// codesnip-guard: minimum_spanning_arborescence
#[cfg_attr(any(),rustfmt::skip)]mod minimum_spanning_arborescence{use super::{EdgeListGraph,Group,MergingUnionFind,MonoidAct,PairingHeap,comparator::Less};impl EdgeListGraph{#[doc=" tarjan"]pub fn minimum_spanning_arborescence<G,F>(&self,root:usize,weight:F)->Option<(G::T,Vec<usize>)>where G:Group<T:Ord>,F:Fn(usize)->G::T{struct WeightAct<G>(std::marker::PhantomData<fn()->G>);impl<G>MonoidAct for WeightAct<G>where G:Group{type Key=(G::T,usize);type Act=G::T;type ActMonoid=G;fn act(x:&Self::Key,a:&Self::Act)->Self::Key{(G::operate(&x.0,a),x.1)}fn act_assign(x:&mut Self::Key,a:&Self::Act){x.0=G::operate(&x.0,a);}}let mut uf=MergingUnionFind::new_with_merger(self.vertices_size(),|_|PairingHeap::<(G::T,usize),Less,WeightAct<G>>::default(),|x,y|x.append(y));let mut state=vec![0;self.vertices_size()];state[root]=2;for(id,&(_,to))in self.edges().enumerate(){uf.merge_data_mut(to).push((weight(id),id));}let mut paredge=vec![0;self.edges_size()];let mut ord=vec![];let mut leaf=vec![self.edges_size();self.vertices_size()];let mut cycle=0usize;let mut acc=G::unit();for mut cur in self.vertices(){if state[cur]!=0{continue;}let mut path=vec![];let mut ch=vec![];while state[cur]!=2{path.push(cur);state[cur]=1;let(w,eid)={match uf.merge_data_mut(cur).pop(){Some((w,eid))=>(w,eid),None=>return None,}};uf.merge_data_mut(cur).apply_all(G::inverse(&w));acc=G::operate(&acc,&w);ord.push(eid);let(u,v)=self[eid];if leaf[v]>=self.edges_size(){leaf[v]=eid;}while cycle>0{paredge[ch.pop().unwrap()]=eid;cycle-=1;}ch.push(eid);if state[uf.find_root(u)]==1{while let Some(t)=path.pop(){state[t]=2;cycle+=1;if!uf.unite(u,t){break;}}state[uf.find_root(u)]=1;}cur=uf.find_root(u);}for u in path.into_iter(){state[u]=2;}}let mut tree=vec![root;self.vertices_size()];let mut used=vec![false;self.edges_size()];for eid in ord.into_iter().rev(){if!used[eid]{let(u,v)=self[eid];tree[v]=u;let mut x=leaf[v];while x!=eid{used[x]=true;x=paredge[x];}}}Some((acc,tree))}}}
// codesnip-guard: Comparator
#[cfg_attr(any(),rustfmt::skip)]pub use self::comparator::Comparator;#[cfg_attr(any(),rustfmt::skip)]pub mod comparator{use std::cmp::Ordering;pub trait Comparator<T>{fn compare(&mut self,a:&T,b:&T)->Ordering;}impl<T,F>Comparator<T>for F where F:FnMut(&T,&T)->Ordering{fn compare(&mut self,a:&T,b:&T)->Ordering{(self)(a,b)}}#[derive(Debug,Clone,Copy,Default,PartialEq,Eq,PartialOrd,Ord,Hash)]pub struct Less;impl<T>Comparator<T>for Less where T:Ord{fn compare(&mut self,a:&T,b:&T)->Ordering{a.cmp(b)}}#[derive(Debug,Clone,Copy,Default,PartialEq,Eq,PartialOrd,Ord,Hash)]pub struct Greater;impl<T>Comparator<T>for Greater where T:Ord{fn compare(&mut self,a:&T,b:&T)->Ordering{b.cmp(a)}}#[derive(Debug,Clone,Copy,Default,PartialEq,Eq,PartialOrd,Ord,Hash)]pub struct ByKey<F>(pub F);impl<T,F,K>Comparator<T>for ByKey<F>where F:FnMut(&T)->K,K:Ord{fn compare(&mut self,a:&T,b:&T)->Ordering{(self.0)(a).cmp(&(self.0)(b))}}}
// codesnip-guard: EdgeListGraph
#[cfg_attr(any(),rustfmt::skip)]pub use self::edge_list::{EdgeListGraph,EdgeListGraphScanner};#[cfg_attr(any(),rustfmt::skip)]mod edge_list{use super::{MarkedScan,Scan,ScanSource};use std::{marker::PhantomData,ops::Range,slice::Iter};#[derive(Clone,Debug)]#[doc=" Graph represented by a list of edges."]pub struct EdgeListGraph{vsize:usize,edges:Vec<(usize,usize)>}impl EdgeListGraph{#[doc=" Construct empty graph."]pub fn new(vsize:usize)->Self{Self{vsize,edges:Vec::new()}}#[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)->Range<usize>{0..self.vertices_size()}pub fn edges(&self)->Iter<'_,(usize,usize)>{self.edges.iter()}#[doc=" Construct graph from edges."]pub fn from_edges(vsize:usize,edges:Vec<(usize,usize)>)->Self{Self{vsize,edges}}}impl std::ops::Index<usize>for EdgeListGraph{type Output=(usize,usize);fn index(&self,index:usize)->&Self::Output{&self.edges[index]}}pub struct EdgeListGraphScanner<U:Scan<Output=usize>,T:Scan>{vsize:usize,esize:usize,_marker:PhantomData<fn()->(U,T)>}impl<U:Scan<Output=usize>,T:Scan>EdgeListGraphScanner<U,T>{pub fn new(vsize:usize,esize:usize)->Self{Self{vsize,esize,_marker:PhantomData}}}impl<U:Scan<Output=usize>,T:Scan>MarkedScan for EdgeListGraphScanner<U,T>{type Output=(EdgeListGraph,Vec<<T as Scan>::Output>);fn mscan<I:ScanSource>(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=EdgeListGraph::from_edges(self.vsize,edges);Some((graph,rest))}}}
// codesnip-guard: LastOperation
#[cfg_attr(any(),rustfmt::skip)]pub use self::last_operation_impl::LastOperation;#[cfg_attr(any(),rustfmt::skip)]mod last_operation_impl{use super::*;use std::marker::PhantomData;#[doc=" retain the last element"]pub struct LastOperation<T>where T:Clone{_marker:PhantomData<fn()->T>}impl<T>Magma for LastOperation<T>where T:Clone{type T=Option<T>;#[inline]fn operate(x:&Self::T,y:&Self::T)->Self::T{y.as_ref().or(x.as_ref()).cloned()}}impl<T>Unital for LastOperation<T>where T:Clone{#[inline]fn unit()->Self::T{None}}impl<T>Associative for LastOperation<T>where T:Clone{}impl<T>Idempotent for LastOperation<T>where T:Clone{}}
// codesnip-guard: LinearOperation
#[cfg_attr(any(),rustfmt::skip)]pub use self::linear_operation_impl::LinearOperation;#[cfg_attr(any(),rustfmt::skip)]mod linear_operation_impl{use super::*;use std::{marker::PhantomData,ops::{Add,Div,Mul,Neg,Sub}};#[doc=" $(a, b) \\circ (c, d) = \\lambda x. c \\times (a \\times x + b) + d$"]pub struct LinearOperation<T>where T:Clone+Zero+Add<Output=T>+One+Mul<Output=T>{_marker:PhantomData<fn()->T>}impl<T>LinearOperation<T>where T:Clone+Zero+Add<Output=T>+One+Mul<Output=T>{pub fn apply(f:&(T,T),x:&T)->T{f.0 .clone()*x.clone()+f.1 .clone()}}impl<T>Magma for LinearOperation<T>where T:Clone+Zero+One+Add<Output=T>+Mul<Output=T>{type T=(T,T);#[inline]fn operate(x:&Self::T,y:&Self::T)->Self::T{(y.0 .clone()*x.0 .clone(),y.0 .clone()*x.1 .clone()+y.1 .clone())}}impl<T>Unital for LinearOperation<T>where T:Clone+Zero+One+Add<Output=T>+Mul<Output=T>{#[inline]fn unit()->Self::T{(One::one(),Zero::zero())}}impl<T>Associative for LinearOperation<T>where T:Clone+Zero+One+Add<Output=T>+Mul<Output=T>{}impl<T>Invertible for LinearOperation<T>where T:Clone+Zero+One+Add<Output=T>+Sub<Output=T>+Neg<Output=T>+Mul<Output=T>+Div<Output=T>{fn inverse(x:&Self::T)->Self::T{let y=<T as One>::one().div(x.0 .clone());(y.clone(),-y.mul(x.1 .clone()))}}}
// codesnip-guard: MonoidAct
#[cfg_attr(any(),rustfmt::skip)]pub use self::action::*;#[cfg_attr(any(),rustfmt::skip)]mod action{use super::*;use std::{marker::PhantomData,ops::{Add,Mul}};pub trait MonoidAct{type Key;type Act:Clone;type ActMonoid:Monoid<T=Self::Act>;fn act(x:&Self::Key,a:&Self::Act)->Self::Key;fn act_assign(x:&mut Self::Key,a:&Self::Act){*x=Self::act(x,a);}fn unit()->Self::Act{<Self::ActMonoid as Unital>::unit()}fn operate(x:&Self::Act,y:&Self::Act)->Self::Act{<Self::ActMonoid as Magma>::operate(x,y)}fn operate_assign(x:&mut Self::Act,y:&Self::Act){*x=<Self::ActMonoid as Magma>::operate(x,y);}}pub struct EmptyAct<T>{_marker:PhantomData<fn()->T>}impl<T>MonoidAct for EmptyAct<T>where T:Clone{type Key=T;type Act=();type ActMonoid=();fn act(x:&Self::Key,_a:&Self::Act)->Self::Key{x.clone()}}pub struct FlattenAct<M>{_marker:PhantomData<fn()->M>}impl<M>MonoidAct for FlattenAct<M>where M:Monoid{type Key=M::T;type Act=M::T;type ActMonoid=M;fn act(x:&Self::Key,a:&Self::Act)->Self::Key{M::operate(x,a)}}pub struct LinearAct<T>{_marker:PhantomData<fn()->T>}impl<T>MonoidAct for LinearAct<T>where T:Clone+Zero+One+Add<Output=T>+Mul<Output=T>{type Key=T;type Act=(T,T);type ActMonoid=LinearOperation<T>;fn act(x:&Self::Key,(a,b):&Self::Act)->Self::Key{a.clone()*x.clone()+b.clone()}}pub struct UpdateAct<T>{_marker:PhantomData<fn()->T>}impl<T>MonoidAct for UpdateAct<T>where T:Clone{type Key=T;type Act=Option<T>;type ActMonoid=LastOperation<T>;fn act(x:&Self::Key,a:&Self::Act)->Self::Key{a.as_ref().unwrap_or(x).clone()}}}
// codesnip-guard: PairingHeap
#[cfg_attr(any(),rustfmt::skip)]pub use self::pairing_heap::PairingHeap;#[cfg_attr(any(),rustfmt::skip)]mod pairing_heap{use super::{Comparator,EmptyAct,MonoidAct,Unital,comparator::Less};use std::{cmp::Ordering,fmt::{self,Debug,Formatter},iter::FusedIterator,mem::{replace,swap},ops::{Deref,DerefMut}};#[derive(Clone)]struct Node<T,A>where A:MonoidAct<Key=T,Act:PartialEq>{value:T,first_child:Option<Box<Node<T,A>>>,next_sibling:Option<Box<Node<T,A>>>,lazy:A::Act}impl<T,A>Node<T,A>where A:MonoidAct<Key=T,Act:PartialEq>{fn new(value:T)->Self{Self{value,first_child:None,next_sibling:None,lazy:A::unit()}}fn apply(&mut self,act:&A::Act){A::act_assign(&mut self.value,act);A::operate_assign(&mut self.lazy,act);}fn propagate(&mut self){if!<A::ActMonoid as Unital>::is_unit(&self.lazy){let act=replace(&mut self.lazy,A::unit());if let Some(node)=self.first_child.as_mut(){node.apply(&act);}if let Some(node)=self.next_sibling.as_mut(){node.apply(&act);}}}}impl<T,A>Debug for Node<T,A>where T:Debug,A:MonoidAct<Key=T,Act:PartialEq+Debug>{fn fmt(&self,f:&mut Formatter<'_>)->fmt::Result{f.debug_struct("Node").field("value",&self.value).field("first_child",&self.first_child).field("next_sibling",&self.next_sibling).field("lazy",&self.lazy).finish()}}#[derive(Clone)]pub struct PairingHeap<T,C=Less,A=EmptyAct<T>>where A:MonoidAct<Key=T,Act:PartialEq>{root:Option<Box<Node<T,A>>>,len:usize,cmp:C}impl<T,C,A>PairingHeap<T,C,A>where C:Comparator<T>,A:MonoidAct<Key=T,Act:PartialEq>{pub fn with_comparator(cmp:C)->Self{Self{root:None,len:0,cmp}}pub fn len(&self)->usize{self.len}pub fn is_empty(&self)->bool{self.len==0}pub fn peek(&self)->Option<&T>{self.root.as_ref().map(|node|&node.value)}pub fn push(&mut self,value:T){let node=Box::new(Node::new(value));let root=self.root.take();self.root=self.merge_option(root,Some(node));self.len+=1;}pub fn append(&mut self,other:&mut Self){if other.is_empty(){return;}let left=self.root.take();self.root=self.merge_option(left,other.root.take());self.len+=other.len;other.len=0;}pub fn pop(&mut self)->Option<T>{self.root.take().map(|mut root|{self.len-=1;root.propagate();let children=root.first_child.take();self.root=self.merge_pairs(children);root.value})}pub fn peek_mut(&mut self)->Option<PeekMut<'_,T,C,A>>{let mut root=self.root.take()?;root.propagate();let children=root.first_child.take();debug_assert!(root.next_sibling.is_none());root.next_sibling=None;self.root=self.merge_pairs(children);Some(PeekMut{heap:self,node:Some(root)})}pub fn clear(&mut self){self.root=None;self.len=0;}pub fn apply_all(&mut self,act:A::Act){if let Some(root)=self.root.as_mut(){root.apply(&act);}}pub fn into_sorted_vec(mut self)->Vec<T>{let mut result=Vec::with_capacity(self.len);while let Some(value)=self.pop(){result.push(value);}result}fn merge_option(&mut self,a:Option<Box<Node<T,A>>>,b:Option<Box<Node<T,A>>>)->Option<Box<Node<T,A>>>{match(a,b){(None,None)=>None,(Some(node),None)|(None,Some(node))=>Some(node),(Some(mut a),Some(mut b))=>{a.propagate();b.propagate();if self.cmp.compare(&a.value,&b.value)==Ordering::Greater{swap(&mut a,&mut b);}b.next_sibling=a.first_child.take();a.first_child=Some(b);Some(a)}}}fn merge_pairs(&mut self,mut head:Option<Box<Node<T,A>>>)->Option<Box<Node<T,A>>>{let mut pairs=None;while let Some(mut first)=head{first.propagate();let next=first.next_sibling.take();let mut pair=if let Some(mut second)=next{second.propagate();head=second.next_sibling.take();self.merge_option(Some(first),Some(second)).unwrap()}else{head=None;first};pair.next_sibling=pairs;pairs=Some(pair);}let mut result=None;while let Some(mut node)=pairs{pairs=node.next_sibling.take();result=self.merge_option(Some(node),result);}result}}impl<T,C,A>Default for PairingHeap<T,C,A>where C:Comparator<T>+Default,A:MonoidAct<Key=T,Act:PartialEq>{fn default()->Self{Self::with_comparator(C::default())}}impl<T,A>PairingHeap<T,Less,A>where T:Ord,A:MonoidAct<Key=T,Act:PartialEq>{pub fn new()->Self{Self::default()}}impl<T,C,A>Debug for PairingHeap<T,C,A>where T:Debug,C:Debug+Comparator<T>,A:MonoidAct<Key=T,Act:PartialEq+Debug>{fn fmt(&self,f:&mut Formatter<'_>)->fmt::Result{f.debug_struct("PairingHeap").field("len",&self.len).field("root",&self.root).field("cmp",&self.cmp).finish()}}impl<T,C,A>Extend<T>for PairingHeap<T,C,A>where C:Comparator<T>,A:MonoidAct<Key=T,Act:PartialEq>{fn extend<I:IntoIterator<Item=T>>(&mut self,iter:I){for value in iter{self.push(value);}}}impl<T,C,A>FromIterator<T>for PairingHeap<T,C,A>where C:Comparator<T>+Default,A:MonoidAct<Key=T,Act:PartialEq>{fn from_iter<I:IntoIterator<Item=T>>(iter:I)->Self{let mut heap=Self::default();heap.extend(iter);heap}}pub struct PeekMut<'a,T,C=Less,A=EmptyAct<T>>where C:Comparator<T>,A:MonoidAct<Key=T,Act:PartialEq>{heap:&'a mut PairingHeap<T,C,A>,node:Option<Box<Node<T,A>>>}impl<'a,T,C,A>PeekMut<'a,T,C,A>where C:Comparator<T>,A:MonoidAct<Key=T,Act:PartialEq>{pub fn pop(mut this:Self)->T{this.heap.len-=1;let node=this.node.take().expect("PeekMut already consumed");let Node{value,..}=*node;value}}impl<'a,T,C,A>Deref for PeekMut<'a,T,C,A>where C:Comparator<T>,A:MonoidAct<Key=T,Act:PartialEq>{type Target=T;fn deref(&self)->&Self::Target{&self.node.as_ref().expect("PeekMut already consumed").value}}impl<'a,T,C,A>DerefMut for PeekMut<'a,T,C,A>where C:Comparator<T>,A:MonoidAct<Key=T,Act:PartialEq>{fn deref_mut(&mut self)->&mut Self::Target{&mut self.node.as_mut().expect("PeekMut already consumed").value}}impl<'a,T,C,A>Drop for PeekMut<'a,T,C,A>where C:Comparator<T>,A:MonoidAct<Key=T,Act:PartialEq>{fn drop(&mut self){if let Some(mut node)=self.node.take(){debug_assert!(node.next_sibling.is_none());let root=self.heap.root.take();node.first_child=None;self.heap.root=self.heap.merge_option(root,Some(node));}}}pub struct IntoIter<T,C=Less,A=EmptyAct<T>>where C:Comparator<T>,A:MonoidAct<Key=T,Act:PartialEq>{heap:PairingHeap<T,C,A>}impl<T,C,A>IntoIter<T,C,A>where C:Comparator<T>,A:MonoidAct<Key=T,Act:PartialEq>{fn new(heap:PairingHeap<T,C,A>)->Self{Self{heap}}}impl<T,C,A>Iterator for IntoIter<T,C,A>where C:Comparator<T>,A:MonoidAct<Key=T,Act:PartialEq>{type Item=T;fn next(&mut self)->Option<Self::Item>{self.heap.pop()}fn size_hint(&self)->(usize,Option<usize>){let len=self.heap.len();(len,Some(len))}}impl<T,C,A>ExactSizeIterator for IntoIter<T,C,A>where C:Comparator<T>,A:MonoidAct<Key=T,Act:PartialEq>{fn len(&self)->usize{self.heap.len()}}impl<T,C,A>FusedIterator for IntoIter<T,C,A>where C:Comparator<T>,A:MonoidAct<Key=T,Act:PartialEq>{}impl<T,C,A>IntoIterator for PairingHeap<T,C,A>where C:Comparator<T>,A:MonoidAct<Key=T,Act:PartialEq>{type Item=T;type IntoIter=IntoIter<T,C,A>;fn into_iter(self)->Self::IntoIter{IntoIter::new(self)}}}
// codesnip-guard: TupleOperation
#[cfg_attr(any(),rustfmt::skip)]mod tuple_operation_impl{use super::*;macro_rules!impl_tuple_operation{(@impl)=>{impl Magma for(){type T=();fn operate(_x:&Self::T,_y:&Self::T)->Self::T{}}impl Unital for(){fn unit()->Self::T{}}impl Associative for(){}impl Commutative for(){}impl Idempotent for(){}impl Invertible for(){fn inverse(_x:&Self::T)->Self::T{}}};(@impl$($T:ident$i:tt)*)=>{impl<$($T:Magma),*>Magma for($($T,)*){type T=($(<$T as Magma>::T,)*);fn operate(x:&Self::T,y:&Self::T)->Self::T{($(<$T as Magma>::operate(&x.$i,&y.$i),)*)}}impl<$($T:Unital),*>Unital for($($T,)*){fn unit()->Self::T{($(<$T as Unital>::unit(),)*)}}impl<$($T:Associative),*>Associative for($($T,)*){}impl<$($T:Commutative),*>Commutative for($($T,)*){}impl<$($T:Idempotent),*>Idempotent for($($T,)*){}impl<$($T:Invertible),*>Invertible for($($T,)*){fn inverse(x:&Self::T)->Self::T{($(<$T as Invertible>::inverse(&x.$i),)*)}}};(@inner$($T:ident$i:tt)*;$U:ident$j:tt$($t:tt)*)=>{impl_tuple_operation!(@impl$($T$i)*);impl_tuple_operation!(@inner$($T$i)*$U$j;$($t)*);};(@inner$($T:ident$i:tt)*;)=>{impl_tuple_operation!(@impl$($T$i)*);};($($t:tt)*)=>{impl_tuple_operation!(@inner;$($t)*);};}impl_tuple_operation!(A 0 B 1 C 2 D 3 E 4 F 5 G 6 H 7 I 8 J 9);}
// codesnip-guard: UnionFind
#[cfg_attr(any(),rustfmt::skip)]pub use self::union_find::{MergingUnionFind,PotentializedUnionFind,UndoableUnionFind,UnionFind,UnionFindBase};#[cfg_attr(any(),rustfmt::skip)]pub mod union_find{use super::{Group,Monoid};use std::{collections::HashMap,fmt::{self,Debug},marker::PhantomData,mem::{MaybeUninit,needs_drop,swap}};pub struct UnionFindBase<U,F,M,P,H>where U:UnionStrategy,F:FindStrategy,M:UfMergeSpec,P:Monoid,H:UndoStrategy<UfCell<M::Data,P>>{cells:Vec<UfCell<M::Data,P>>,merger:M,history:H::History,_marker:PhantomData<fn()->(U,F)>}impl<U,F,M,P,H>Clone for UnionFindBase<U,F,M,P,H>where U:UnionStrategy,F:FindStrategy,M:UfMergeSpec<Data:Clone>+Clone,P:Monoid,H:UndoStrategy<UfCell<M::Data,P>,History:Clone>{fn clone(&self)->Self{Self{cells:self.cells.clone(),merger:self.merger.clone(),history:self.history.clone(),_marker:self._marker}}}impl<U,F,M,P,H>Debug for UnionFindBase<U,F,M,P,H>where U:UnionStrategy,F:FindStrategy,M:UfMergeSpec<Data:Debug>,P:Monoid<T:Debug>,H:UndoStrategy<UfCell<M::Data,P>,History:Debug>{fn fmt(&self,f:&mut fmt::Formatter<'_>)->fmt::Result{f.debug_struct("UnionFindBase").field("cells",&self.cells).field("history",&self.history).finish()}}pub struct UfCell<D,P>where P:Monoid{parent_or_info:i32,data:MaybeUninit<D>,potential:P::T}impl<D,P>Clone for UfCell<D,P>where D:Clone,P:Monoid{fn clone(&self)->Self{let is_root=self.is_root();let potential=if is_root{P::unit()}else{self.potential.clone()};Self{parent_or_info:self.parent_or_info,data:if is_root{MaybeUninit::new(self.data().clone())}else{MaybeUninit::uninit()},potential}}}impl<D,P>Debug for UfCell<D,P>where D:Debug,P:Monoid<T:Debug>{fn fmt(&self,f:&mut fmt::Formatter<'_>)->fmt::Result{if let Some(info)=self.root_info(){f.debug_tuple("Root").field(&(info,self.data())).finish()}else{f.debug_tuple("Child").field(&(self.parent().unwrap(),&self.potential)).finish()}}}impl<D,P>UfCell<D,P>where P:Monoid{fn root(info:u32,data:D)->Self{let potential=P::unit();Self{parent_or_info:!(info as i32),data:MaybeUninit::new(data),potential}}fn root_info(&self)->Option<u32>{(self.parent_or_info<0).then_some((!self.parent_or_info)as u32)}fn set_root_info(&mut self,info:u32){self.parent_or_info=!(info as i32);}fn parent(&self)->Option<usize>{(self.parent_or_info>=0).then_some(self.parent_or_info as usize)}fn set_child(&mut self,parent:usize,potential:P::T){let was_root=self.is_root();self.parent_or_info=parent as i32;if needs_drop::<D>()&&was_root{unsafe{self.data.assume_init_drop()};}self.potential=potential;}fn is_root(&self)->bool{self.parent_or_info<0}fn data(&self)->&D{unsafe{self.data.assume_init_ref()}}fn data_mut(&mut self)->&mut D{unsafe{self.data.assume_init_mut()}}}impl<D,P>Drop for UfCell<D,P>where P:Monoid{fn drop(&mut self){if needs_drop::<D>()&&self.is_root(){unsafe{self.data.assume_init_drop()};}}}pub trait FindStrategy{const CHENGE_ROOT:bool;}pub enum PathCompression{}impl FindStrategy for PathCompression{const CHENGE_ROOT:bool=true;}impl FindStrategy for(){const CHENGE_ROOT:bool=false;}pub trait UnionStrategy{fn single_info()->u32;fn check_directoin(parent:&u32,child:&u32)->bool;fn unite(parent:&u32,child:&u32)->u32;}pub enum UnionBySize{}impl UnionStrategy for UnionBySize{fn single_info()->u32{1}fn check_directoin(parent:&u32,child:&u32)->bool{parent>=child}fn unite(parent:&u32,child:&u32)->u32{parent+child}}pub enum UnionByRank{}impl UnionStrategy for UnionByRank{fn single_info()->u32{0}fn check_directoin(parent:&u32,child:&u32)->bool{parent>=child}fn unite(parent:&u32,child:&u32)->u32{parent+(parent==child)as u32}}impl UnionStrategy for(){fn single_info()->u32{0}fn check_directoin(_parent:&u32,_child:&u32)->bool{false}fn unite(_parent:&u32,_child:&u32)->u32{0}}pub trait UfMergeSpec{type Data;fn merge(&mut self,to:&mut Self::Data,from:&mut Self::Data);}#[derive(Debug,Clone)]pub struct FnMerger<T,F>{f:F,_marker:PhantomData<fn()->T>}impl<T,F>UfMergeSpec for FnMerger<T,F>where F:FnMut(&mut T,&mut T){type Data=T;fn merge(&mut self,to:&mut Self::Data,from:&mut Self::Data){(self.f)(to,from)}}impl UfMergeSpec for(){type Data=();fn merge(&mut self,_to:&mut Self::Data,_from:&mut Self::Data){}}pub trait UndoStrategy<T>{const UNDOABLE:bool;type History:Default;fn unite(history:&mut Self::History,x:usize,y:usize,cells:&[T]);fn undo_unite(history:&mut Self::History,cells:&mut[T]);}pub enum Undoable{}impl<T>UndoStrategy<T>for Undoable where T:Clone{const UNDOABLE:bool=true;type History=Vec<[(usize,T);2]>;fn unite(history:&mut Self::History,x:usize,y:usize,cells:&[T]){let cx=cells[x].clone();let cy=cells[y].clone();history.push([(x,cx),(y,cy)]);}fn undo_unite(history:&mut Self::History,cells:&mut[T]){if let Some([(x,cx),(y,cy)])=history.pop(){cells[x]=cx;cells[y]=cy;}}}impl<T>UndoStrategy<T>for(){const UNDOABLE:bool=false;type History=();fn unite(_history:&mut Self::History,_x:usize,_y:usize,_cells:&[T]){}fn undo_unite(_history:&mut Self::History,_cells:&mut[T]){}}impl<U,F,P,H>UnionFindBase<U,F,(),P,H>where U:UnionStrategy,F:FindStrategy,P:Monoid,H:UndoStrategy<UfCell<(),P>>{pub fn new(n:usize)->Self{let cells:Vec<_>=(0..n).map(|_|UfCell::root(U::single_info(),())).collect();Self{cells,merger:(),history:Default::default(),_marker:PhantomData}}pub fn push(&mut self){self.cells.push(UfCell::root(U::single_info(),()));}}impl<U,F,T,Merge,P,H>UnionFindBase<U,F,FnMerger<T,Merge>,P,H>where U:UnionStrategy,F:FindStrategy,Merge:FnMut(&mut T,&mut T),P:Monoid,H:UndoStrategy<UfCell<T,P>>{pub fn new_with_merger(n:usize,mut init:impl FnMut(usize)->T,merge:Merge)->Self{let cells:Vec<_>=(0..n).map(|i|UfCell::root(U::single_info(),init(i))).collect();Self{cells,merger:FnMerger{f:merge,_marker:PhantomData},history:Default::default(),_marker:PhantomData}}}impl<F,M,P,H>UnionFindBase<UnionBySize,F,M,P,H>where F:FindStrategy,M:UfMergeSpec,P:Monoid,H:UndoStrategy<UfCell<M::Data,P>>{pub fn size(&mut self,x:usize)->usize{let root=self.find_root(x);self.root_info(root).unwrap()as usize}}impl<U,F,M,P,H>UnionFindBase<U,F,M,P,H>where U:UnionStrategy,F:FindStrategy,M:UfMergeSpec,P:Monoid,H:UndoStrategy<UfCell<M::Data,P>>{fn root_info(&self,x:usize)->Option<u32>{self.cells[x].root_info()}fn set_root_info(&mut self,x:usize,info:u32){self.cells[x].set_root_info(info);}pub fn same(&mut self,x:usize,y:usize)->bool{self.find_root(x)==self.find_root(y)}pub fn merge_data(&mut self,x:usize)->&M::Data{let root=self.find_root(x);self.cells[root].data()}pub fn merge_data_mut(&mut self,x:usize)->&mut M::Data{let root=self.find_root(x);self.cells[root].data_mut()}pub fn roots(&self)->impl Iterator<Item=usize>+'_{(0..self.cells.len()).filter(|&x|self.cells[x].is_root())}pub fn all_group_members(&mut self)->HashMap<usize,Vec<usize>>{let mut groups_map=HashMap::new();for x in 0..self.cells.len(){let r=self.find_root(x);groups_map.entry(r).or_insert_with(Vec::new).push(x);}groups_map}pub fn find(&mut self,x:usize)->(usize,P::T){let mut current=x;let mut potential=P::unit();while let Some(parent)=self.cells[current].parent(){let current_potential=self.cells[current].potential.clone();potential=P::operate(&current_potential,&potential);if F::CHENGE_ROOT&&let Some(parent_parent)=self.cells[parent].parent(){let potential=P::operate(&self.cells[parent].potential,&current_potential);self.cells[current].set_child(parent_parent,potential);}current=parent;}(current,potential)}pub fn find_root(&mut self,x:usize)->usize{let mut current=x;while let Some(parent)=self.cells[current].parent(){if F::CHENGE_ROOT&&let Some(parent_parent)=self.cells[parent].parent(){let potential=P::operate(&self.cells[parent].potential,&self.cells[current].potential);self.cells[current].set_child(parent_parent,potential);}current=parent;}current}pub fn unite_noninv(&mut self,x:usize,y:usize,potential:P::T)->bool{let(rx,potx)=self.find(x);let ry=self.find_root(y);if rx==ry||y!=ry{return false;}H::unite(&mut self.history,rx,ry,&self.cells);{let ptr=self.cells.as_mut_ptr();let(cx,cy)=unsafe{(&mut*ptr.add(rx),&mut*ptr.add(ry))};self.merger.merge(cx.data_mut(),cy.data_mut());}let info=U::unite(&self.root_info(rx).unwrap(),&self.root_info(ry).unwrap());self.set_root_info(rx,info);self.cells[ry].set_child(rx,P::operate(&potx,&potential));true}}impl<U,F,M,P,H>UnionFindBase<U,F,M,P,H>where U:UnionStrategy,F:FindStrategy,M:UfMergeSpec,P:Group,H:UndoStrategy<UfCell<M::Data,P>>{pub fn difference(&mut self,x:usize,y:usize)->Option<P::T>{let(rx,potx)=self.find(x);let(ry,poty)=self.find(y);if rx==ry{Some(P::operate(&P::inverse(&potx),&poty))}else{None}}pub fn unite_with(&mut self,x:usize,y:usize,potential:P::T)->bool{let(mut rx,potx)=self.find(x);let(mut ry,poty)=self.find(y);if rx==ry{return false;}let mut xinfo=self.root_info(rx).unwrap();let mut yinfo=self.root_info(ry).unwrap();let inverse=!U::check_directoin(&xinfo,&yinfo);let potential=if inverse{P::rinv_operate(&poty,&P::operate(&potx,&potential))}else{P::operate(&potx,&P::rinv_operate(&potential,&poty))};if inverse{swap(&mut rx,&mut ry);swap(&mut xinfo,&mut yinfo);}H::unite(&mut self.history,rx,ry,&self.cells);{let ptr=self.cells.as_mut_ptr();let(cx,cy)=unsafe{(&mut*ptr.add(rx),&mut*ptr.add(ry))};self.merger.merge(cx.data_mut(),cy.data_mut());}self.set_root_info(rx,U::unite(&xinfo,&yinfo));self.cells[ry].set_child(rx,potential);true}pub fn unite(&mut self,x:usize,y:usize)->bool{self.unite_with(x,y,P::unit())}}impl<U,M,P,H>UnionFindBase<U,(),M,P,H>where U:UnionStrategy,M:UfMergeSpec,P:Monoid,H:UndoStrategy<UfCell<M::Data,P>>{pub fn undo(&mut self){H::undo_unite(&mut self.history,&mut self.cells);}}pub type UnionFind=UnionFindBase<UnionBySize,PathCompression,(),(),()>;pub type MergingUnionFind<T,M>=UnionFindBase<UnionBySize,PathCompression,FnMerger<T,M>,(),()>;pub type PotentializedUnionFind<P>=UnionFindBase<UnionBySize,PathCompression,(),P,()>;pub type UndoableUnionFind=UnionFindBase<UnionBySize,(),(),(),Undoable>;}
// codesnip-guard: algebra
#[cfg_attr(any(),rustfmt::skip)]pub use self::magma::*;#[cfg_attr(any(),rustfmt::skip)]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;fn reverse_operate(x:&Self::T,y:&Self::T)->Self::T{Self::operate(y,x)}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:Magma{}#[doc=" associative binary operation"]pub trait SemiGroup:Magma+Associative{}impl<S>SemiGroup for S where S:Magma+Associative{}#[doc=" $\\exists e \\in T, \\forall a \\in T, e \\circ a = a \\circ e = a$"]pub trait Unital:Magma{#[doc=" identity element: $e$"]fn unit()->Self::T;fn is_unit(x:&Self::T)->bool where Self::T:PartialEq{x==&Self::unit()}fn set_unit(x:&mut Self::T){*x=Self::unit();}}pub trait ExpBits{type Iter:Iterator<Item=bool>;fn bits(self)->Self::Iter;}pub trait SignedExpBits{type T:ExpBits;fn neg_and_bits(self)->(bool,Self::T);}pub struct Bits<T>{n:T}macro_rules!impl_exp_bits_for_uint{($($t:ty)*)=>{$(impl Iterator for Bits<$t>{type Item=bool;fn next(&mut self)->Option<bool>{if self.n==0{None}else{let bit=(self.n&1)==1;self.n>>=1;Some(bit)}}}impl ExpBits for$t{type Iter=Bits<$t>;fn bits(self)->Self::Iter{Bits{n:self}}}impl SignedExpBits for$t{type T=$t;fn neg_and_bits(self)->(bool,Self::T){(false,self)}})*};}impl_exp_bits_for_uint!(u8 u16 u32 u64 u128 usize);macro_rules!impl_signed_exp_bits_for_sint{($($s:ty,$u:ty;)*)=>{$(impl SignedExpBits for$s{type T=$u;fn neg_and_bits(self)->(bool,Self::T){(self<0,self.unsigned_abs())}})*};}impl_signed_exp_bits_for_sint!(i8,u8;i16,u16;i32,u32;i64,u64;i128,u128;isize,usize;);#[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<E>(mut x:Self::T,exp:E)->Self::T where E:ExpBits{let mut bits=exp.bits();let Some(first)=bits.next()else{return Self::unit();};let mut res=if first{x.clone()}else{Self::unit()};for bit in bits{x=Self::operate(&x,&x);if bit{res=Self::operate(&res,&x);}}res}fn fold<I>(iter:I)->Self::T where I:IntoIterator<Item=Self::T>{let mut iter=iter.into_iter();if let Some(item)=iter.next(){iter.fold(item,|acc,x|Self::operate(&acc,&x))}else{Self::unit()}}}impl<M>Monoid for M where M:SemiGroup+Unital{}#[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+Unital{#[doc=" $a$ where $a \\circ x = e$"]fn inverse(x:&Self::T)->Self::T;fn rinv_operate(x:&Self::T,y:&Self::T)->Self::T{Self::operate(x,&Self::inverse(y))}fn rinv_operate_assign(x:&mut Self::T,y:&Self::T){*x=Self::rinv_operate(x,y);}}#[doc=" associative binary operation and an identity element and inverse elements"]pub trait Group:Monoid+Invertible{fn signed_pow<E>(x:Self::T,exp:E)->Self::T where E:SignedExpBits{let(neg,exp)=E::neg_and_bits(exp);let res=Self::pow(x,exp);if neg{Self::inverse(&res)}else{res}}}impl<G>Group for G where G:Monoid+Invertible{}#[doc=" $\\forall a,\\forall b \\in T, a \\circ b = b \\circ a$"]pub trait Commutative:Magma{}#[doc=" commutative monoid"]pub trait AbelianMonoid:Monoid+Commutative{}impl<M>AbelianMonoid for M where M:Monoid+Commutative{}#[doc=" commutative group"]pub trait AbelianGroup:Group+Commutative{}impl<G>AbelianGroup for G where G:Group+Commutative{}#[doc=" $\\forall a \\in T, a \\circ a = a$"]pub trait Idempotent:Magma{}#[doc=" idempotent monoid"]pub trait IdempotentMonoid:Monoid+Idempotent{}impl<M>IdempotentMonoid for M where M:Monoid+Idempotent{}#[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),*))};}#[macro_export]macro_rules!define_monoid{($Name:ident,$t:ty,|$x:ident,$y:ident|$op:expr,$unit:expr)=>{struct$Name;impl Magma for$Name{type T=$t;fn operate($x:&Self::T,$y:&Self::T)->Self::T{$op}}impl Unital for$Name{fn unit()->Self::T{$unit}}impl Associative for$Name{}};}}
// codesnip-guard: array
#[cfg_attr(any(),rustfmt::skip)]mod array{#[macro_export]macro_rules!array{[@inner$data:ident=[$init:expr;$len:expr]]=>{{use::std::mem::{ManuallyDrop,MaybeUninit};let mut$data:[MaybeUninit<_>;$len]=unsafe{MaybeUninit::uninit().assume_init()};$init;#[repr(C)]union __Transmuter<const N:usize,T:Clone>{src:ManuallyDrop<[MaybeUninit<T>;N]>,dst:ManuallyDrop<[T;N]>,}ManuallyDrop::into_inner(unsafe{__Transmuter{src:ManuallyDrop::new($data)}.dst})}};[||$e:expr;$len:expr]=>{$crate::array![@inner data=[data.iter_mut().for_each(|item|*item=MaybeUninit::new($e));$len]]};[|$i:pat_param|$e:expr;$len:expr]=>{$crate::array![@inner data=[data.iter_mut().enumerate().for_each(|($i,item)|*item=MaybeUninit::new($e));$len]]};[$e:expr;$len:expr]=>{{let e=$e;$crate::array![||Clone::clone(&e);$len]}};}}
// codesnip-guard: scanner
#[cfg_attr(any(),rustfmt::skip)]pub use self::scanner::*;#[cfg_attr(any(),rustfmt::skip)]mod scanner{use std::{iter::{FromIterator,from_fn,repeat_with},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 Scan:Sized{type Output;fn scan<S:ScanSource>(source:&mut S)->Option<Self::Output>;fn scan_vec<S:ScanSource>(source:&mut S,size:usize,capacity:usize)->Vec<Self::Output>{let mut values=Vec::with_capacity(capacity.max(size));values.extend((0..size).map(|_|source.scan::<Self>()));values}}pub trait MarkedScan:Sized{type Output;fn mscan<S:ScanSource>(self,source:&mut S)->Option<Self::Output>;}pub trait ScanSource:Sized{#[doc=" Reads a token under the source's input requirements."]#[doc=" Checked sources return `None` at EOF; unchecked sources require available input."]fn next_token(&mut self)->Option<&str>;#[doc=" Skips separators without consuming the next token."]#[inline]fn skip_whitespace(&mut self){}#[inline]fn read_u8(&mut self)->Option<u8>{self.next_token()?.parse().ok()}#[inline]fn read_u16(&mut self)->Option<u16>{self.next_token()?.parse().ok()}#[inline]fn read_u32(&mut self)->Option<u32>{self.next_token()?.parse().ok()}fn read_u32_vec(&mut self,size:usize,capacity:usize)->Vec<u32>{let mut values=Vec::with_capacity(capacity.max(size));values.extend((0..size).map(|_|self.scan::<u32>()));values}#[inline]fn read_u64(&mut self)->Option<u64>{self.next_token()?.parse().ok()}#[inline]fn read_u128(&mut self)->Option<u128>{self.next_token()?.parse().ok()}#[inline]fn read_usize(&mut self)->Option<usize>{self.next_token()?.parse().ok()}#[inline]fn read_i8(&mut self)->Option<i8>{self.next_token()?.parse().ok()}#[inline]fn read_i16(&mut self)->Option<i16>{self.next_token()?.parse().ok()}#[inline]fn read_i32(&mut self)->Option<i32>{self.next_token()?.parse().ok()}#[inline]fn read_i64(&mut self)->Option<i64>{self.next_token()?.parse().ok()}#[inline]fn read_i128(&mut self)->Option<i128>{self.next_token()?.parse().ok()}#[inline]fn read_isize(&mut self)->Option<isize>{self.next_token()?.parse().ok()}#[doc=" Panics if reading fails."]#[inline]fn scan<T:Scan>(&mut self)->T::Output{T::scan(self).expect("scan error")}#[doc=" Panics if reading fails."]#[inline]fn mscan<T:MarkedScan>(&mut self,marker:T)->T::Output{marker.mscan(self).expect("scan error")}fn scan_vec<T:Scan>(&mut self,size:usize,capacity:usize)->Vec<T::Output>{if size==0{self.skip_whitespace();}T::scan_vec(self,size,capacity)}#[inline]fn iter<T:Scan>(&mut self)->ScannerIter<'_,Self,T>{ScannerIter{inner:self,_marker:PhantomData}}}#[derive(Clone,Debug)]pub struct Scanner<'a,I:Iterator<Item=&'a str>=std::str::SplitAsciiWhitespace<'a>>{iter:I}impl<'a>Scanner<'a>{pub fn new(s:&'a str)->Self{Self{iter:s.split_ascii_whitespace()}}}impl<'a,I:Iterator<Item=&'a str>>Scanner<'a,I>{pub fn new_from_iter(iter:I)->Self{Self{iter}}}impl<'a,I:Iterator<Item=&'a str>>ScanSource for Scanner<'a,I>{fn next_token(&mut self)->Option<&str>{self.iter.next()}}macro_rules!impl_scan{($($t:ty)*)=>{$(impl Scan for$t{type Output=Self;fn scan<I:ScanSource>(iter:&mut I)->Option<Self>{iter.next_token()?.parse::<$t>().ok()}})*};}impl_scan!(char f32 f64 String);macro_rules!impl_integer_scan{($($t:ty=>$read:ident),*$(,)?)=>{$(impl Scan for$t{type Output=Self;#[inline]fn scan<S:ScanSource>(source:&mut S)->Option<Self>{source.$read()}})*};}impl_integer_scan!(u8=>read_u8,u16=>read_u16,u64=>read_u64,u128=>read_u128,usize=>read_usize,i8=>read_i8,i16=>read_i16,i32=>read_i32,i64=>read_i64,i128=>read_i128,isize=>read_isize,);impl Scan for u32{type Output=Self;#[inline]fn scan<S:ScanSource>(source:&mut S)->Option<Self>{source.read_u32()}fn scan_vec<S:ScanSource>(source:&mut S,size:usize,capacity:usize)->Vec<Self>{source.read_u32_vec(size,capacity)}}macro_rules!impl_scan_tuple{(@impl$($T:ident)*)=>{impl<$($T:Scan),*>Scan for($($T,)*){type Output=($(<$T as Scan>::Output,)*);fn scan<It:ScanSource>(_iter:&mut It)->Option<Self::Output>{Some(($(<$T as Scan>::scan(_iter)?,)*))}}};(@inner$($T:ident)*,)=>{impl_scan_tuple!(@impl$($T)*);};(@inner$($T:ident)*,$U:ident$($Rest:ident)*)=>{impl_scan_tuple!(@impl$($T)*);impl_scan_tuple!(@inner$($T)*$U,$($Rest)*);};($($T:ident)*)=>{impl_scan_tuple!(@inner,$($T)*);};}impl_scan_tuple!(A B C D E F G H I J K);pub struct ScannerIter<'a,S,T>{inner:&'a mut S,_marker:PhantomData<fn()->T>}impl<S:ScanSource,T:Scan>Iterator for ScannerIter<'_,S,T>{type Item=T::Output;#[inline]fn next(&mut self)->Option<Self::Item>{T::scan(self.inner)}}#[doc=" scan a value with Scanner"]#[doc=""]#[doc=" - `scan_value!(scanner, ELEMENT)`"]#[doc=""]#[doc=" ELEMENT :="]#[doc=" - `$ty`: Scan"]#[doc=" - `&str`: borrowed token; the source stays borrowed until its last use"]#[doc=" - `@$expr`: MarkedScan"]#[doc=" - `$ty = $expr`: MarkedScan"]#[doc=" - `[ELEMENT; $expr]`: vector"]#[doc=" - `[$ty; $len; capacity $capacity]`: vector with reserved capacity"]#[doc=" - `[ELEMENT; const $expr]`: array"]#[doc=" - `[ELEMENT]`: iterator"]#[doc=" - `[ELEMENT; iter $expr]`: iterator of the specified length"]#[doc=" - `($(ELEMENT)*,)`: tuple"]#[macro_export]macro_rules!scan_value{(@repeat$scanner:expr,[$($t:tt)*]$len:expr)=>{{$crate::scan_value!(@iter$scanner,[$($t)*]$len).collect::<Vec<_>>()}};(@repeat$scanner:expr,[$($t:tt)*])=>{{::std::iter::repeat_with(||$crate::scan_value!(@inner$scanner,[]$($t)*))}};(@iter$scanner:expr,[$($t:tt)*]$len:expr)=>{{let size=$len;if size==0{$scanner.skip_whitespace();}$crate::scan_value!(@repeat$scanner,[$($t)*]).take(size)}};(@array$scanner:expr,[$($t:tt)*]$len:expr)=>{{if$len==0{$scanner.skip_whitespace();}$crate::array![||$crate::scan_value!(@inner$scanner,[]$($t)*);$len]}};(@tuple$scanner:expr,[$([$($args:tt)*])*])=>{($($($args)*,)*)};(@sparen$scanner:expr,[]@$e:expr;$($t:tt)*)=>{$crate::scan_value!(@sparen$scanner,[@$e]$($t)*)};(@sparen$scanner:expr,[]($($tt:tt)*);$($t:tt)*)=>{$crate::scan_value!(@sparen$scanner,[($($tt)*)]$($t)*)};(@sparen$scanner:expr,[][$($tt:tt)*];$($t:tt)*)=>{$crate::scan_value!(@sparen$scanner,[[$($tt)*]]$($t)*)};(@sparen$scanner:expr,[]$ty:ty=$e:expr;$($t:tt)*)=>{$crate::scan_value!(@sparen$scanner,[$ty=$e]$($t)*)};(@sparen$scanner:expr,[]$ty:ty;$($t:tt)*)=>{$crate::scan_value!(@sparen$scanner,[$ty]$($t)*)};(@sparen$scanner:expr,[]$($args:tt)*)=>{$crate::scan_value!(@repeat$scanner,[$($args)*])};(@sparen$scanner:expr,[$($args:tt)+]const$len:expr)=>{$crate::scan_value!(@array$scanner,[$($args)+]$len)};(@sparen$scanner:expr,[$($args:tt)+]iter$len:expr)=>{$crate::scan_value!(@iter$scanner,[$($args)+]$len)};(@sparen$scanner:expr,[$($args:tt)+]$len:expr;capacity$capacity:expr)=>{{let size=$len;let capacity=$capacity;$scanner.scan_vec::<$($args)+>(size,capacity)}};(@sparen$scanner:expr,[$($args:tt)+]$len:expr)=>{$crate::scan_value!(@repeat$scanner,[$($args)+]$len)};(@$tag:ident$scanner:expr,[[$($args:tt)*]])=>{$($args)*};(@$tag:ident$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$scanner:expr,[$($args:tt)*][$($tt:tt)*]$($t:tt)*)=>{$crate::scan_value!(@$tag$scanner,[$($args)*[$crate::scan_value!(@sparen$scanner,[]$($tt)*)]]$($t)*)};(@$tag:ident$scanner:expr,[$($args:tt)*]&str$(,$($t:tt)*)?)=>{$crate::scan_value!(@$tag$scanner,[$($args)*[$scanner.next_token().expect("scan error")]]$(,$($t)*)?)};(@$tag:ident$scanner:expr,[$($args:tt)*]$ty:ty=$e:expr$(,$($t:tt)*)?)=>{$crate::scan_value!(@$tag$scanner,[$($args)*[{let _tmp:$ty=$scanner.mscan($e);_tmp}]]$(,$($t)*)?)};(@$tag:ident$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$scanner:expr,[$($args:tt)*])=>{::std::compile_error!(::std::stringify!($($args)*))};(src=$src:expr,$($t:tt)*)=>{{let mut __scanner=Scanner::new($src);$crate::scan_value!(@inner __scanner,[]$($t)*)}};(iter=$iter:expr,$($t:tt)*)=>{{let mut __scanner=Scanner::new_from_iter($iter);$crate::scan_value!(@inner __scanner,[]$($t)*)}};($scanner:expr,$($t:tt)*)=>{$crate::scan_value!(@inner$scanner,[]$($t)*)}}#[doc=" scan and bind values with Scanner"]#[doc=""]#[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$(,$($t:tt)*)?)=>{$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)*]&str$(,$($t:tt)*)?)=>{$crate::scan!(@let$scanner,[$($p)*][$($tt)*&str]$(,$($t)*)?)};(@ty$scanner:expr,[$($p:tt)*][$($tt:tt)*]$ty:ty=$e:expr$(,$($t:tt)*)?)=>{$crate::scan!(@let$scanner,[$($p)*][$($tt)*$ty=$e]$(,$($t)*)?)};(@ty$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)*)};(src=$src:expr,$($t:tt)*)=>{let mut __scanner=Scanner::new($src);$crate::scan!(@pat __scanner,[][]$($t)*)};(iter=$iter:expr,$($t:tt)*)=>{let mut __scanner=Scanner::new_from_iter($iter);$crate::scan!(@pat __scanner,[][]$($t)*)};($scanner:expr,$($t:tt)*)=>{$crate::scan!(@pat$scanner,[][]$($t)*)}}#[doc=" define enum scan rules"]#[doc=""]#[doc=" # Example"]#[doc=" ```rust"]#[doc=" # use competitive::{define_enum_scan, tools::{CharsWithBase, Scan, ScanSource, Scanner, Usize1}};"]#[doc=" define_enum_scan! {"]#[doc="   enum Query: u8 {"]#[doc="     0 => Noop,"]#[doc="     1 => Args { i: Usize1, s: char },"]#[doc="     9 => Complex { n: usize, c: [(usize, Vec<usize> = CharsWithBase('a')); n] },"]#[doc="   }"]#[doc=" }"]#[doc=" ```"]#[macro_export]macro_rules!define_enum_scan{(@field_ty@repeat[$($t:tt)*]$($len:expr)?)=>{Vec<$crate::define_enum_scan!(@field_ty$($t)*)>};(@field_ty@array[$($t:tt)*]$len:expr)=>{[$crate::define_enum_scan!(@field_ty$($t)*);$len]};(@field_ty@tuple[$([$($args:tt)*])*])=>{($($($args)*,)*)};(@field_ty@sparen[]($($tt:tt)*);$($t:tt)*)=>{$crate::define_enum_scan!(@field_ty@sparen[($($tt)*)]$($t)*)};(@field_ty@sparen[][$($tt:tt)*];$($t:tt)*)=>{$crate::define_enum_scan!(@field_ty@sparen[[$($tt)*]]$($t)*)};(@field_ty@sparen[]$ty:ty=$e:expr;$($t:tt)*)=>{$crate::define_enum_scan!(@field_ty@sparen[$ty=$e]$($t)*)};(@field_ty@sparen[]$ty:ty;$($t:tt)*)=>{$crate::define_enum_scan!(@field_ty@sparen[$ty]$($t)*)};(@field_ty@sparen[]$($args:tt)*)=>{$crate::define_enum_scan!(@field_ty@repeat[$($args)*])};(@field_ty@sparen[$($args:tt)+]const$len:expr)=>{$crate::define_enum_scan!(@field_ty@array[$($args)+]$len)};(@field_ty@sparen[$($args:tt)+]$len:expr)=>{$crate::define_enum_scan!(@field_ty@repeat[$($args)+]$len)};(@field_ty@$tag:ident[$($args:tt)*]($($tuple:tt)*)$($t:tt)*)=>{$crate::define_enum_scan!(@field_ty@$tag[$($args)*[$crate::define_enum_scan!(@field_ty@tuple[]$($tuple)*)]]$($t)*)};(@field_ty@$tag:ident[$($args:tt)*][$($tt:tt)*]$($t:tt)*)=>{$crate::define_enum_scan!(@field_ty@$tag[$($args)*[$crate::define_enum_scan!(@field_ty@sparen[]$($tt)*)]]$($t)*)};(@field_ty@$tag:ident[$($args:tt)*]$ty:ty=$e:expr$(,$($t:tt)*)?)=>{$crate::define_enum_scan!(@field_ty@$tag[$($args)*[$ty]]$(,$($t)*)?)};(@field_ty@$tag:ident[$($args:tt)*]$ty:ty$(,$($t:tt)*)?)=>{$crate::define_enum_scan!(@field_ty@$tag[$($args)*[<$ty as Scan>::Output]]$(,$($t)*)?)};(@field_ty@$tag:ident[$($args:tt)*],$($t:tt)*)=>{$crate::define_enum_scan!(@field_ty@$tag[$($args)*]$($t)*)};(@field_ty@$tag:ident[[$($args:tt)*]])=>{$($args)*};(@field_ty@$tag:ident[$($args:tt)*])=>{::std::compile_error!(::std::stringify!($($args)*))};(@field_ty$($t:tt)*)=>{$crate::define_enum_scan!(@field_ty@inner[]$($t)*)};(@tag_expr raw,$iter:ident)=>{ScanSource::next_token($iter)?};(@tag_expr$d:ty,$iter:ident)=>{<$d as Scan>::scan($iter)?};(@variant([$($attr:tt)*]$vis:vis$T:ident$d:tt)[$($vars:tt)*])=>{$crate::define_enum_scan!{@def$($attr)*$vis enum$T:$d{$($vars)*}}};(@variant$ctx:tt[$($vars:tt)*]$p:pat=>$v:ident{$($fs:tt)*}$($rest:tt)*)=>{$crate::define_enum_scan!{@field$ctx[$($vars)*]$p=>$v[]$($fs)*;$($rest)*}};(@variant$ctx:tt[$($vars:tt)*]$p:pat=>$v:ident$($rest:tt)*)=>{$crate::define_enum_scan!{@variant$ctx[$($vars)*$p=>$v,]$($rest)*}};(@variant$ctx:tt[$($vars:tt)*],$($rest:tt)*)=>{$crate::define_enum_scan!{@variant$ctx[$($vars)*]$($rest)*}};(@endfield$ctx:tt[$($vars:tt)*]$p:pat=>$v:ident[$($fs:tt)*][$f:ident:$($spec:tt)*],$($rest:tt)*)=>{$crate::define_enum_scan!{@field$ctx[$($vars)*]$p=>$v[$($fs)*[$f:$($spec)*]]$($rest)*}};(@endfield$ctx:tt[$($vars:tt)*]$p:pat=>$v:ident[$($fs:tt)*][$f:ident:$($spec:tt)*];$($rest:tt)*)=>{$crate::define_enum_scan!{@variant$ctx[$($vars)*$p=>$v{$($fs)*[$f:$($spec)*]},]$($rest)*}};(@field$ctx:tt[$($vars:tt)*]$p:pat=>$v:ident[$($fs:tt)*];$($rest:tt)*)=>{$crate::define_enum_scan!{@variant$ctx[$($vars)*$p=>$v{$($fs)*},]$($rest)*}};(@field$ctx:tt[$($vars:tt)*]$p:pat=>$v:ident[$($fs:tt)*]$f:ident:($($tuple:tt)*)$sep:tt$($rest:tt)*)=>{$crate::define_enum_scan!{@endfield$ctx[$($vars)*]$p=>$v[$($fs)*][$f:($($tuple)*)]$sep$($rest)*}};(@field$ctx:tt[$($vars:tt)*]$p:pat=>$v:ident[$($fs:tt)*]$f:ident:[$($x:tt)*]$sep:tt$($rest:tt)*)=>{$crate::define_enum_scan!{@endfield$ctx[$($vars)*]$p=>$v[$($fs)*][$f:[$($x)*]]$sep$($rest)*}};(@field$ctx:tt[$($vars:tt)*]$p:pat=>$v:ident[$($fs:tt)*]$f:ident:$ty:ty=$e:expr,$($rest:tt)*)=>{$crate::define_enum_scan!{@endfield$ctx[$($vars)*]$p=>$v[$($fs)*][$f:$ty=$e],$($rest)*}};(@field$ctx:tt[$($vars:tt)*]$p:pat=>$v:ident[$($fs:tt)*]$f:ident:$ty:ty;$($rest:tt)*)=>{$crate::define_enum_scan!{@endfield$ctx[$($vars)*]$p=>$v[$($fs)*][$f:$ty];$($rest)*}};(@field$ctx:tt[$($vars:tt)*]$p:pat=>$v:ident[$($fs:tt)*]$f:ident:$ty:ty=$e:expr;$($rest:tt)*)=>{$crate::define_enum_scan!{@endfield$ctx[$($vars)*]$p=>$v[$($fs)*][$f:$ty=$e];$($rest)*}};(@field$ctx:tt[$($vars:tt)*]$p:pat=>$v:ident[$($fs:tt)*]$f:ident:$ty:ty,$($rest:tt)*)=>{$crate::define_enum_scan!{@endfield$ctx[$($vars)*]$p=>$v[$($fs)*][$f:$ty],$($rest)*}};(@def$(#[$attr:meta])*$vis:vis enum$T:ident:$d:tt{$($p:pat=>$v:ident$({$([$f:ident:$($spec:tt)*])*})?,)*})=>{$(#[$attr])*$vis enum$T{$($v$({$($f:$crate::define_enum_scan!(@field_ty$($spec)*)),*})?),*}impl Scan for$T{type Output=Self;fn scan<I:ScanSource>(iter:&mut I)->Option<Self>{let tag=$crate::define_enum_scan!(@tag_expr$d,iter);match tag{$($p=>{$($(let$f=$crate::scan_value!((*iter),$($spec)*);)*)?Some($T::$v$({$($f),*})?)}),*_=>None,}}}};($(#[$attr:meta])*$vis:vis enum$T:ident:raw{$($body:tt)*})=>{$crate::define_enum_scan!{@variant([$(#[$attr])*]$vis$T raw)[]$($body)*}};($(#[$attr:meta])*$vis:vis enum$T:ident:$d:ty{$($body:tt)*})=>{$crate::define_enum_scan!{@variant([$(#[$attr])*]$vis$T$d)[]$($body)*}};}#[derive(Debug,Copy,Clone)]pub enum Usize1{}impl Scan for Usize1{type Output=usize;fn scan<I:ScanSource>(iter:&mut I)->Option<Self::Output>{<usize as Scan>::scan(iter)?.checked_sub(1)}}#[derive(Debug,Copy,Clone)]pub struct CharWithBase(pub char);impl MarkedScan for CharWithBase{type Output=usize;fn mscan<I:ScanSource>(self,iter:&mut I)->Option<Self::Output>{Some((<char as Scan>::scan(iter)?as u8-self.0 as u8)as usize)}}#[derive(Debug,Copy,Clone)]pub enum Chars{}impl Scan for Chars{type Output=Vec<char>;fn scan<I:ScanSource>(iter:&mut I)->Option<Self::Output>{Some(iter.next_token()?.chars().collect())}}#[derive(Debug,Copy,Clone)]pub struct CharsWithBase(pub char);impl MarkedScan for CharsWithBase{type Output=Vec<usize>;fn mscan<I:ScanSource>(self,iter:&mut I)->Option<Self::Output>{Some(iter.next_token()?.chars().map(|c|(c as u8-self.0 as u8)as usize).collect())}}#[derive(Debug,Copy,Clone)]pub enum Byte1{}impl Scan for Byte1{type Output=u8;fn scan<I:ScanSource>(iter:&mut I)->Option<Self::Output>{let bytes=iter.next_token()?.as_bytes();assert_eq!(bytes.len(),1);Some(bytes[0])}}#[derive(Debug,Copy,Clone)]pub struct ByteWithBase(pub u8);impl MarkedScan for ByteWithBase{type Output=usize;fn mscan<I:ScanSource>(self,iter:&mut I)->Option<Self::Output>{Some((<char as Scan>::scan(iter)?as u8-self.0)as usize)}}#[derive(Debug,Copy,Clone)]pub enum Bytes{}impl Scan for Bytes{type Output=Vec<u8>;fn scan<I:ScanSource>(iter:&mut I)->Option<Self::Output>{Some(iter.next_token()?.bytes().collect())}}#[derive(Debug,Copy,Clone)]pub struct BytesWithBase(pub u8);impl MarkedScan for BytesWithBase{type Output=Vec<usize>;fn mscan<I:ScanSource>(self,iter:&mut I)->Option<Self::Output>{Some(iter.next_token()?.bytes().map(|c|(c-self.0)as usize).collect())}}#[derive(Debug,Copy,Clone)]pub struct Collect<T,B=Vec<<T as Scan>::Output>>where T:Scan,B:FromIterator<<T as Scan>::Output>{size:usize,_marker:PhantomData<fn()->(T,B)>}impl<T,B>Collect<T,B>where T:Scan,B:FromIterator<<T as Scan>::Output>{pub fn new(size:usize)->Self{Self{size,_marker:PhantomData}}}impl<T,B>MarkedScan for Collect<T,B>where T:Scan,B:FromIterator<<T as Scan>::Output>{type Output=B;fn mscan<I:ScanSource>(self,iter:&mut I)->Option<Self::Output>{if self.size==0{iter.skip_whitespace();}repeat_with(| |<T as Scan>::scan(iter)).take(self.size).collect()}}#[derive(Debug,Copy,Clone)]pub struct SizedCollect<T,B=Vec<<T as Scan>::Output>>where T:Scan,B:FromIterator<<T as Scan>::Output>{_marker:PhantomData<fn()->(T,B)>}impl<T,B>Scan for SizedCollect<T,B>where T:Scan,B:FromIterator<<T as Scan>::Output>{type Output=B;fn scan<I:ScanSource>(iter:&mut I)->Option<Self::Output>{let size=usize::scan(iter)?;if size==0{iter.skip_whitespace();}repeat_with(| |<T as Scan>::scan(iter)).take(size).collect()}}#[derive(Debug,Copy,Clone)]pub struct Splitted<T,P>where T:Scan{pat:P,_marker:PhantomData<fn()->T>}impl<T,P>Splitted<T,P>where T:Scan{pub fn new(pat:P)->Self{Self{pat,_marker:PhantomData}}}impl<T>MarkedScan for Splitted<T,char>where T:Scan{type Output=Vec<<T as Scan>::Output>;fn mscan<I:ScanSource>(self,iter:&mut I)->Option<Self::Output>{let mut iter=Scanner::new_from_iter(iter.next_token()?.split(self.pat));Some(from_fn(| |<T as Scan>::scan(&mut iter)).collect())}}impl<T>MarkedScan for Splitted<T,&str>where T:Scan{type Output=Vec<<T as Scan>::Output>;fn mscan<I:ScanSource>(self,iter:&mut I)->Option<Self::Output>{let mut iter=Scanner::new_from_iter(iter.next_token()?.split(self.pat));Some(from_fn(| |<T as Scan>::scan(&mut iter)).collect())}}impl<T,F>MarkedScan for F where F:Fn(&str)->Option<T>{type Output=T;fn mscan<I:ScanSource>(self,iter:&mut I)->Option<Self::Output>{self(iter.next_token()?)}}}
// codesnip-guard: zero_one
#[cfg_attr(any(),rustfmt::skip)]pub use self::zero_one::{One,Zero};#[cfg_attr(any(),rustfmt::skip)]mod zero_one{pub trait Zero:Sized{fn zero()->Self;#[inline]fn is_zero(&self)->bool where Self:PartialEq{self==&Self::zero()}#[inline]fn set_zero(&mut self){*self=Self::zero();}}pub trait One:Sized{fn one()->Self;#[inline]fn is_one(&self)->bool where Self:PartialEq{self==&Self::one()}#[inline]fn set_one(&mut self){*self=Self::one();}}macro_rules!impl_zero_one{($({$(<$T:ident:$Bound:ident>)?$Trait:ident$method:ident$($t:ty)*,$e:expr})*)=>{$(impl_zero_one!(@impl[$(<$T:$Bound>)?]$Trait$method[$($t)*],$e);)*};(@impl[<$T:ident:$Bound:ident>]$Trait:ident$method:ident[$($t:ty)*],$e:expr)=>{$(impl<$T:$Bound>$Trait for$t{fn$method()->Self{$e}})*};(@impl[]$Trait:ident$method:ident[$($t:ty)*],$e:expr)=>{$(impl$Trait for$t{fn$method()->Self{$e}})*};}impl_zero_one!({Zero zero u8 u16 u32 u64 usize i8 i16 i32 i64 isize u128 i128,0}{Zero zero f32 f64,0.}{One one u8 u16 u32 u64 usize i8 i16 i32 i64 isize u128 i128,1}{One one f32 f64,1.}{<T:Zero>Zero zero std::num::Wrapping<T>,Self(T::zero())}{<T:One>One one std::num::Wrapping<T>,Self(T::one())});}