)*)};(@$tag:ident$scanner:expr,[$($args:tt)*][($($tt:tt)*);$len:expr]$($t:tt)*)=>{$crate::scan_value!(@$tag$scanner,[$($args)*[$crate::scan_value!(@repeat$scanner,[($($tt)*)]$len)]]$($t)*)};(@$tag:ident$scanner:expr,[$($args:tt)*][$ty:ty;$len:expr]$($t:tt)*)=>{$crate::scan_value!(@$tag$scanner,[$($args)*[$crate::scan_value!(@repeat$scanner,[$ty]$len)]]$($t)*)};(@$tag:ident$scanner:expr,[$($args:tt)*][$($tt:tt)*]$($t:tt)*)=>{$crate::scan_value!(@$tag$scanner,[$($args)*[$crate::scan_value!(@repeat$scanner,[$($tt)*])]]$($t)*)};(@$tag:ident$scanner:expr,[$($args:tt)*]$ty:ty)=>{$crate::scan_value!(@$tag$scanner,[$($args)*[$scanner.scan::<$ty>()]])};(@$tag:ident$scanner:expr,[$($args:tt)*]$ty:ty,$($t:tt)*)=>{$crate::scan_value!(@$tag$scanner,[$($args)*[$scanner.scan::<$ty>()]]$($t)*)};(@$tag:ident$scanner:expr,[$($args:tt)*],$($t:tt)*)=>{$crate::scan_value!(@$tag$scanner,[$($args)*]$($t)*)};(@$tag:ident$scanner:expr,[$($args:tt)*])=>{::std::compile_error!(::std::stringify!($($args)*))};($scanner:expr,$($t:tt)*)=>{$crate::scan_value!(@inner$scanner,[]$($t)*)}}#[doc=" - `scan!(scanner, $($pat $(: ELEMENT)?),*)`"]#[macro_export]macro_rules!scan{(@assert$p:pat)=>{};(@assert$($p:tt)*)=>{::std::compile_error!(::std::concat!("expected pattern, found `",::std::stringify!($($p)*),"`"));};(@pat$scanner:expr,[][])=>{};(@pat$scanner:expr,[][],$($t:tt)*)=>{$crate::scan!(@pat$scanner,[][]$($t)*)};(@pat$scanner:expr,[$($p:tt)*][]$x:ident$($t:tt)*)=>{$crate::scan!(@pat$scanner,[$($p)*$x][]$($t)*)};(@pat$scanner:expr,[$($p:tt)*][]::$($t:tt)*)=>{$crate::scan!(@pat$scanner,[$($p)*::][]$($t)*)};(@pat$scanner:expr,[$($p:tt)*][]&$($t:tt)*)=>{$crate::scan!(@pat$scanner,[$($p)*&][]$($t)*)};(@pat$scanner:expr,[$($p:tt)*][]($($x:tt)*)$($t:tt)*)=>{$crate::scan!(@pat$scanner,[$($p)*($($x)*)][]$($t)*)};(@pat$scanner:expr,[$($p:tt)*][][$($x:tt)*]$($t:tt)*)=>{$crate::scan!(@pat$scanner,[$($p)*[$($x)*]][]$($t)*)};(@pat$scanner:expr,[$($p:tt)*][]{$($x:tt)*}$($t:tt)*)=>{$crate::scan!(@pat$scanner,[$($p)*{$($x)*}][]$($t)*)};(@pat$scanner:expr,[$($p:tt)*][]:$($t:tt)*)=>{$crate::scan!(@ty$scanner,[$($p)*][]$($t)*)};(@pat$scanner:expr,[$($p:tt)*][]$($t:tt)*)=>{$crate::scan!(@let$scanner,[$($p)*][usize]$($t)*)};(@ty$scanner:expr,[$($p:tt)*][$($tt:tt)*]@$e:expr)=>{$crate::scan!(@let$scanner,[$($p)*][$($tt)*@$e])};(@ty$scanner:expr,[$($p:tt)*][$($tt:tt)*]@$e:expr,$($t:tt)*)=>{$crate::scan!(@let$scanner,[$($p)*][$($tt)*@$e],$($t)*)};(@ty$scanner:expr,[$($p:tt)*][$($tt:tt)*]($($x:tt)*)$($t:tt)*)=>{$crate::scan!(@let$scanner,[$($p)*][$($tt)*($($x)*)]$($t)*)};(@ty$scanner:expr,[$($p:tt)*][$($tt:tt)*][$($x:tt)*]$($t:tt)*)=>{$crate::scan!(@let$scanner,[$($p)*][$($tt)*[$($x)*]]$($t)*)};(@ty$scanner:expr,[$($p:tt)*][$($tt:tt)*]$ty:ty)=>{$crate::scan!(@let$scanner,[$($p)*][$($tt)*$ty])};(@ty$scanner:expr,[$($p:tt)*][$($tt:tt)*]$ty:ty,$($t:tt)*)=>{$crate::scan!(@let$scanner,[$($p)*][$($tt)*$ty],$($t)*)};(@let$scanner:expr,[$($p:tt)*][$($tt:tt)*]$($t:tt)*)=>{$crate::scan!{@assert$($p)*}let$($p)* =$crate::scan_value!($scanner,$($tt)*);$crate::scan!(@pat$scanner,[][]$($t)*)};($scanner:expr,$($t:tt)*)=>{$crate::scan!(@pat$scanner,[][]$($t)*)}}#[derive(Debug,Copy,Clone)]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 as IterScan>::scan(iter)?.checked_sub(1)}}#[derive(Debug,Copy,Clone)]pub struct CharWithBase(pub char);impl MarkedIterScan for CharWithBase{type Output=usize;#[inline]fn mscan<'a,I:Iterator<Item=&'a str>>(self,iter:&mut I)->Option<Self::Output>{Some((<char as IterScan>::scan(iter)?as u8-self.0 as u8)as usize)}}#[derive(Debug,Copy,Clone)]pub struct Chars;impl IterScan for Chars{type Output=Vec<char>;#[inline]fn scan<'a,I:Iterator<Item=&'a str>>(iter:&mut I)->Option<Self::Output>{Some(iter.next()?.chars().collect())}}#[derive(Debug,Copy,Clone)]pub struct CharsWithBase(pub char);impl MarkedIterScan for CharsWithBase{type Output=Vec<usize>;#[inline]fn mscan<'a,I:Iterator<Item=&'a str>>(self,iter:&mut I)->Option<Self::Output>{Some(iter.next()?.chars().map(|c|(c as u8-self.0 as u8)as usize).collect())}}#[derive(Debug,Copy,Clone)]pub struct ByteWithBase(pub u8);impl MarkedIterScan for ByteWithBase{type Output=usize;#[inline]fn mscan<'a,I:Iterator<Item=&'a str>>(self,iter:&mut I)->Option<Self::Output>{Some((<char as IterScan>::scan(iter)?as u8-self.0)as usize)}}#[derive(Debug,Copy,Clone)]pub struct Bytes;impl IterScan for Bytes{type Output=Vec<u8>;#[inline]fn scan<'a,I:Iterator<Item=&'a str>>(iter:&mut I)->Option<Self::Output>{Some(iter.next()?.bytes().collect())}}#[derive(Debug,Copy,Clone)]pub struct BytesWithBase(pub u8);impl MarkedIterScan for BytesWithBase{type Output=Vec<usize>;#[inline]fn mscan<'a,I:Iterator<Item=&'a str>>(self,iter:&mut I)->Option<Self::Output>{Some(iter.next()?.bytes().map(|c|(c-self.0)as usize).collect())}}#[derive(Debug,Copy,Clone)]pub struct Collect<T,B=Vec<<T as IterScan>::Output>>where T:IterScan,B:FromIterator<<T as IterScan>::Output>{size:usize,_marker:PhantomData<fn()->(T,B)>}impl<T,B>Collect<T,B>where T:IterScan,B:FromIterator<<T as IterScan>::Output>{pub fn new(size:usize)->Self{Self{size,_marker:PhantomData}}}impl<T,B>MarkedIterScan for Collect<T,B>where T:IterScan,B:FromIterator<<T as IterScan>::Output>{type Output=B;#[inline]fn mscan<'a,I:Iterator<Item=&'a str>>(self,iter:&mut I)->Option<Self::Output>{repeat_with(||<T as IterScan>::scan(iter)).take(self.size).collect()}}#[derive(Debug,Copy,Clone)]pub struct SizedCollect<T,B=Vec<<T as IterScan>::Output>>where T:IterScan,B:FromIterator<<T as IterScan>::Output>{_marker:PhantomData<fn()->(T,B)>}impl<T,B>IterScan for SizedCollect<T,B>where T:IterScan,B:FromIterator<<T as IterScan>::Output>{type Output=B;#[inline]fn scan<'a,I:Iterator<Item=&'a str>>(iter:&mut I)->Option<Self::Output>{let size=usize::scan(iter)?;repeat_with(||<T as IterScan>::scan(iter)).take(size).collect()}}impl<T,F>MarkedIterScan for F where F:Fn(&str)->Option<T>{type Output=T;fn mscan<'a,I:Iterator<Item=&'a str>>(self,iter:&mut I)->Option<Self::Output>{self(iter.next()?)}}}
pub use self::counter::{BTreeCounter,HashCounter};
mod counter{use std::{borrow::Borrow,collections::{btree_map,hash_map,BTreeMap,HashMap},fmt::{self,Debug},hash::Hash,iter::{Extend,FromIterator},ops::RangeBounds};#[derive(Clone)]pub struct HashCounter<T>{map:HashMap<T,usize>}impl<T>Debug for HashCounter<T>where T:Debug{fn fmt(&self,f:&mut fmt::Formatter<'_>)->fmt::Result{f.debug_map().entries(self.iter()).finish()}}impl<T>Default for HashCounter<T>where T:Eq+Hash{fn default()->Self{Self{map:HashMap::default()}}}impl<T>HashCounter<T>{pub fn len(&self)->usize{self.map.len()}pub fn is_empty(&self)->bool{self.map.is_empty()}pub fn clear(&mut self){self.map.clear();}pub fn keys(&self)->hash_map::Keys<'_,T,usize>{self.map.keys()}pub fn values(&self)->hash_map::Values<'_,T,usize>{self.map.values()}pub fn iter(&self)->hash_map::Iter<'_,T,usize>{self.map.iter()}pub fn drain(&mut self)->hash_map::Drain<'_,T,usize>{self.map.drain()}}impl<T>HashCounter<T>where T:Eq+Hash{pub fn new()->Self{Self::default()}pub fn with_capacity(capacity:usize)->Self{Self{map:HashMap::with_capacity(capacity)}}pub fn get(&self,item:&T)->usize{self.map.get(item).cloned().unwrap_or_default()}pub fn add(&mut self,item:T){self.add_count(item,1)}pub fn add_count(&mut self,item:T,count:usize){*self.map.entry(item).or_default()+=count;}pub fn remove(&mut self,item:&T)->bool{self.remove_count(item,1)==1}pub fn remove_count(&mut self,item:&T,count:usize)->usize{if let Some(cnt)=self.map.get_mut(item){if*cnt<=count{let cnt=*cnt;self.map.remove(item);cnt}else{*cnt-=count;count}}else{0}}pub fn append(&mut self,other:&mut Self){if self.map.len()<other.map.len(){std::mem::swap(self,other);}self.extend(other.map.drain());}}impl<T>Extend<T>for HashCounter<T>where T:Eq+Hash{fn extend<I:IntoIterator<Item=T>>(&mut self,iter:I){for item in iter{self.add(item)}}}impl<T>Extend<(T,usize)>for HashCounter<T>where T:Eq+Hash{fn extend<I:IntoIterator<Item=(T,usize)>>(&mut self,iter:I){for(item,count)in iter{self.add_count(item,count)}}}impl<T>FromIterator<T>for HashCounter<T>where T:Eq+Hash{fn from_iter<I:IntoIterator<Item=T>>(iter:I)->Self{let mut map=Self::default();map.extend(iter);map}}impl<T>FromIterator<(T,usize)>for HashCounter<T>where T:Eq+Hash{fn from_iter<I:IntoIterator<Item=(T,usize)>>(iter:I)->Self{let mut map=Self::default();map.extend(iter);map}}#[derive(Clone)]pub struct BTreeCounter<T>{map:BTreeMap<T,usize>}impl<T>Debug for BTreeCounter<T>where T:Debug{fn fmt(&self,f:&mut fmt::Formatter<'_>)->fmt::Result{f.debug_map().entries(self.iter()).finish()}}impl<T>Default for BTreeCounter<T>where T:Ord{fn default()->Self{Self{map:BTreeMap::default()}}}impl<T>BTreeCounter<T>{pub fn len(&self)->usize{self.map.len()}pub fn is_empty(&self)->bool{self.map.is_empty()}pub fn keys(&self)->btree_map::Keys<'_,T,usize>{self.map.keys()}pub fn values(&self)->btree_map::Values<'_,T,usize>{self.map.values()}pub fn iter(&self)->btree_map::Iter<'_,T,usize>{self.map.iter()}pub fn range<Q,R>(&self,range:R)->btree_map::Range<'_,T,usize>where Q:Ord,R:RangeBounds<Q>,T:Borrow<Q>+Ord{self.map.range(range)}}impl<T>BTreeCounter<T>where T:Ord{pub fn new()->Self{Self::default()}pub fn clear(&mut self){self.map.clear();}pub fn get(&self,item:&T)->usize{self.map.get(item).cloned().unwrap_or_default()}pub fn add(&mut self,item:T){self.add_count(item,1)}pub fn add_count(&mut self,item:T,count:usize){*self.map.entry(item).or_default()+=count;}pub fn remove(&mut self,item:&T)->bool{self.remove_count(item,1)==1}pub fn remove_count(&mut self,item:&T,count:usize)->usize{if let Some(cnt)=self.map.get_mut(item){if*cnt<=count{let cnt=*cnt;self.map.remove(item);cnt}else{*cnt-=count;count}}else{0}}}impl<T>Extend<T>for BTreeCounter<T>where T:Ord{fn extend<I:IntoIterator<Item=T>>(&mut self,iter:I){for item in iter{self.add(item)}}}impl<T>Extend<(T,usize)>for BTreeCounter<T>where T:Ord{fn extend<I:IntoIterator<Item=(T,usize)>>(&mut self,iter:I){for(item,count)in iter{self.add_count(item,count)}}}impl<T>FromIterator<T>for BTreeCounter<T>where T:Ord{fn from_iter<I:IntoIterator<Item=T>>(iter:I)->Self{let mut map=Self::default();map.extend(iter);map}}impl<T>FromIterator<(T,usize)>for BTreeCounter<T>where T:Ord{fn from_iter<I:IntoIterator<Item=(T,usize)>>(iter:I)->Self{let mut map=Self::default();map.extend(iter);map}}}
pub fn primes(n:usize)->Vec<usize>{if n<2{return vec![];}let mut res=vec![2];let sqrt_n=(n as f32).sqrt()as usize|1;let mut seive=vec![true;n/2];for i in(3..=sqrt_n).step_by(2){if seive[i/2-1]{res.push(i);for j in(i*i..=n).step_by(i*2){seive[j/2-1]=false;}}}for i in(std::cmp::max(3,sqrt_n+2)..=n).step_by(2){if seive[i/2-1]{res.push(i);}}res}
pub use self::bitset::BitSet;
mod bitset{#![allow(clippy::suspicious_op_assign_impl)]use std::ops::{BitAnd,BitAndAssign,BitOr,BitOrAssign,BitXor,BitXorAssign,Not,Shl,ShlAssign,Shr,ShrAssign};#[derive(Clone,Debug,Default,PartialEq,Eq,PartialOrd,Ord,Hash)]pub struct BitSet{size:usize,bits:Vec<u64>}impl BitSet{pub fn new(size:usize)->Self{Self{size,bits:vec![0;(size+63)/64]}}pub fn ones(size:usize)->Self{let mut self_=Self{size,bits:vec![std::u64::MAX;(size+63)/64]};self_.trim();self_}#[inline]pub fn get(&self,i:usize)->bool{self.bits[i>>6]&1<<(i&63)!=0}#[inline]pub fn set(&mut self,i:usize,b:bool){if b{self.bits[i>>6]|=1<<(i&63);}else{self.bits[i>>6]&=!(1<<(i&63));}}#[inline]pub fn count_ones(&self)->u64{self.bits.iter().map(|x|x.count_ones()as u64).sum()}#[inline]pub fn count_zeros(&self)->u64{self.size as u64-self.count_ones()}#[inline]fn trim(&mut self){if self.size&63!=0{if let Some(x)=self.bits.last_mut(){*x&=0xffff_ffff_ffff_ffff>>(64-(self.size&63));}}}#[inline]pub fn shl_bitor_assign(&mut self,rhs:usize){let n=self.bits.len();let k=rhs>>6;let d=rhs&63;if k<n{if d==0{for i in(0..n-k).rev(){self.bits[i+k]|=self.bits[i];}}else{for i in(1..n-k).rev(){self.bits[i+k]|=self.bits[i]<<d|self.bits[i-1]>>(64-d);}self.bits[k]|=self.bits[0]<<d;}self.trim();}}#[inline]pub fn shr_bitor_assign(&mut self,rhs:usize){let n=self.bits.len();let k=rhs>>6;let d=rhs&63;if k<n{if d==0{for i in k..n{self.bits[i-k]|=self.bits[i];}}else{for i in k..n-1{self.bits[i-k]|=self.bits[i]>>d|self.bits[i+1]<<(64-d);}self.bits[n-k-1]|=self.bits[n-1]>>d;}}}}impl ShlAssign<usize>for BitSet{#[inline]fn shl_assign(&mut self,rhs:usize){let n=self.bits.len();let k=rhs>>6;let d=rhs&63;if k>=n{for x in self.bits.iter_mut(){*x=0;}}else{if d==0{for i in(0..n-k).rev(){self.bits[i+k]=self.bits[i];}}else{for i in(1..n-k).rev(){self.bits[i+k]=self.bits[i]<<d|self.bits[i-1]>>(64-d);}self.bits[k]=self.bits[0]<<d;}for x in self.bits[..k].iter_mut(){*x=0;}self.trim();}}}impl Shl<usize>for BitSet{type Output=Self;#[inline]fn shl(mut self,rhs:usize)->Self::Output{self<<=rhs;self}}impl ShrAssign<usize>for BitSet{#[inline]fn shr_assign(&mut self,rhs:usize){let n=self.bits.len();let k=rhs>>6;let d=rhs&63;if k>=n{for x in self.bits.iter_mut(){*x=0;}}else{if d==0{for i in k..n{self.bits[i-k]=self.bits[i];}}else{for i in k..n-1{self.bits[i-k]=self.bits[i]>>d|self.bits[i+1]<<(64-d);}self.bits[n-k-1]=self.bits[n-1]>>d;}for x in self.bits[n-k..].iter_mut(){*x=0;}}}}impl Shr<usize>for BitSet{type Output=Self;#[inline]fn shr(mut self,rhs:usize)->Self::Output{self>>=rhs;self}}impl<'a>BitOrAssign<&'a BitSet>for BitSet{#[inline]fn bitor_assign(&mut self,rhs:&'a Self){for(l,r)in self.bits.iter_mut().zip(rhs.bits.iter()){*l|=*r;}self.trim();}}impl<'a>BitOr<&'a BitSet>for BitSet{type Output=Self;#[inline]fn bitor(mut self,rhs:&'a Self)->Self::Output{self|=rhs;self}}impl<'a,'b>BitOr<&'b BitSet>for&'a BitSet{type Output=BitSet;#[inline]fn bitor(self,rhs:&'b BitSet)->Self::Output{let mut res=self.clone();res|=rhs;res}}impl<'a>BitAndAssign<&'a BitSet>for BitSet{#[inline]fn bitand_assign(&mut self,rhs:&'a Self){for(l,r)in self.bits.iter_mut().zip(rhs.bits.iter()){*l&=*r;}}}impl<'a>BitAnd<&'a BitSet>for BitSet{type Output=Self;#[inline]fn bitand(mut self,rhs:&'a Self)->Self::Output{self&=rhs;self}}impl<'a,'b>BitAnd<&'b BitSet>for&'a BitSet{type Output=BitSet;#[inline]fn bitand(self,rhs:&'b BitSet)->Self::Output{let mut res=self.clone();res&=rhs;res}}impl<'a>BitXorAssign<&'a BitSet>for BitSet{#[inline]fn bitxor_assign(&mut self,rhs:&'a Self){for(l,r)in self.bits.iter_mut().zip(rhs.bits.iter()){*l^=*r;}self.trim();}}impl<'a>BitXor<&'a BitSet>for BitSet{type Output=Self;#[inline]fn bitxor(mut self,rhs:&'a Self)->Self::Output{self^=rhs;self}}impl<'a,'b>BitXor<&'b BitSet>for&'a BitSet{type Output=BitSet;#[inline]fn bitxor(self,rhs:&'b BitSet)->Self::Output{let mut res=self.clone();res^=rhs;res}}impl Not for BitSet{type Output=Self;#[inline]fn not(mut self)->Self::Output{for x in self.bits.iter_mut(){*x=!*x;}self.trim();self}}impl<'a>Not for&'a BitSet{type Output=BitSet;#[inline]fn not(self)->Self::Output{!self.clone()}}}
#[derive(Clone,Debug)]pub struct PrimeTable{table:Vec<u32>}
impl PrimeTable{pub fn new(max_n:u32)->Self{let mut table=vec![1;(max_n as usize+1)/2];table[0]=0;for i in(3..).step_by(2){let i2=i*i;if i2>max_n{break;}if table[i as usize>>1]==1{for j in(i2..=max_n).step_by(i as usize*2){if table[j as usize>>1]==1{table[j as usize>>1]=i;}}}}PrimeTable{table}}pub fn is_prime(&self,n:u32)->bool{n==2||n%2==1&&self.table[n as usize>>1]==1}pub fn trial_division<F>(&self,mut n:u32,mut f:F)where F:FnMut(u32,u32){let k=n.trailing_zeros();if k>0{f(2,k);}n>>=k;while self.table[n as usize>>1]>1{let p=self.table[n as usize>>1];let mut cnt=1;n/=p;while self.table[n as usize>>1]==p{n/=p;cnt+=1;}if n==p{cnt+=1;n/=p;}f(p,cnt);}if n>1{f(n,1);}}pub fn prime_factors(&self,n:u32)->Vec<(u32,u32)>{let mut factors=vec![];self.trial_division(n,|p,c|factors.push((p,c)));factors}pub fn count_divisors(&self,n:u32)->u32{let mut divisor_cnt=1;self.trial_division(n,|_,cnt|divisor_cnt*=cnt+1);divisor_cnt}}
#[derive(Clone,Debug)]pub struct Xorshift{y:u64}
impl Xorshift{pub fn new(seed:u64)->Self{Xorshift{y:seed}}pub fn time()->Self{let seed=std::time::SystemTime::now().duration_since(std::time::UNIX_EPOCH).ok().unwrap_or_default().as_secs()as u64;Xorshift::new(seed)}#[inline]pub fn rand64(&mut self)->u64{self.y^=self.y<<5;self.y^=self.y>>17;self.y^=self.y<<11;self.y}#[inline]pub fn rand(&mut self,k:u64)->u64{self.rand64()%k}#[inline]pub fn rands(&mut self,k:u64,n:usize)->Vec<u64>{(0..n).map(|_|self.rand(k)).collect::<Vec<_>>()}#[inline]pub fn randf(&mut self)->f64{const UPPER_MASK:u64=0x3FF0_0000_0000_0000;const LOWER_MASK:u64=0x000F_FFFF_FFFF_FFFF;let tmp=UPPER_MASK|(self.rand64()&LOWER_MASK);let result:f64=f64::from_bits(tmp);result-1.0}#[inline]pub fn gen_bool(&mut self,p:f64)->bool{self.randf()<p}pub fn shuffle<T>(&mut self,slice:&mut[T]){let mut n=slice.len();while n>1{let i=self.rand(n as _)as usize;n-=1;slice.swap(i,n);}}}
impl Default for Xorshift{fn default()->Self{Xorshift::new(0x2b99_2ddf_a232_49d6)}}