pub fn main() {
    crate::prepare!();
    sc!(n, m, (g, _): @UndirectedGraphScanner::<Usize1>::new(n, m));
    sc!(abc: [[usize; 3]; n]);
    let s: Vec<usize> = abc.iter().map(|a| a.iter().sum()).collect();
    let x = binary_search(
        |&x| {
            let mut a = [x, 1, 1];
            if s[0] >= a.iter().sum::<usize>() {
                return false;
            }
            let mut heap = BinaryHeap::new();
            let i = if abc[0][1] < abc[0][2] { 2 } else { 1usize };
            a[i] = abc[0][i];
            let mut vis = vec![false; n];
            for adj in g.adjacencies(0) {
                if s[adj.to] < a.iter().sum::<usize>() {
                    vis[adj.to] = true;
                    heap.push(Reverse((s[adj.to], adj.to)));
                    for j in 0..3 {
                        chmax!(a[j], abc[adj.to][j]);
                    }
                }
            }
            while let Some(Reverse((_, u))) = heap.pop() {
                if s[u] >= a.iter().sum::<usize>() {
                    continue;
                }
                if u == n - 1 {
                    return true;
                }
                for j in 0..3 {
                    for k in 0..3 {
                        chmax!(a[j], abc[u][k]);
                    }
                }
                for adj in g.adjacencies(u) {
                    if !vis[adj.to] {
                        vis[adj.to] = true;
                        heap.push(Reverse((s[adj.to], adj.to)));
                    }
                }
            }
            false
        },
        1_000_000_000usize,
        0,
    );
    pp!(x, 1, 1);
}
#[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($))};}}
pub use self::iter_print::IterPrint;
mod iter_print{use std::{fmt::Display,io::{Error,Write}};pub trait IterPrint{fn iter_print<W,S>(self,writer:&mut W,sep:S,is_head:bool)->Result<(),Error>where W:Write,S:Display;}macro_rules!iter_print_tuple_impl{(@impl$($A:ident$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,!$(,)?)=>{};(@@inner$writer:expr,$sep:expr,$is_head:expr,!$($t:tt)*)=>{$crate::iter_print!(@@inner$writer,$sep,$is_head,$($t)*);};(@@inner$writer:expr,$sep:expr,$is_head:expr,)=>{$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$writer,' ',true,$($t)*);}};}}
pub use self::scanner::*;
mod scanner{use std::{iter::{from_fn,repeat_with,FromIterator},marker::PhantomData};pub fn read_stdin_all()->String{use std::io::Read as _;let mut s=String::new();std::io::stdin().read_to_string(&mut s).expect("io error");s}pub fn read_stdin_all_unchecked()->String{use std::io::Read as _;let mut buf=Vec::new();std::io::stdin().read_to_end(&mut buf).expect("io error");unsafe{String::from_utf8_unchecked(buf)}}pub fn read_all(mut reader:impl std::io::Read)->String{let mut s=String::new();reader.read_to_string(&mut s).expect("io error");s}pub fn read_all_unchecked(mut reader:impl std::io::Read)->String{let mut buf=Vec::new();reader.read_to_end(&mut buf).expect("io error");unsafe{String::from_utf8_unchecked(buf)}}pub fn read_stdin_line()->String{let mut s=String::new();std::io::stdin().read_line(&mut s).expect("io error");s}pub trait IterScan:Sized{type Output;fn scan<'a,I:Iterator<Item=&'a str>>(iter:&mut I)->Option<Self::Output>;}pub trait MarkedIterScan:Sized{type Output;fn mscan<'a,I:Iterator<Item=&'a str>>(self,iter:&mut I)->Option<Self::Output>;}#[derive(Clone,Debug)]pub struct Scanner<'a>{iter:std::str::SplitAsciiWhitespace<'a>}impl<'a>Scanner<'a>{#[inline]pub fn new(s:&'a str)->Self{let iter=s.split_ascii_whitespace();Self{iter}}#[inline]pub fn scan<T>(&mut self)-><T as IterScan>::Output where T:IterScan{<T as IterScan>::scan(&mut self.iter).expect("scan error")}#[inline]pub fn mscan<T>(&mut self,marker:T)-><T as MarkedIterScan>::Output where T:MarkedIterScan{marker.mscan(&mut self.iter).expect("scan error")}#[inline]pub fn scan_vec<T>(&mut self,size:usize)->Vec<<T as IterScan>::Output>where T:IterScan{(0..size).map(|_|<T as IterScan>::scan(&mut self.iter).expect("scan error")).collect()}#[inline]pub fn iter<'b,T>(&'b mut self)->ScannerIter<'a,'b,T>where T:IterScan{ScannerIter{inner:self,_marker:std::marker::PhantomData}}}macro_rules!iter_scan_impls{($($t:ty)*)=>{$(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()}}#[derive(Debug,Copy,Clone)]pub struct Splitted<T,P>where T:IterScan{pat:P,_marker:PhantomData<fn()->T>}impl<T,P>Splitted<T,P>where T:IterScan{pub fn new(pat:P)->Self{Self{pat,_marker:PhantomData}}}impl<T>MarkedIterScan for Splitted<T,char>where T:IterScan{type Output=Vec<<T as IterScan>::Output>;fn mscan<'a,I:Iterator<Item=&'a str>>(self,iter:&mut I)->Option<Self::Output>{let mut iter=iter.next()?.split(self.pat);Some(from_fn(||<T as IterScan>::scan(&mut iter)).collect())}}impl<T>MarkedIterScan for Splitted<T,&str>where T:IterScan{type Output=Vec<<T as IterScan>::Output>;fn mscan<'a,I:Iterator<Item=&'a str>>(self,iter:&mut I)->Option<Self::Output>{let mut iter=iter.next()?.split(self.pat);Some(from_fn(||<T as IterScan>::scan(&mut iter)).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::sparse_graph::*;
mod sparse_graph{use super::{IterScan,MarkedIterScan};use std::{marker::PhantomData,ops,slice};type Marker<T>=PhantomData<fn()->T>;#[derive(Clone,Copy,Debug,Default,Eq,PartialEq,Ord,PartialOrd,Hash)]pub struct DirectedEdge;#[derive(Clone,Copy,Debug,Default,Eq,PartialEq,Ord,PartialOrd,Hash)]pub struct UndirectedEdge;#[derive(Clone,Copy,Debug,Default,Eq,PartialEq,Ord,PartialOrd,Hash)]pub struct BidirectionalEdge;#[derive(Clone,Copy,Debug,Default,Eq,PartialEq,Ord,PartialOrd,Hash)]pub struct Adjacency{pub id:usize,pub to:usize}impl Adjacency{pub fn new(id:usize,to:usize)->Adjacency{Adjacency{id,to}}}#[doc=" Static Sparse Graph represented as Compressed Sparse Row."]#[derive(Debug,Clone)]pub struct SparseGraph<D>{vsize:usize,pub start:Vec<usize>,pub elist:Vec<Adjacency>,pub edges:Vec<(usize,usize)>,_marker:Marker<D>}impl<D>SparseGraph<D>{#[doc=" Return the number of vertices."]pub fn vertices_size(&self)->usize{self.vsize}#[doc=" Return the number of edges."]pub fn edges_size(&self)->usize{self.edges.len()}#[doc=" Return an iterator over graph vertices."]pub fn vertices(&self)->ops::Range<usize>{0..self.vertices_size()}#[doc=" Return a slice of adjacency vertices."]pub fn adjacencies(&self,v:usize)->slice::Iter<'_,Adjacency>{self.elist[self.start[v]..self.start[v+1]].iter()}}pub trait SparseGraphConstruction:Sized{fn construct_graph(vsize:usize,edges:Vec<(usize,usize)>)->SparseGraph<Self>;}impl<D:SparseGraphConstruction>SparseGraph<D>{#[doc=" Construct graph from edges."]pub fn from_edges(vsize:usize,edges:Vec<(usize,usize)>)->Self{D::construct_graph(vsize,edges)}}impl SparseGraphConstruction for DirectedEdge{fn construct_graph(vsize:usize,edges:Vec<(usize,usize)>)->SparseGraph<Self>{let mut start:Vec<_>=vec![0usize;vsize+1];for(from,_)in edges.iter().cloned(){start[from]+=1;}for i in 1..=vsize{start[i]+=start[i-1];}let mut elist=Vec::<Adjacency>::with_capacity(edges.len());let ptr=elist.as_mut_ptr();for(id,(from,to))in edges.iter().cloned().enumerate(){start[from]-=1;unsafe{ptr.add(start[from]).write(Adjacency::new(id,to))};}unsafe{elist.set_len(edges.len())};SparseGraph{vsize,start,elist,edges,_marker:PhantomData}}}impl SparseGraphConstruction for UndirectedEdge{fn construct_graph(vsize:usize,edges:Vec<(usize,usize)>)->SparseGraph<Self>{let mut start:Vec<_>=vec![0usize;vsize+1];for(from,to)in edges.iter().cloned(){start[to]+=1;start[from]+=1;}for i in 1..=vsize{start[i]+=start[i-1];}let mut elist=Vec::<Adjacency>::with_capacity(edges.len()*2);let ptr=elist.as_mut_ptr();for(id,(from,to))in edges.iter().cloned().enumerate(){start[from]-=1;unsafe{ptr.add(start[from]).write(Adjacency::new(id,to))};start[to]-=1;unsafe{ptr.add(start[to]).write(Adjacency::new(id,from))};}unsafe{elist.set_len(edges.len()*2)};SparseGraph{vsize,start,elist,edges,_marker:PhantomData}}}impl SparseGraphConstruction for BidirectionalEdge{fn construct_graph(vsize:usize,edges:Vec<(usize,usize)>)->SparseGraph<Self>{let mut start:Vec<_>=vec![0usize;vsize+1];for(from,to)in edges.iter().cloned(){start[to]+=1;start[from]+=1;}for i in 1..=vsize{start[i]+=start[i-1];}let mut elist=Vec::<Adjacency>::with_capacity(edges.len()*2);let ptr=elist.as_mut_ptr();for(id,(from,to))in edges.iter().cloned().enumerate(){start[from]-=1;unsafe{ptr.add(start[from]).write(Adjacency::new(id*2,to))};start[to]-=1;unsafe{ptr.add(start[to]).write(Adjacency::new(id*2+1,from))};}unsafe{elist.set_len(edges.len()*2)};SparseGraph{vsize,start,elist,edges,_marker:PhantomData}}}pub type DirectedSparseGraph=SparseGraph<DirectedEdge>;pub type UndirectedSparseGraph=SparseGraph<UndirectedEdge>;pub type BidirectionalSparseGraph=SparseGraph<BidirectionalEdge>;pub struct SparseGraphScanner<U:IterScan<Output=usize>,T:IterScan,D>{vsize:usize,esize:usize,_marker:Marker<(U,T,D)>}impl<U:IterScan<Output=usize>,T:IterScan,D>SparseGraphScanner<U,T,D>{pub fn new(vsize:usize,esize:usize)->Self{Self{vsize,esize,_marker:PhantomData}}}impl<U:IterScan<Output=usize>,T:IterScan,D:SparseGraphConstruction>MarkedIterScan for SparseGraphScanner<U,T,D>{type Output=(SparseGraph<D>,Vec<<T as IterScan>::Output>);fn mscan<'a,I:Iterator<Item=&'a str>>(self,iter:&mut I)->Option<Self::Output>{let mut edges=Vec::with_capacity(self.esize);let mut rest=Vec::with_capacity(self.esize);for _ in 0..self.esize{edges.push((U::scan(iter)?,U::scan(iter)?));rest.push(T::scan(iter)?);}let graph=SparseGraph::from_edges(self.vsize,edges);Some((graph,rest))}}pub type DirectedGraphScanner<U,T=()>=SparseGraphScanner<U,T,DirectedEdge>;pub type UndirectedGraphScanner<U,T=()>=SparseGraphScanner<U,T,UndirectedEdge>;pub type BidirectionalGraphScanner<U,T=()>=SparseGraphScanner<U,T,BidirectionalEdge>;pub struct TreeGraphScanner<U:IterScan<Output=usize>,T:IterScan=()>{vsize:usize,_marker:Marker<(U,T)>}impl<U:IterScan<Output=usize>,T:IterScan>TreeGraphScanner<U,T>{pub fn new(vsize:usize)->Self{Self{vsize,_marker:PhantomData}}}impl<U:IterScan<Output=usize>,T:IterScan>MarkedIterScan for TreeGraphScanner<U,T>{type Output=(UndirectedSparseGraph,Vec<<T as IterScan>::Output>);fn mscan<'a,I:Iterator<Item=&'a str>>(self,iter:&mut I)->Option<Self::Output>{UndirectedGraphScanner::<U,T>::new(self.vsize,self.vsize-1).mscan(iter)}}}
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)}}pub fn parallel_binary_search<T,F,G>(mut f:F,q:usize,ok:T,err:T)->Vec<T>where T:Bisect,F:FnMut(&[T])->G,G:Fn(usize)->bool{let mut ok=vec![ok;q];let mut err=vec![err;q];while!ok.iter().zip(&err).all(|(ok,err)|ok.section_end(err)){let m:Vec<_>=ok.iter().zip(&err).map(|(ok,err)|ok.halve(err)).collect();let g=f(&m);for(i,m)in m.into_iter().enumerate(){if g(i){ok[i]=m;}else{err[i]=m;}}}ok}}
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)*))};}}