Problem:
Score : 700 points

Problem Statement

In the State of Takahashi in AtCoderian Federation, there are N cities, numbered 1, 2, ..., N.
M bidirectional roads connect these cities.
The i-th road connects City A_i and City B_i.
Every road connects two distinct cities.
Also, for any two cities, there is at most one road that directly connects them.

One day, it was decided that the State of Takahashi would be divided into two states, Taka and Hashi.
After the division, each city in Takahashi would belong to either Taka or Hashi.
It is acceptable for all the cities to belong Taka, or for all the cities to belong Hashi.
Here, the following condition should be satisfied:

Any two cities in the same state, Taka or Hashi, are directly connected by a road.

Find the minimum possible number of roads whose endpoint cities belong to the same state.
If it is impossible to divide the cities into Taka and Hashi so that the condition is satisfied, print -1.

Constraints

2 \leq N \leq 700

0 \leq M \leq N(N-1)/2

1 \leq A_i \leq N

1 \leq B_i \leq N

A_i \neq B_i

If i \neq j, at least one of the following holds: A_i \neq A_j and B_i \neq B_j.

If i \neq j, at least one of the following holds: A_i \neq B_j and B_i \neq A_j.

Input

Input is given from Standard Input in the following format:

N M
A_1 B_1
A_2 B_2
:
A_M B_M

Output

Print the answer.

Sample Input 1

5 5
1 2
1 3
3 4
3 5
4 5

Sample Output 1

4

For example, if the cities 1, 2 belong to Taka and the cities 3, 4, 5 belong to Hashi, the condition is satisfied.
Here, the number of roads whose endpoint cities belong to the same state, is 4.

Sample Input 2

5 1
1 2

Sample Output 2

-1

In this sample, the condition cannot be satisfied regardless of which cities belong to each state.

Sample Input 3

4 3
1 2
1 3
2 3

Sample Output 3

3

Sample Input 4

10 39
7 2
7 1
5 6
5 8
9 10
2 8
8 7
3 10
10 1
8 10
2 3
7 4
3 9
4 10
3 4
6 1
6 7
9 5
9 7
6 9
9 4
4 6
7 5
8 3
2 5
9 2
10 7
8 6
8 9
7 3
5 3
4 5
6 3
2 10
5 10
4 2
6 2
8 4
10 6

Sample Output 4

21

Solution in Rust (1.42.0) (judge verdict: Accepted)

#![allow(unused_imports)]
#![allow(dead_code)]
#![allow(unused_mut)]
// #![allow(non_camel_case_types)]
use crate::rust::libs::util::{io::*,util::*,lower_bound::*,memoize::*};
use crate::rust::libs::math::{mod_int::*,prime_factor::*};
use crate::rust::libs::data_structure::{union_find::UF,segment_tree::*};
use crate::rust::libs::algebraic_structure::monoid::{plus::*,max::*,min::*};
use std::ops::Range;
use  std::collections::*;
use std::cmp::*;
use std::process::*;
use bitset_fixed::BitSet;
const MOD: u32 = 1_000_000_007;
const INF:usize=1usize<<60;
const_mod!(P,MOD);

fn main(){
    input!{
        n:usize,m:usize,
        v:[(usize1,usize1);m],
    }
    let mut v2=make_vec!(true,n,n);
    for i in 0..n{
        v2[i][i]=false;
    }
    for i in 0..m{
        v2[v[i].0][v[i].1]=false;
        v2[v[i].1][v[i].0]=false;
    }
    let mut uf=UF::new(n*2);
    for i in 0..n{
        for j in 0..n{
            if v2[i][j]{
                uf.unite(i, n+j);
                uf.unite(j, n+i);
            }
        }
    }
    for i in 0..n{
        if uf.same(i,n+i){
            println!("-1");
            return;
        }
    }
    let mut uf2=UF::new(n);
    for i in 0..n{
        let mut v=Vec::new();
        for j in 0..n{
            if v2[i][j]{
                v.push(j);
            }
        }
        if v.len()==0{continue;}
        for i in 0..v.len()-1{
            uf2.unite(v[i],v[i+1]);
        }
    }
    let mut v3=Vec::new();
    for i in 0..n{
        if i==uf2.root(i){
            v3.push((uf2.size(i),i));
        }
    }
    let mut b=BitSet::new(n);
    b.set(0, true);
    let mut s=BTreeSet::new();
    let mut v4=Vec::<BitSet>::new();
    v4.push(b);
    //let mut v5=Vec::<(usize,usize,usize,usize)>::new();
    for i in 0..n{
        if i!=uf2.root(i){continue;}
        if s.contains(&i){continue;}
        let mut v=Vec::new();
        for j in 0..n{
            if v2[i][j]{
                v.push(j);
            }
        }
        let mut b=v4[v4.len()-1].clone();
        if v.len()==0{
            //v5.push((0,uf2.size(i),n,i));
            v4.push(b.clone()|&(b<<uf2.size(i)));
        }else{
            let t=uf2.root(v[0]);
            //v5.push((uf2.size(i),uf2.size(v[0]),i,t));
            s.insert(t);
            v4.push(b.clone()<<uf2.size(i)|&(b<<uf2.size(v[0])));
        }
    }
    let mut now=INF;
    for i in 0..n{
        if !v4[v4.len()-1][i]{continue;}
        if d(n/2,now)>d(n/2,i){
            now=i;
        }
    }
    println!("{}",now*(now-1)/2+(n-now)*(n-now-1)/2)
    // let mut ans=BTreeSet::new();
    // for i in (0..v5.len()).rev(){
    //     if v4[i][now-v5[i].0]{
    //         ans.insert(v5[i].2);
    //     }else{
    //         ans.insert(v5[i].3);
    //     }
    // }
    // let mut ans2=Vec::new();
    // for i in 0..n{
    //     if ans.contains(&uf2.root(i)){
    //         ans2.push(i);
    //     }
    // }
    // for i in 0..ans2.len(){
    //     print!("{}{}",ans2[i]+1,if i==ans2.len()-1{"\n"}else{" "});
    // }
}




pub mod rust {

pub mod libs {

pub mod algebraic_structure {

pub mod monoid {

pub mod max {

use crate::rust::libs::algebraic_structure::monoid::monoid::Monoid;
use std::option::Option;
#[derive(Debug,Copy,Clone)]
pub struct Max<T>{
    val:Option<T>,
}
impl<T:Ord+Copy> Monoid for Max<T>{
    type MonoidType=T;
    fn new()->Self{
        Self{
            val:None,
        }
    }
    fn make(t:T)->Self{
        Self{
            val:Some(t),
        }
    }
    fn f(&self,t:&Self)->Self{
        if self.val.is_none() {*t}
        else if t.val.is_none() {*self}
        else{
            Self{
                val:Some(T::max(self.val.unwrap(),t.val.unwrap())),
            }
        }
    }
    fn get(self)->Option<T>{
        self.val
    }
}

}  // mod max

pub mod min {

use crate::rust::libs::algebraic_structure::monoid::monoid::Monoid;
use std::option::Option;
#[derive(Debug,Copy,Clone)]
pub struct Min<T>{
    val:Option<T>,
}
impl<T:Ord+Copy> Monoid for Min<T>{
    type MonoidType=T;
    fn new()->Self{
        Self{
            val:None,
        }
    }
    fn make(t:T)->Self{
        Self{
            val:Some(t),
        }
    }
    fn f(&self,t:&Self)->Self{
        if self.val.is_none() {*t}
        else if t.val.is_none() {*self}
        else{
            Self{
                val:Some(T::min(self.val.unwrap(),t.val.unwrap())),
            }
        }
    }
    fn get(self)->Option<T>{
        self.val
    }
}

}  // mod min

pub mod monoid {

pub trait Monoid{
    type MonoidType;
    fn new()->Self;
    fn make(t:Self::MonoidType)->Self;
    fn get(self)->Option<Self::MonoidType>;
    fn f(&self,t:&Self)->Self;
}

}  // mod monoid

pub mod plus {

use crate::rust::libs::algebraic_structure::monoid::monoid::Monoid;
use std::option::Option;
use std::ops::Add;
#[derive(Debug,Copy,Clone)]
pub struct Plus<T>{
    val:Option<T>,
}
impl<T:Add<T,Output=T>+Copy> Monoid for Plus<T>{
    type MonoidType=T;
    fn new()->Self{
        Self{
            val:None,
        }
    }
    fn make(t:T)->Self{
        Self{
            val:Some(t),
        }
    }
    fn f(&self,t:&Self)->Self{
        if self.val.is_none() {*t}
        else if t.val.is_none() {*self}
        else{
            Self{
                val:Some(self.val.unwrap()+t.val.unwrap()),
            }
        }
    }
    fn get(self)->Option<T>{
        self.val
    }
}

}  // mod plus

}  // mod monoid

}  // mod algebraic_structure

pub mod data_structure {

pub mod segment_tree {

use crate::rust::libs::algebraic_structure::monoid::monoid::Monoid;
use std::ops::Range;
pub struct SegmentTree<T>{
    n:usize,
    v:Vec<T>,
}

impl<T:Monoid+Copy+std::fmt::Debug> SegmentTree<T>where T::MonoidType:Copy{
    pub fn new(n:usize)->Self{
        Self{
            n:n,
            v:vec![T::new();n*2],
        }
    }
    pub fn make(v:&[T::MonoidType])->Self{
        let n=v.len();
        let mut tmp=vec![T::new();n*2];
        for i in 0..n{
            tmp[v.len()+i]=T::make(v[i]);
        }
        for i in (1..n).rev(){
            tmp[i]=tmp[i*2].f(&tmp[i*2+1]);
        }
        Self{
            n:n,
            v:tmp,
        }
    }
    pub fn get(&self,ran:Range<usize>)->Option<T::MonoidType>{
        let mut l=ran.start+self.n;
        let mut r=ran.end+self.n;
        let mut s=T::new();
        let mut t=T::new();
        while l<r{
            if (l&1)==1{s=s.f(&self.v[l]);l+=1;}
            if (r&1)==1{r-=1;t=self.v[r].f(&t);}
            l>>=1;r>>=1;
        }
        s.f(&t).get()
    }
    pub fn set(&mut self,t:usize,val:T::MonoidType){
        let mut tp=t+self.n;
        self.v[tp]=self.v[tp].f(&T::make(val));
        while tp>1{
            tp=tp>>1;
            self.v[tp]=self.v[tp*2].f(&self.v[tp*2+1]);
        }
    }
    pub fn out(self){
        println!("{:?}",self.v);
    }
}

}  // mod segment_tree

pub mod union_find {


pub struct UF{
    par:Vec<usize>,
    rank:Vec<usize>,
}
impl UF{
    pub fn new(n:usize)->UF{
        let mut v=vec![0;n];
        for i in 0..n{
            v[i]=i;
        }
        UF{
            par:v,
            rank:vec![1;n],
        }
    }
    pub fn root(&mut self,x:usize)->usize{
        if x==self.par[x]{
            x
        }else{
            let par=self.par[x];
            let res=self.root(par);
            self.par[x]=res;
            res
        }
    }
    pub fn same(&mut self,a:usize,b:usize)->bool{
        self.root(a)==self.root(b)
    }
    pub fn unite(&mut self,a:usize,b:usize)->bool{
        let ap=self.root(a);
        let bp=self.root(b);
        if ap==bp{
            return false;
        }
        if self.rank[ap]<self.rank[bp]{
            self.par[bp]=ap;
            self.rank[ap]+=self.rank[bp];
        }else{
            self.par[ap]=bp;
            self.rank[bp]+=self.rank[ap];
        }
        return true;
    }
    pub fn size(&mut self,a:usize)->usize{
        let ap=self.root(a);
        self.rank[ap]
    }
}

}  // mod union_find

}  // mod data_structure

pub mod math {

pub mod mod_int {

use std::ops::{Add,AddAssign,Sub,SubAssign,Mul,MulAssign,Div,DivAssign,Neg};
use std::str::FromStr;
use std::num::ParseIntError;
use std::iter::{Sum,Product};

pub fn inv_mod(a:u64,m:u64)->u64{
    let m=m as i64;
    let mut a=a as i64;
    let mut b=m as i64;
    let mut u=1i64;
    let mut v=0i64;
    while b>0 {
        let t=a/b;
        a-=t*b;
        u-=t*v;
        std::mem::swap(&mut a,&mut b);
        std::mem::swap(&mut u,&mut v);
    }
    let ans =(if u>=0{u%m}else{m+(u%m)%m})as u64;
    ans
}

pub trait Mod:Sized{
    fn m()->u32;
    fn m64()->u64;
    fn mi64()->i64;
}
#[macro_export]
macro_rules! const_mod{
    ($st:ident,$m:expr)=>{
        struct $st{}
        impl Mod for $st {
            fn m()->u32{$m}
            fn m64()->u64{$m as u64}
            fn mi64()->i64{$m as i64}
        }
        //const MAX=10000000;
        type Fp=ModInt<P>;
        //const fact_table:[Fp;MAX]=(0..MAX)
    }
}
pub struct ModInt<M:Mod>{a:u32,_p:std::marker::PhantomData<M>}

impl<M: Mod> ModInt<M>{
    pub fn new(a:u32)->Self{
        ModInt{a,_p:std::marker::PhantomData}
    }
    pub fn newu64(a:u64)->Self{
        ModInt{a:(a%M::m64())as u32,_p:std::marker::PhantomData}
    }
    pub fn newi64(a:i64)->Self{
        ModInt{a:((a%M::mi64()+M::mi64())%M::mi64()) as u32,_p:std::marker::PhantomData}
    }
    pub fn value(&self)->u32{self.a}
    pub fn pow(&self,p:u64)->Self{
        let mut exp=p;
        let mut now=*self;
        let mut ans=ModInt::new(1);
        while exp>0{
            if (exp&1)==1{ans*=now;}
            now*=now;
            exp>>=1;
        }
        ans
    }
    // pub fn comb(k:i32)->Self{
    //     Self::new(k)
    // }
    pub fn inv(&self)->Self{Self::new(inv_mod(self.a as u64,M::m64())as u32)}
}

impl<M:Mod>Clone for ModInt<M>{
    fn clone(&self)->Self{ModInt::new(self.a)}
}
impl<M:Mod>Copy for ModInt<M>{}
impl<M:Mod>From<i64>for ModInt<M>{
    fn from(i:i64)->Self{Self::newi64(i)}
}
impl<M:Mod>From<i32>for ModInt<M>{
    fn from(i:i32)->Self{Self::newi64(i as i64)}
}

impl<M:Mod>FromStr for ModInt<M>{
    type Err = ParseIntError;
    fn from_str(i:&str)->Result<Self, Self::Err>{
        let res=i.parse::<i64>()?;
        Ok(Self::newi64(res))
    }
}
impl<M:Mod>Sum for ModInt<M>{
    fn sum<I>(iter: I) -> Self where I: Iterator<Item = Self>,{
        iter.fold(Self::new(0), |b, i| b + i)
    }
}

impl<M:Mod>Product for ModInt<M>{
    fn product<I>(iter: I) -> Self where I: Iterator<Item = Self>,{
        iter.fold(Self::new(0), |b, i| b * i)
    }
}
impl<M:Mod>Add for ModInt<M>{
    type Output=Self;
    fn add(self,rhs:Self)->Self{
        let a=self.a+rhs.a;
        ModInt::new(if a>=M::m(){a-M::m()}else{a})
    }
}
impl<M:Mod>Sub for ModInt<M>{
    type Output=Self;
    fn sub(self,rhs:Self)->Self{
        ModInt::new(if self.a<rhs.a{M::m()+self.a-rhs.a}else{self.a-rhs.a})
    }
}
impl<M:Mod>Mul for ModInt<M>{
    type Output=Self;
    fn mul(self,rhs:Self)->Self{
        ModInt::newu64(self.a as u64*rhs.a as u64)
    }
}
impl<M:Mod>Div for ModInt<M>{
    type Output=Self;
    fn div(self,rhs:Self)->Self{
        self*rhs.inv()
    }
}
impl<M:Mod>Neg for ModInt<M> {
    type Output = Self;
    fn neg(self) -> Self {
        ModInt::new(M::m()-self.value())
    }
}
impl<M:Mod>AddAssign for ModInt<M>{fn add_assign(&mut self,rhs:Self){*self=*self+rhs;}}
impl<M:Mod>SubAssign for ModInt<M>{fn sub_assign(&mut self,rhs:Self){*self=*self-rhs;}}
impl<M:Mod>MulAssign for ModInt<M>{fn mul_assign(&mut self,rhs:Self){*self=*self*rhs;}}
impl<M:Mod>DivAssign for ModInt<M>{fn div_assign(&mut self,rhs:Self){*self=*self/rhs;}}

impl<M:Mod>std::fmt::Debug for ModInt<M>{
    fn fmt(&self,f:&mut std::fmt::Formatter)->Result<(),std::fmt::Error>{
        write!(f,"M{}",self.a)
    }
}
impl<M:Mod> std::fmt::Display for ModInt<M> {
    fn fmt(&self, f: &mut std::fmt::Formatter) -> Result<(), std::fmt::Error> {
        self.value().fmt(f)
    }
}

// impl<M:Mod> Sum for ModInt<M>{
//     fn sum<I>(iter: I) -> ModInt<M>
//     where
//         I: Iterator<Item = ModInt<M>>,
//     {
//         iter.fold(Self::new(0), |b, i| b + i)
//     }
// }

}  // mod mod_int

pub mod prime_factor {

use std::collections::BTreeMap;
pub fn prime_factor(n:usize)->BTreeMap<usize,usize>{
    let mut ret:BTreeMap<usize,usize>=BTreeMap::<usize,usize>::new();
    let mut m=n;
    let mut i=2;
    while i*i<=m {
        while m%i==0{
            let tmp=ret.entry(i).or_insert(0);
            *tmp+=1;
            m/=i;
        }
        i+=1;
    }
    ret
}

}  // mod prime_factor

}  // mod math

pub mod util {

pub mod io {

#[macro_export]
macro_rules! input {
    (source = $s:expr, $($r:tt)*) => {
        let mut iter = $s.split_whitespace();
        input_inner!{iter, $($r)*}
    };
    ($($r:tt)*) => {
        let mut s = {
            use std::io::Read;
            let mut s = String::new();
            std::io::stdin().read_to_string(&mut s).unwrap();
            s
        };
        let mut iter = s.split_whitespace();
        input_inner!{iter, $($r)*}
    };
}

#[macro_export]
macro_rules! input_inner {
    ($iter:expr) => {};
    ($iter:expr, ) => {};

    ($iter:expr, $var:ident : $t:tt $($r:tt)*) => {
        let $var = read_value!($iter, $t);
        input_inner!{$iter $($r)*}
    };
    ($iter:expr, mut $var:ident : $t:tt $($r:tt)*) => {
        let mut $var = read_value!($iter, $t);
        input_inner!{$iter $($r)*}
    };
}

#[macro_export] 
macro_rules! read_value {
    ($iter:expr, [tree;$len:expr]) => {
        {
            let mut g:Vec<Vec<usize>>=vec![Vec::new();$len];
            for (s,t) in read_value!($iter,[(usize1,usize1);$len-1]){
                g[s].push(t);
                g[t].push(s);
            }
            g
        }
    };
    ($iter:expr, [graph;$vertex:expr,$edge:expr]) => {
        {
            let mut g:Vec<Vec<usize>>=vec![Vec::new();$vertex];
            for (s,t) in read_value!($iter,[(usize1,usize1);$edge]){
                g[s].push(t);
                g[t].push(s);
            }
            g
        }
    };
    ($iter:expr, [directed;$vertex:expr,$edge:expr]) => {
        {
            let mut g:Vec<Vec<usize>>=vec![Vec::new();$vertex];
            for (s,t) in read_value!($iter,[(usize1,usize1);$edge]){
                g[s].push(t);
            }
            g
        }
    };
    ($iter:expr, ( $($t:tt),* )) => {
        ( $(read_value!($iter, $t)),* )
    };

    ($iter:expr, [ $t:tt ; $len:expr ]) => {
        (0..$len).map(|_| read_value!($iter, $t)).collect::<Vec<_>>()
    };

    ($iter:expr, chars) => {
        read_value!($iter, String).chars().collect::<Vec<char>>()
    };

    ($iter:expr, bytes) => {
        read_value!($iter, String).into_bytes()
    };

    ($iter:expr, usize1) => {
        read_value!($iter, usize) - 1
    };
    ($iter:expr, Fp) => {
        Fp::newi64(read_value!($iter,i64))
    };

    ($iter:expr, $t:ty) => {
        $iter.next().unwrap().parse::<$t>().expect("Parse error")
    };
}


}  // mod io

pub mod lower_bound {

pub trait LowerBound<T> {
    fn lower_bound(&self,v:T)->usize;
}

impl<T:Ord> LowerBound<T> for Vec<T>{
    fn lower_bound(&self,x:T)->usize{
        let mut l:usize=0;
        let mut r:usize=self.len()+1;
        while r-l>1{
            let m=(l+r)/2;
            if self[m-1]<x {l=m;}
            else {r=m;}
        }
        r-1
    }
}
pub trait UpperBound<T> {
    fn upper_bound(&self,v:T)->usize;
}

impl<T:Ord> UpperBound<T> for Vec<T>{
    fn upper_bound(&self,x:T)->usize{
        let mut l:usize=0;
        let mut r:usize=self.len()+1;
        while r-l>1{
            let m=(l+r)/2;
            if self[m-1]<=x {l=m;}
            else {r=m;}
        }
        r-1
    }
}

}  // mod lower_bound

pub mod memoize {

#[macro_export]
macro_rules! make_vec{
    ( $val:expr , $head:expr)=>{
        vec![$val;$head]
    };
    ( $val:expr , $head:expr , $($tail:expr),+ )=>{
        vec![make_vec!($val,$($tail),+);$head]
    };
}

#[macro_export]
macro_rules! access{
    ($v:expr,$tail:expr)=>{
        $v[$tail]
    };
    ($v:expr,$tail:expr,)=>{
        $v[$tail]
    };
    ($v:expr,$($r:expr),+,$tail:expr)=>{
        access!($v,$($r),+)[$tail]
    };
}
#[macro_export]
macro_rules! make_type_vec{
    ($v:ty,$tail:expr)=>{
        Vec<$v>
    };
    ($v:ty,$tail:expr,)=>{
        Vec<$v>
    };
    ($v:ty,$($r:expr),+,$tail:expr)=>{
        Vec<make_type_vec!($v,$($r),+)>
    };
}
#[macro_export]
macro_rules! access_local{
    ($v:expr,$($r:expr),+)=>{
        v.with()
    };
}
#[macro_export]
macro_rules! memoized{
    (fn $func:tt ($($val:tt [$r:expr]:$typ:ty),*)->$ret:ty{$($t:tt)*} ( $($st:expr),* );)=>{
        {
            use std::cell::RefCell;
            use std::borrow::BorrowMut;
            fn $func($($val : $typ),*)->$ret{
                thread_local! {
                    pub static MEMO :RefCell<make_type_vec!(Option<$ret>,$($r),*)>= RefCell::new(make_vec!(None,$($r),*));
                }                
                let __function__=|$($val : $typ),*|->$ret {$($t)*};
                
                if MEMO.with(|v|access!(v.borrow(),$($val),*).is_none()){
                    MEMO.with(|v|access!(v.borrow_mut(),$($val),*)=Some(__function__($($val),*)));
                }
                MEMO.with(|v|access!(v.borrow(),$($val),*).clone()).unwrap()
            }
            $func($($st),*)
        }
    };
    (fn $func:tt ($($val:tt [$r:expr]:$typ:ty),*)[$($cap_val:tt : $cap_typ:ty),*]->$ret:ty{$($t:tt)*} $func2:tt( $($st:expr),* );)=>{
        {
            use std::cell::RefCell;
            assert!(stringify!($func)==stringify!($func2));
            fn __function2__($($val : $typ),*,$($cap_val:$cap_typ),*)->$ret{
                thread_local! {
                    pub static MEMO :RefCell<make_type_vec!(Option<$ret>,$($r),*)>= RefCell::new(make_vec!(None,$($r),*));
                }
                let $func=|$($val : $typ),*|->$ret {__function2__($($val),*,$($cap_val),*)};
                let __function__=|$($val : $typ),*,$($cap_val:$cap_typ),*|->$ret {
                    $($t)*
                };
                if MEMO.with(|v|access!(v.borrow(),$($val),*).is_none()){
                    MEMO.with(|v|access!(v.borrow_mut(),$($val),*)=Some(__function__($($val),*,$($cap_val),*)));
                }
                MEMO.with(|v|access!(v.borrow(),$($val),*).clone()).unwrap()
            }
            __function2__($($st),*)
        }
    };
}

}  // mod memoize

pub mod util {

use std::ops::Add;
pub trait CumSum<T> {
    fn cumsum(&self)->Vec<T>;
}

impl<T:Add<Output=T>+Default+Copy> CumSum<T> for Vec<T>{
    fn cumsum(&self)->Vec<T>{
        let mut ret=Vec::new();
        ret.push(T::default());
        for i in 0..self.len(){
            ret.push(ret[i]+self[i]);
        }
        ret
    }
}


pub fn type_of<T>(_: T) -> String{
    let a = std::any::type_name::<T>();
    return a.to_string();
}

#[macro_export]
macro_rules! btoi{
    ( $val:expr)=>{
        if $val{1}else{0}
    };
}

pub trait Isomorphism<T> {
    fn isomorphism(&self)->Vec<T>;
}

use std::ops::{Rem,Div,Mul};
use std::default::Default;
pub fn gcd<T:Rem<Output=T>+Eq+Default+Copy>(a:T,b:T)->T{
    if b==T::default(){a}else{gcd(b, a % b)}
}
pub fn lcm<T:Rem<Output=T>+Eq+Default+Copy+Div<Output=T>+Mul<Output=T>>(a:T,b:T)->T{
    a/gcd(a,b)*b
}

use crate::rust::libs::util::lower_bound::*;
pub trait Lis<T> {
    fn lis(&self)->Vec<T>;
}

impl<T:Ord+Copy> Lis<T> for Vec<T>{
    fn lis(&self)->Vec<T>{
        let mut ret=Vec::<T>::new();
        for i in 0..self.len(){
            let t=ret.lower_bound(self[i]);
            if t==ret.len(){ret.push(self[i]);}
            else {ret[t]=self[i];}
        }
        ret
    }
}

use std::convert::TryInto;
pub trait Ac<T>{
    fn ac(&self,idx:T)->T;
}
impl<T> Ac<T> for Vec<T>where T:TryInto<usize>+Copy{
    fn ac(&self,idx:T)->T{
        match idx.try_into(){
            Ok(i)=>self[i],
            Err(_e)=>{
                panic!("cannot convert to usize");
            }
        }
    }
}

pub fn d(s:usize,t:usize)->usize{
    ((s as i64)-(t as i64)).abs()as usize
}

}  // mod util

}  // mod util

}  // mod libs

}  // mod rust