pub fn main() {
    crate::prepare!();
    sc!(n, q, tri: [(i64, i64, i64, i64, i64, i64); n]);
    let mut qs = vec![];
    for _ in 0..q {
        sc!(ty);
        if ty == 1 {
            sc!(t: (i64, i64, i64, i64, i64, i64));
            qs.push(((min!(t.0, t.2, t.4), max!(t.0, t.2, t.4)), Some(t)));
        } else {
            sc!(l: i64, r: i64);
            qs.push(((l, r), None));
        }
    }
    let mut xy: Vec<_> = tri
        .iter()
        .map(|t| (min!(t.0, t.2, t.4), max!(t.0, t.2, t.4)))
        .chain(qs.iter().map(|t| t.0))
        .collect();
    const INF: i64 = 1_000_000_007;
    xy.push((INF, 0));
    let mut seg = SegmentTree2d::<MaxOperation<i64>, i64, i64>::new(&xy);
    for (a, b, c, d, e, f) in tri {
        let s = ((c - a) * (f - b) - (e - a) * (d - b)).abs();
        let x = min!(a, c, e);
        let y = max!(a, c, e);
        seg.update(x, y, s);
    }
    for ((x, y), opt) in qs {
        if let Some((a, b, c, d, e, f)) = opt {
            let s = ((c - a) * (f - b) - (e - a) * (d - b)).abs();
            seg.update(x, y, s);
        } else {
            pp!(seg.fold(x, INF, 0, y + 1).max(-1));
        }
    }
}
pub struct SegmentTree2d<M, X, Y>
where
    M: Monoid,
{
    xs: Vec<X>,
    ys: Vec<Y>,
    index: Vec<Vec<usize>>,
    segs: Vec<SegmentTree<M>>,
}
impl<M, X, Y> SegmentTree2d<M, X, Y>
where
    M: Monoid,
    X: Ord + Clone,
    Y: Ord + Clone,
{
    pub fn new(points: &[(X, Y)]) -> Self {
        let mut xs: Vec<_> = points.iter().map(|(x, _)| x.clone()).collect();
        let mut ys: Vec<_> = points.iter().map(|(_, y)| y.clone()).collect();
        xs.sort();
        xs.dedup();
        ys.sort();
        ys.dedup();
        let n = xs.len();
        let mut index = vec![vec![]; n * 2];
        for (x, y) in points {
            let i = xs.binary_search(x).unwrap();
            let j = ys.binary_search(y).unwrap();
            index[i + n].push(j);
        }
        for i in n..n * 2 {
            index[i].sort();
            index[i].dedup();
        }
        for i in (1..n).rev() {
            let (p, l, r) = index.get_distinct_mut((i, i * 2, i * 2 + 1));
            p.extend(l.iter());
            p.extend(r.iter());
            index[i].sort();
            index[i].dedup();
        }
        let segs = index
            .iter()
            .map(Vec::len)
            .map(|len| SegmentTree::new(len))
            .collect();
        Self {
            xs,
            ys,
            index,
            segs,
        }
    }
    pub fn update(&mut self, x: X, y: Y, v: M::T) {
        let mut i = self.xs.binary_search(&x).expect("not exist X key") + self.xs.len();
        let j = self.ys.binary_search(&y).expect("not exist Y key");
        while i > 0 {
            let jj = self.index[i].binary_search(&j).unwrap();
            self.segs[i].update(jj, v.clone());
            i /= 2;
        }
    }
    pub fn fold(&self, xl: X, xr: X, yl: Y, yr: Y) -> M::T {
        let mut il = self.xs.position_bisect(|x| x >= &xl) + self.xs.len();
        let mut ir = self.xs.position_bisect(|x| x >= &xr) + self.xs.len();
        let jl = self.ys.position_bisect(|y| y >= &yl);
        let jr = self.ys.position_bisect(|y| y >= &yr);
        // let mut il = self.xs.binary_search(&xl).expect("not exist X key") + self.xs.len();
        // let mut ir = self.xs.binary_search(&xr).expect("not exist X key") + self.xs.len();
        // let jl = self.ys.binary_search(&yl).expect("not exist Y key");
        // let jr = self.ys.binary_search(&yr).expect("not exist Y key");
        let mut v = M::unit();
        while il < ir {
            if il & 1 != 0 {
                let jjl = self.index[il].position_bisect(|j| j >= &jl);
                let jjr = self.index[il].position_bisect(|j| j >= &jr);
                // let jjl = self.index[il].binary_search(&jl).unwrap();
                // let jjr = self.index[il].binary_search(&jr).unwrap();
                v = M::operate(&v, &self.segs[il].fold(jjl, jjr));
                il += 1;
            }
            if ir & 1 != 0 {
                ir -= 1;
                let jjl = self.index[ir].position_bisect(|j| j >= &jl);
                let jjr = self.index[ir].position_bisect(|j| j >= &jr);
                // let jjl = self.index[ir].binary_search(&jl).unwrap();
                // let jjr = self.index[ir].binary_search(&jr).unwrap();
                v = M::operate(&self.segs[ir].fold(jjl, jjr), &v);
            }
            il /= 2;
            ir /= 2;
        }
        v
    }
}
#[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"]#[doc=" - `@iter $expr`: print iterator"]#[doc=" - `@tuple $expr`: print tuple (need to import [`IterPrint`], each elements impls `Display`)"]#[doc=" - `$expr`: print expr"]#[doc=" - `;`: println"]#[doc=""]#[doc=" [`IterPrint`]: IterPrint"]#[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,$sep,true,item);}}};(@@tuple$writer:expr,$sep:expr,$is_head:expr,$tuple:expr)=>{IterPrint::iter_print($tuple,&mut$writer,$sep,$is_head).expect("io error");};(@@assert_tag item)=>{};(@@assert_tag iter)=>{};(@@assert_tag iterns)=>{};(@@assert_tag tuple)=>{};(@@assert_tag$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,)=>{$crate::iter_print!(@@line_feed$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::ord_tools::PartialOrdExt;
mod ord_tools{pub trait PartialOrdExt:Sized{fn chmin(&mut self,other:Self);fn chmax(&mut self,other:Self);fn minmax(self,other:Self)->(Self,Self);}impl<T>PartialOrdExt for T where T:PartialOrd{#[inline]fn chmin(&mut self,other:Self){if*self>other{*self=other;}}#[inline]fn chmax(&mut self,other:Self){if*self<other{*self=other;}}#[inline]fn minmax(self,other:Self)->(Self,Self){if self<other{(self,other)}else{(other,self)}}}#[macro_export]macro_rules!min{($l:expr)=>{$l};($l:expr,)=>{$crate::min!($l)};($l:expr,$r:expr)=>{($l).min($r)};($l:expr,$r:expr,)=>{$crate::min!($l,$r)};($l:expr,$r:expr,$($t:tt)*)=>{$crate::min!($crate::min!($l,$r),$($t)*)};}#[macro_export]macro_rules!chmin{($l:expr)=>{};($l:expr,)=>{};($l:expr,$r:expr)=>{{let r=$r;if$l>r{$l=r;}}};($l:expr,$r:expr,)=>{$crate::chmin!($l,$r)};($l:expr,$r:expr,$($t:tt)*)=>{$crate::chmin!($l,$r);$crate::chmin!($l,$($t)*)};}#[macro_export]macro_rules!max{($l:expr)=>{$l};($l:expr,)=>{$crate::max!($l)};($l:expr,$r:expr)=>{($l).max($r)};($l:expr,$r:expr,)=>{$crate::max!($l,$r)};($l:expr,$r:expr,$($t:tt)*)=>{$crate::max!($crate::max!($l,$r),$($t)*)};}#[macro_export]macro_rules!chmax{($l:expr)=>{};($l:expr,)=>{};($l:expr,$r:expr)=>{{let r=$r;if$l<r{$l=r;}}};($l:expr,$r:expr,)=>{$crate::chmax!($l,$r)};($l:expr,$r:expr,$($t:tt)*)=>{$crate::chmax!($l,$r);$crate::chmax!($l,$($t)*)};}#[macro_export]macro_rules!minmax{($($t:tt)*)=>{($crate::min!($($t)*),$crate::max!($($t)*))};}}
pub use self::segment_tree::SegmentTree;
mod segment_tree{use super::{AbelianMonoid,Monoid};#[derive(Clone,Debug)]pub struct SegmentTree<M>where M:Monoid{n:usize,seg:Vec<M::T>}impl<M>SegmentTree<M>where M:Monoid{pub fn new(n:usize)->Self{let seg=vec![M::unit();2*n];Self{n,seg}}pub fn from_vec(v:Vec<M::T>)->Self{let n=v.len();let mut seg=vec![M::unit();2*n];for(i,x)in v.into_iter().enumerate(){seg[n+i]=x;}for i in(1..n).rev(){seg[i]=M::operate(&seg[2*i],&seg[2*i+1]);}Self{n,seg}}pub fn set(&mut self,k:usize,x:M::T){debug_assert!(k<self.n);let mut k=k+self.n;self.seg[k]=x;k/=2;while k>0{self.seg[k]=M::operate(&self.seg[2*k],&self.seg[2*k+1]);k/=2;}}pub fn update(&mut self,k:usize,x:M::T){debug_assert!(k<self.n);let mut k=k+self.n;self.seg[k]=M::operate(&self.seg[k],&x);k/=2;while k>0{self.seg[k]=M::operate(&self.seg[2*k],&self.seg[2*k+1]);k/=2;}}pub fn get(&self,k:usize)->M::T{debug_assert!(k<self.n);self.seg[k+self.n].clone()}pub fn fold(&self,l:usize,r:usize)->M::T{debug_assert!(r<=self.n);debug_assert!(l<=r);let mut l=l+self.n;let mut r=r+self.n;let mut vl=M::unit();let mut vr=M::unit();while l<r{if l&1!=0{vl=M::operate(&vl,&self.seg[l]);l+=1;}if r&1!=0{r-=1;vr=M::operate(&self.seg[r],&vr);}l/=2;r/=2;}M::operate(&vl,&vr)}fn bisect_perfect<F>(&self,mut pos:usize,mut acc:M::T,f:F)->(usize,M::T)where F:Fn(&M::T)->bool{while pos<self.n{pos<<=1;let nacc=M::operate(&acc,&self.seg[pos]);if!f(&nacc){acc=nacc;pos+=1;}}(pos-self.n,acc)}fn rbisect_perfect<F>(&self,mut pos:usize,mut acc:M::T,f:F)->(usize,M::T)where F:Fn(&M::T)->bool{while pos<self.n{pos=pos*2+1;let nacc=M::operate(&self.seg[pos],&acc);if!f(&nacc){acc=nacc;pos-=1;}}(pos-self.n,acc)}#[doc=" Returns the first index that satisfies a accumlative predicate."]pub fn position_acc<F>(&self,l:usize,r:usize,f:F)->Option<usize>where F:Fn(&M::T)->bool{let mut l=l+self.n;let r=r+self.n;let mut k=0usize;let mut acc=M::unit();while l<r>>k{if l&1!=0{let nacc=M::operate(&acc,&self.seg[l]);if f(&nacc){return Some(self.bisect_perfect(l,acc,f).0);}acc=nacc;l+=1;}l>>=1;k+=1;}for k in(0..k).rev(){let r=r>>k;if r&1!=0{let nacc=M::operate(&acc,&self.seg[r-1]);if f(&nacc){return Some(self.bisect_perfect(r-1,acc,f).0);}acc=nacc;}}None}#[doc=" Returns the last index that satisfies a accumlative predicate."]pub fn rposition_acc<F>(&self,l:usize,r:usize,f:F)->Option<usize>where F:Fn(&M::T)->bool{let mut l=l+self.n;let mut r=r+self.n;let mut c=0usize;let mut k=0usize;let mut acc=M::unit();while l>>k<r{c<<=1;if l&1<<k!=0{l+=1<<k;c+=1;}if r&1!=0{r-=1;let nacc=M::operate(&self.seg[r],&acc);if f(&nacc){return Some(self.rbisect_perfect(r,acc,f).0);}acc=nacc;}r>>=1;k+=1;}for k in(0..k).rev(){if c&1!=0{l-=1<<k;let l=l>>k;let nacc=M::operate(&self.seg[l],&acc);if f(&nacc){return Some(self.rbisect_perfect(l,acc,f).0);}acc=nacc;}c>>=1;}None}pub fn as_slice(&self)->&[M::T]{&self.seg[self.n..]}}impl<M>SegmentTree<M>where M:AbelianMonoid{pub fn fold_all(&self)->M::T{self.seg[1].clone()}}}
mod magma{#![doc=" algebraic traits"]#[doc=" binary operaion: $T \\circ T \\to T$"]pub trait Magma{#[doc=" type of operands: $T$"]type T:Clone;#[doc=" binary operaion: $\\circ$"]fn operate(x:&Self::T,y:&Self::T)->Self::T;#[inline]fn reverse_operate(x:&Self::T,y:&Self::T)->Self::T{Self::operate(y,x)}#[inline]fn operate_assign(x:&mut Self::T,y:&Self::T){*x=Self::operate(x,y);}}#[doc=" $\\forall a,\\forall b,\\forall c \\in T, (a \\circ b) \\circ c = a \\circ (b \\circ c)$"]pub trait Associative{}#[doc=" associative binary operation"]pub trait SemiGroup:Magma+Associative{}impl<S:Magma+Associative>SemiGroup for S{}#[doc=" $\\exists e \\in T, \\forall a \\in T, e \\circ a = a \\circ e = e$"]pub trait Unital:Magma{#[doc=" identity element: $e$"]fn unit()->Self::T;#[inline]fn is_unit(x:&Self::T)->bool where<Self as Magma>::T:PartialEq{x==&Self::unit()}#[inline]fn set_unit(x:&mut Self::T){*x=Self::unit();}}#[doc=" associative binary operation and an identity element"]pub trait Monoid:SemiGroup+Unital{#[doc=" binary exponentiation: $x^n = x\\circ\\ddots\\circ x$"]fn pow(mut x:Self::T,mut n:usize)->Self::T{let mut res=Self::unit();while n>0{if n&1==1{res=Self::operate(&res,&x);}x=Self::operate(&x,&x);n>>=1;}res}}impl<M:SemiGroup+Unital>Monoid for M{}#[doc=" $\\exists e \\in T, \\forall a \\in T, \\exists b,c \\in T, b \\circ a = a \\circ c = e$"]pub trait Invertible:Magma{#[doc=" $a$ where $a \\circ x = e$"]fn inverse(x:&Self::T)->Self::T;#[inline]fn rinv_operate(x:&Self::T,y:&Self::T)->Self::T{Self::operate(x,&Self::inverse(y))}}#[doc=" associative binary operation and an identity element and inverse elements"]pub trait Group:Monoid+Invertible{}impl<G:Monoid+Invertible>Group for G{}#[doc=" $\\forall a,\\forall b \\in T, a \\circ b = b \\circ a$"]pub trait Commutative{}#[doc=" commutative monoid"]pub trait AbelianMonoid:Monoid+Commutative{}impl<M:Monoid+Commutative>AbelianMonoid for M{}#[doc=" commutative group"]pub trait AbelianGroup:Group+Commutative{}impl<G:Group+Commutative>AbelianGroup for G{}#[doc=" $\\forall a \\in T, a \\circ a = a$"]pub trait Idempotent{}#[doc=" idempotent monoid"]pub trait IdempotentMonoid:Monoid+Idempotent{}impl<M:Monoid+Idempotent>IdempotentMonoid for M{}#[macro_export]macro_rules!monoid_fold{($m:ty)=>{<$m as Unital>::unit()};($m:ty,)=>{<$m as Unital>::unit()};($m:ty,$f:expr)=>{$f};($m:ty,$f:expr,$($ff:expr),*)=>{<$m as Magma>::operate(&($f),&monoid_fold!($m,$($ff),*))};}}
pub use self::magma::*;
pub use self::min_operation_impl::MinOperation;
mod min_operation_impl{use super::*;use std::marker::PhantomData;#[doc=" binary operation to select smaller element"]pub struct MinOperation<T:Clone+Ord+Bounded>{_marker:PhantomData<fn()->T>}impl<T:Clone+Ord+Bounded>Magma for MinOperation<T>{type T=T;#[inline]fn operate(x:&Self::T,y:&Self::T)->Self::T{x.min(y).clone()}}impl<T:Clone+Ord+Bounded>Unital for MinOperation<T>{#[inline]fn unit()->Self::T{<T as Bounded>::maximum()}}impl<T:Clone+Ord+Bounded>Associative for MinOperation<T>{}impl<T:Clone+Ord+Bounded>Commutative for MinOperation<T>{}impl<T:Clone+Ord+Bounded>Idempotent for MinOperation<T>{}}
pub use self::bounded::Bounded;
mod bounded{#[doc=" Trait for max/min bounds"]pub trait Bounded:Sized+PartialOrd{fn maximum()->Self;fn minimum()->Self;fn is_maximum(&self)->bool{self==&Self::maximum()}fn is_minimum(&self)->bool{self==&Self::minimum()}fn set_maximum(&mut self){*self=Self::maximum()}fn set_minimum(&mut self){*self=Self::minimum()}}macro_rules!bounded_num_impls{($($t:ident)*)=>{$(impl Bounded for$t{fn maximum()->Self{std::$t::MAX}fn minimum()->Self{std::$t::MIN}})*};}bounded_num_impls!(u8 u16 u32 u64 u128 usize i8 i16 i32 i64 i128 isize f32 f64);macro_rules!bounded_tuple_impls{(@impl$($T:ident)*)=>{impl<$($T:Bounded),*>Bounded for($($T,)*){fn maximum()->Self{($(<$T as Bounded>::maximum(),)*)}fn minimum()->Self{($(<$T as Bounded>::minimum(),)*)}}};(@inner$($T:ident)*,)=>{bounded_tuple_impls!(@impl$($T)*);};(@inner$($T:ident)*,$U:ident$($Rest:ident)*)=>{bounded_tuple_impls!(@impl$($T)*);bounded_tuple_impls!(@inner$($T)*$U,$($Rest)*);};($($T:ident)*)=>{bounded_tuple_impls!(@inner,$($T)*);};}bounded_tuple_impls!(A B C D E F G H I J);impl Bounded for bool{fn maximum()->Self{true}fn minimum()->Self{false}}impl<T>Bounded for Option<T>where T:Bounded{fn maximum()->Self{Some(<T as Bounded>::maximum())}fn minimum()->Self{None}}impl<T>Bounded for std::cmp::Reverse<T>where T:Bounded{fn maximum()->Self{std::cmp::Reverse(<T as Bounded>::minimum())}fn minimum()->Self{std::cmp::Reverse(<T as Bounded>::maximum())}}}
pub trait GetDistinctMut<I>{type Output;fn get_distinct_mut(self,index:I)->Self::Output;}
impl<'a,T>GetDistinctMut<(usize,usize)>for&'a mut[T]{type Output=(&'a mut T,&'a mut T);fn get_distinct_mut(self,(i0,i1):(usize,usize))->Self::Output{assert_ne!(i0,i1);assert!(i0<self.len());assert!(i1<self.len());let ptr=self.as_mut_ptr();unsafe{(&mut*ptr.add(i0),&mut*ptr.add(i1))}}}
impl<'a,T>GetDistinctMut<(usize,usize,usize)>for&'a mut[T]{type Output=(&'a mut T,&'a mut T,&'a mut T);fn get_distinct_mut(self,(i0,i1,i2):(usize,usize,usize))->Self::Output{assert_ne!(i0,i1);assert_ne!(i0,i2);assert!(i0<self.len());assert!(i1<self.len());assert!(i2<self.len());let ptr=self.as_mut_ptr();unsafe{(&mut*ptr.add(i0),&mut*ptr.add(i1),&mut*ptr.add(i2))}}}
pub use self::max_operation_impl::MaxOperation;
mod max_operation_impl{use super::*;use std::marker::PhantomData;#[doc=" binary operation to select larger element"]pub struct MaxOperation<T:Clone+Ord+Bounded>{_marker:PhantomData<fn()->T>}impl<T:Clone+Ord+Bounded>Magma for MaxOperation<T>{type T=T;#[inline]fn operate(x:&Self::T,y:&Self::T)->Self::T{x.max(y).clone()}}impl<T:Clone+Ord+Bounded>Unital for MaxOperation<T>{#[inline]fn unit()->Self::T{<T as Bounded>::minimum()}}impl<T:Clone+Ord+Bounded>Associative for MaxOperation<T>{}impl<T:Clone+Ord+Bounded>Commutative for MaxOperation<T>{}impl<T:Clone+Ord+Bounded>Idempotent for MaxOperation<T>{}}
pub use self::binary_search::*;
mod binary_search{#[doc=" binary search helper"]pub trait Bisect:Clone{#[doc=" return between two elements"]fn halve(&self,other:&Self)->Self;#[doc=" the end condition of binary search"]fn section_end(&self,other:&Self)->bool;}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{const BISECT_SECTION_END_EPS:$t=1e-8;(self-other).abs()<=BISECT_SECTION_END_EPS}})*};}impl_bisect_unsigned!(u8 u16 u32 u64 u128 usize);impl_bisect_signed!(i8 i16 i32 i64 i128 isize);impl_bisect_float!(f32 f64);#[doc=" binary search for monotone segment"]#[doc=""]#[doc=" if `ok < err` then search [ok, err) where t(`ok`), t, t, .... t, t(`ret`), f,  ... f, f, f, `err`"]#[doc=""]#[doc=" if `err < ok` then search (err, ok] where `err`, f, f, f, ... f, t(`ret`), ... t, t, t(`ok`)"]pub fn binary_search<T,F>(mut f:F,mut ok:T,mut err:T)->T where T:Bisect,F:FnMut(&T)->bool{while!ok.section_end(&err){let m=ok.halve(&err);if f(&m){ok=m;}else{err=m;}}ok}#[doc=" binary search for slice"]pub trait SliceBisectExt<T>{#[doc=" Returns the first element that satisfies a predicate."]fn find_bisect(&self,f:impl FnMut(&T)->bool)->Option<&T>;#[doc=" Returns the last element that satisfies a predicate."]fn rfind_bisect(&self,f:impl FnMut(&T)->bool)->Option<&T>;#[doc=" Returns the first index that satisfies a predicate."]#[doc=" if not found, returns `len()`."]fn position_bisect(&self,f:impl FnMut(&T)->bool)->usize;#[doc=" Returns the last index+1 that satisfies a predicate."]#[doc=" if not found, returns `0`."]fn rposition_bisect(&self,f:impl FnMut(&T)->bool)->usize;}impl<T>SliceBisectExt<T>for[T]{fn find_bisect(&self,f:impl FnMut(&T)->bool)->Option<&T>{self.get(self.position_bisect(f))}fn rfind_bisect(&self,f:impl FnMut(&T)->bool)->Option<&T>{let pos=self.rposition_bisect(f);if pos==0{None}else{self.get(pos-1)}}fn position_bisect(&self,mut f:impl FnMut(&T)->bool)->usize{binary_search(|i|f(&self[*i as usize]),self.len()as i64,-1)as usize}fn rposition_bisect(&self,mut f:impl FnMut(&T)->bool)->usize{binary_search(|i|f(&self[i-1]),0,self.len()+1)}}}