Problem:
Score : 500 points

Problem Statement

N players will participate in a tennis tournament. We will call them Player 1, Player 2, \ldots, Player N.

The tournament is round-robin format, and there will be N(N-1)/2 matches in total.
Is it possible to schedule these matches so that all of the following conditions are satisfied? If the answer is yes, also find the minimum number of days required.

Each player plays at most one matches in a day.

Each player i (1 \leq i \leq N) plays one match against Player A_{i, 1}, A_{i, 2}, \ldots, A_{i, N-1} in this order.

Constraints

3 \leq N \leq 1000

1 \leq A_{i, j} \leq N

A_{i, j} \neq i

A_{i, 1}, A_{i, 2}, \ldots, A_{i, N-1} are all different.

Input

Input is given from Standard Input in the following format:

N
A_{1, 1} A_{1, 2} \ldots A_{1, N-1}
A_{2, 1} A_{2, 2} \ldots A_{2, N-1}
:
A_{N, 1} A_{N, 2} \ldots A_{N, N-1}

Output

If it is possible to schedule all the matches so that all of the conditions are satisfied, print the minimum number of days required; if it is impossible, print -1.

Sample Input 1

3
2 3
1 3
1 2

Sample Output 1

3

All the conditions can be satisfied if the matches are scheduled for three days as follows:

Day 1: Player 1 vs Player 2

Day 2: Player 1 vs Player 3

Day 3: Player 2 vs Player 3

This is the minimum number of days required.

Sample Input 2

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

Sample Output 2

4

All the conditions can be satisfied if the matches are scheduled for four days as follows:

Day 1: Player 1 vs Player 2, Player 3 vs Player 4

Day 2: Player 1 vs Player 3

Day 3: Player 1 vs Player 4, Player 2 vs Player 3

Day 4: Player 2 vs Player 4

This is the minimum number of days required.

Sample Input 3

3
2 3
3 1
1 2

Sample Output 3

-1

Any scheduling of the matches violates some condition.

Solution in Rust (1.15.1) (judge verdict: Time Limit Exceeded)

#[doc = " https://github.com/hatoo/competitive-rust-snippets"]
#[allow(unused_imports)]
use std::cmp::{max, min, Ordering};
#[allow(unused_imports)]
use std::collections::{BTreeMap, BTreeSet, BinaryHeap, HashMap, HashSet, VecDeque};
#[allow(unused_imports)]
use std::io::{stdin, stdout, BufWriter, Write};
#[allow(unused_imports)]
use std::iter::FromIterator;
#[allow(unused_macros)]
macro_rules ! debug { ( $ ( $ a : expr ) ,* ) => { eprintln ! ( concat ! ( $ ( stringify ! ( $ a ) , " = {:?}, " ) ,* ) , $ ( $ a ) ,* ) ; } }
#[macro_export]
macro_rules ! input { ( source = $ s : expr , $ ( $ r : tt ) * ) => { let mut parser = Parser :: from_str ( $ s ) ; input_inner ! { parser , $ ( $ r ) * } } ; ( parser = $ parser : ident , $ ( $ r : tt ) * ) => { input_inner ! { $ parser , $ ( $ r ) * } } ; ( new_stdin_parser = $ parser : ident , $ ( $ r : tt ) * ) => { let stdin = std :: io :: stdin ( ) ; let reader = std :: io :: BufReader :: new ( stdin . lock ( ) ) ; let mut $ parser = Parser :: new ( reader ) ; input_inner ! { $ parser , $ ( $ r ) * } } ; ( $ ( $ r : tt ) * ) => { input ! { new_stdin_parser = parser , $ ( $ r ) * } } ; }
#[macro_export]
macro_rules ! input_inner { ( $ parser : ident ) => { } ; ( $ parser : ident , ) => { } ; ( $ parser : ident , $ var : ident : $ t : tt $ ( $ r : tt ) * ) => { let $ var = read_value ! ( $ parser , $ t ) ; input_inner ! { $ parser $ ( $ r ) * } } ; }
#[macro_export]
macro_rules ! read_value { ( $ parser : ident , ( $ ( $ t : tt ) ,* ) ) => { ( $ ( read_value ! ( $ parser , $ t ) ) ,* ) } ; ( $ parser : ident , [ $ t : tt ; $ len : expr ] ) => { ( 0 ..$ len ) . map ( | _ | read_value ! ( $ parser , $ t ) ) . collect ::< Vec < _ >> ( ) } ; ( $ parser : ident , chars ) => { read_value ! ( $ parser , String ) . chars ( ) . collect ::< Vec < char >> ( ) } ; ( $ parser : ident , usize1 ) => { read_value ! ( $ parser , usize ) - 1 } ; ( $ parser : ident , $ t : ty ) => { $ parser . next ::<$ t > ( ) . expect ( "Parse error" ) } ; }
use std::io;
use std::io::BufRead;
use std::str;
pub struct Parser<R> {
    reader: R,
    buf: Vec<u8>,
    pos: usize,
}
impl Parser<io::Empty> {
    pub fn from_str(s: &str) -> Parser<io::Empty> {
        Parser {
            reader: io::empty(),
            buf: s.as_bytes().to_vec(),
            pos: 0,
        }
    }
}
impl<R: BufRead> Parser<R> {
    pub fn new(reader: R) -> Parser<R> {
        Parser {
            reader: reader,
            buf: vec![],
            pos: 0,
        }
    }
    pub fn update_buf(&mut self) {
        self.buf.clear();
        self.pos = 0;
        loop {
            let (len, complete) = {
                let buf2 = self.reader.fill_buf().unwrap();
                self.buf.extend_from_slice(buf2);
                let len = buf2.len();
                if len == 0 {
                    break;
                }
                (len, buf2[len - 1] <= 0x20)
            };
            self.reader.consume(len);
            if complete {
                break;
            }
        }
    }
    pub fn next<T: str::FromStr>(&mut self) -> Result<T, T::Err> {
        loop {
            let mut begin = self.pos;
            while begin < self.buf.len() && (self.buf[begin] <= 0x20) {
                begin += 1;
            }
            let mut end = begin;
            while end < self.buf.len() && (self.buf[end] > 0x20) {
                end += 1;
            }
            if begin != self.buf.len() {
                self.pos = end;
                return str::from_utf8(&self.buf[begin..end]).unwrap().parse::<T>();
            } else {
                self.update_buf();
            }
        }
    }
}
#[allow(unused_macros)]
macro_rules ! debug { ( $ ( $ a : expr ) ,* ) => { eprintln ! ( concat ! ( $ ( stringify ! ( $ a ) , " = {:?}, " ) ,* ) , $ ( $ a ) ,* ) ; } }
#[doc = " https://github.com/hatoo/competitive-rust-snippets"]
const BIG_STACK_SIZE: bool = true;
#[allow(dead_code)]
fn main() {
    use std::thread;
    if BIG_STACK_SIZE {
        thread::Builder::new()
            .stack_size(32 * 1024 * 1024)
            .name("solve".into())
            .spawn(solve)
            .unwrap()
            .join()
            .unwrap();
    } else {
        solve();
    }
}
fn solve() {
    input!{
        N:usize,
        A:[[usize;N-1];N],
    }
    // 0オリジンにする
    let mut a = vec![vec![0;N-1];N];
    for i in 0..N {
        for j in 0..N-1 {
            a[i][j]=A[i][j]-1;
        }
    }
    // 場所を探索するためのテーブル
    // p[i][j]=iくんがjくんと戦いたい順番
    let mut p = vec![];
    for i in 0..N {
        let mut v = vec![0;N];
        for j in 0..N-1 {
            v[a[i][j]]=j;
        }
        p.push(v);
    }

    let mut g = vec![vec![]; N*N];
    for i in 0..N {
        for j in 1..N-1 {
            let oppo = a[i][j-1];
            let (x,y) = if i<oppo { (i,oppo) } else { (oppo, i) };
            let j0 = x*N+y;

            let oppo = a[i][j];
            let (x,y) = if i<oppo { (i,oppo) } else { (oppo, i) };
            let j1 = x*N+y;

            g[j0].push(j1);
        }
    }

    if cycle_detection_directed(&g) {
        println!("-1");
        return
    }

    let mut ing = vec![vec![]; N*N];
    for i in 0..N*N {
        for &to in &g[i] {
            ing[to].push(i);
        }
    }
    let mut s = vec![];
    for i in 0..N*N {
        if ing[i].len() == 0 {
            s.push(i);
        }
    }

    let mut maxv=0;
    for v in s {
        let mut memo=vec![0;N*N];
        maxv=max(maxv,dfs(v,&g,&mut memo));
    }

    println!("{}",maxv);

    fn dfs(v: usize, g: &[Vec<usize>], memo: &mut [usize]) -> usize {
        if memo[v]>0 {
            return memo[v];
        }
        let mut maxv=0;
        for &u in &g[v] {
            maxv=max(dfs(u, g, memo),maxv);
        }
        memo[v]=1+maxv;
        memo[v]
    }
}
pub fn cycle_detection_directed(g: &[Vec<usize>]) -> bool {
    let n = g.len();
    let mut in_g = vec![HashSet::new();n];
    // O(E)
    for v in 0..n {
        for &u in &g[v] {
            in_g[u].insert(v);
        }
    }
    let mut v_indegree0 = vec![];
    // O(V)
    for v in 0..n {
        if in_g[v].len() == 0 {
            v_indegree0.push(v);
        }
    }

    let mut m=0;
    // O(E)?
    while let Some(v) = v_indegree0.pop() {
        m += 1;
        for &to in &g[v] {
            if in_g[to].remove(&v) && in_g[to].is_empty() {
                v_indegree0.push(to);
            }
        }
    }

    m != n
}
fn solve0() {
    input!{
        N:usize,
        A:[[usize;N-1];N],
    }

    // 0オリジンにする
    let mut a = vec![vec![0;N-1];N];
    for i in 0..N {
        for j in 0..N-1 {
            a[i][j]=A[i][j]-1;
        }
    }
    let mut matching = HashSet::new();
    for i in 0..N {
        let oppo=a[i][0];
        if a[oppo][0]==i {
            matching.insert(i);
            matching.insert(oppo);
        }
    }

    // 場所を探索するためのテーブル
    // p[i][j]=iくんがjくんと戦いたい順番
    let mut p = vec![];
    for i in 0..N {
        let mut v = vec![0;N];
        for j in 0..N-1 {
            v[a[i][j]]=j;
        }
        p.push(v);
    }
    // 次に戦うやつを管理
    let mut head = vec![0;N];

    // シミュレーションする
    // 貪欲でよい
    let mut days=0;
    loop {
        let mut consume=vec![];
        for &i in &matching {
            if !(head[i]<N-1) { continue; }
            // 次の相手
            let oppo=a[i][head[i]];

            if !(i<oppo) { continue; }

            if !(head[oppo]<N-1) { continue; }

            // 今oppoが欲してるものがiならばマッチ
            if p[oppo][i]==head[oppo] {
                consume.push(i);
                consume.push(oppo);
            }
        }
        matching=HashSet::new();
        if consume.len() > 0 {
            for &i in &consume {
                head[i]+=1;
            }
            for &i in &consume {
                if !(head[i]<N-1) { continue; }
                let oppo=a[i][head[i]];
                if !(head[oppo]<N-1) { continue; }
                if a[oppo][head[oppo]]==i {
                    matching.insert(oppo);
                    matching.insert(i);
                }
            }
            days+=1;
        } else {
            break;
        }
    }

    let mut complt=true;
    for i in 0..N {
        if head[i]<N-1 {
            complt=false;
        }
    }

    if complt {
        println!("{}",days);
    } else {
        println!("-1");
    }
}