Problem:
Score : 400 points

Problem Statement

In this problem, we only consider strings consisting of lowercase English letters.

Strings s and t are said to be isomorphic when the following conditions are satisfied:

|s| = |t| holds.

For every pair i, j, one of the following holds:

s_i = s_j and t_i = t_j.

s_i \neq s_j and t_i \neq t_j.

For example, abcac and zyxzx are isomorphic, while abcac and ppppp are not.

A string s is said to be in normal form when the following condition is satisfied:

For every string t that is isomorphic to s, s \leq t holds. Here \leq denotes lexicographic comparison.

For example, abcac is in normal form, but zyxzx is not since it is isomorphic to abcac, which is lexicographically smaller than zyxzx.

You are given an integer N.
Print all strings of length N that are in normal form, in lexicographically ascending order.

Constraints

1 \leq N \leq 10

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N

Output

Assume that there are K strings of length N that are in normal form: w_1, \ldots, w_K in lexicographical order.
Output should be in the following format:

w_1
:
w_K

Sample Input 1

1

Sample Output 1

a

Sample Input 2

2

Sample Output 2

aa
ab

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::*};
use crate::rust::libs::math::{mod_int::*,prime_factor::*};
use crate::rust::libs::data_structure::{union_find::*,segment_tree::*};
use crate::rust::libs::algebraic_structure::monoid::{plus::*,max::*,min::*};
use std::ops::Range;
use  std::collections::*;
const MOD: u32 = 1_000_000_007;
const INF:i64=1i64<<60;
const_mod!(P,MOD);

fn search(s:&str,last:u8,n:usize){
    if s.len()==n{
        println!("{}",s);
        return;
    }
    for i in 0..last{
        search(&(s.to_string()+&(('a' as u8+i)as char).to_string()),last,n);
    }
    search(&(s.to_string()+&(('a' as u8+last)as char).to_string()),last+1,n);
}
fn main() {
    input!{
        n:usize,
    }
    search("",0,n);
}




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)
    }
}

}  // 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, $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 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! 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! btoi{
    ( $val:expr)=>{
        if $val{1}else{0}
    };
}

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

use std::ops::Rem;
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)}
}

}  // mod util

}  // mod util

}  // mod libs

}  // mod rust