macro_rules! input { (source = $s:expr, $($r:tt)*) => { let mut iter = $s.split_whitespace(); let mut next = || { iter.next().unwrap() }; input_inner!{next, $($r)*} }; ($($r:tt)*) => { let stdin = std::io::stdin(); let mut bytes = std::io::Read::bytes(std::io::BufReader::new(stdin.lock())); let mut next = move || -> String{ bytes .by_ref() .map(|r|r.unwrap() as char) .skip_while(|c|c.is_whitespace()) .take_while(|c|!c.is_whitespace()) .collect() }; input_inner!{next, $($r)*} }; } macro_rules! input_inner { ($next:expr) => {}; ($next:expr, ) => {}; ($next:expr, $var:ident : $t:tt $($r:tt)*) => { let $var = read_value!($next, $t); input_inner!{$next $($r)*} }; } macro_rules! read_value { ($next:expr, ( $($t:tt),* )) => { ( $(read_value!($next, $t)),* ) }; ($next:expr, [ $t:tt ; $len:expr ]) => { (0..$len).map(|_| read_value!($next, $t)).collect::>() }; ($next:expr, chars) => { read_value!($next, String).chars().collect::>() }; ($next:expr, usize1) => { read_value!($next, usize) - 1 }; ($next:expr, $t:ty) => { $next().parse::<$t>().expect("Parse error") }; } fn main() { input! { N: usize, mat: [[usize; N]; N], } // 単位元の存在チェック let mut unit = N; // unitは制約外の値を設定しておく for i in 0..N { let mut flag = true; for j in 0..N { if mat[i][j] != j { flag = false; } else if mat[j][i] != j { flag = false; } } if flag { unit = i; } } if unit == N { println!("No"); return; } // 逆元の存在 for i in 0..N { let mut flag = false; for j in 0..N { if mat[i][j] == unit { flag = true; } } if flag == false { println!("No"); return; } } // 結合則のチェック for i in 0..N { for j in 0..N { for k in 0..N { if mat[mat[i][j]][k] != mat[i][mat[j][k]] { println!("No"); return; } } } } println!("Yes"); }