// ---------- begin bitwise transform ---------- pub fn bitwise_transform(a: &mut [T], mut f: F) where F: FnMut(&mut T, &mut T) { let n = a.len().trailing_zeros() as usize; assert!(a.len() == 1 << n); for i in 0..n { for a in a.chunks_exact_mut(2 << i) { let (x, y) = a.split_at_mut(1 << i); for (x, y) in x.iter_mut().zip(y) { f(x, y); } } } } // ---------- end bitwise transform ---------- use std::ops::*; pub trait SubsetConvValue: Copy + Add + Mul + Sub { fn zero() -> Self; } fn subset_rec(x: &mut [T], y: &mut [T], n: usize) { if x.len() == n + 1 { for i in (0..=n).rev() { x[i] = x[..=i].iter().zip(y[..=i].iter().rev()).fold(T::zero(), |s, p| s + *p.0 * *p.1); } return; } let m = x.len() / 2; let (a, b) = x.split_at_mut(m); let (c, d) = y.split_at_mut(m); let x = b.iter_mut().zip(a.iter()); let y = d.iter_mut().zip(c.iter()); for ((b, a), (d, c)) in x.zip(y) { *b = *b + *a; *d = *d + *c; } subset_rec(a, c, n); subset_rec(b, d, n); for (b, a) in b.iter_mut().zip(a.iter()) { *b = *b - *a; } } pub fn subset_convolution(a: &[T], b: &[T]) -> Vec { let size = a.len().next_power_of_two(); assert!(a.len() == size && b.len() == size); let n = size.trailing_zeros() as usize; let mut x = vec![T::zero(); (n + 1) << n]; let mut y = vec![T::zero(); (n + 1) << n]; for (x, a) in [(&mut x, &a), (&mut y, &b)].iter_mut() { for (i, a) in a.iter().enumerate() { x[i * (n + 1) + i.count_ones() as usize] = *a; } } subset_rec(&mut x, &mut y, n); let mut res = vec![T::zero(); 1 << n]; for (i, (res, x)) in res.iter_mut().zip(x.chunks_exact(n + 1)).enumerate() { *res = x[i.count_ones() as usize]; } res } #[derive(Clone, Copy)] struct Value(usize); impl Add for Value { type Output = Self; fn add(self, rhs: Self) -> Self::Output { Value(self.0 ^ rhs.0) } } impl Sub for Value { type Output = Self; fn sub(self, rhs: Self) -> Self::Output { Value(self.0 ^ rhs.0) } } impl Mul for Value { type Output = Self; fn mul(self, rhs: Self) -> Self::Output { let mut res = 0; let mut x = self.0; while x > 0 { let k = x.trailing_zeros(); res ^= rhs.0 << k; x ^= 1 << k; } Value(res) } } impl SubsetConvValue for Value { fn zero() -> Self { Value(0) } } // ---------- begin Scanner(require delimiter) ---------- mod scanner { pub struct Scanner { reader: R, buf: Vec, } #[allow(dead_code)] impl Scanner { pub fn new(reader: R) -> Self { Scanner { reader: reader, buf: Vec::with_capacity(1024), } } fn read(&mut self, del: u8) { self.buf.clear(); self.reader.read_until(del, &mut self.buf).ok(); assert!(self.buf.pop().unwrap() == del); } pub fn next(&mut self, del: u8) -> T { self.read(del); std::str::from_utf8(&self.buf) .unwrap() .trim() .parse::() .ok() .unwrap() } pub fn next_bytes(&mut self, del: u8) -> Vec { self.read(del); std::str::from_utf8(&self.buf) .unwrap() .trim() .bytes() .collect() } } } // ---------- end scanner(require delimiter) ---------- fn main() { let stdin = std::io::stdin(); let mut sc = scanner::Scanner::new(stdin.lock()); run(&mut sc); } fn run(sc: &mut scanner::Scanner) { let n: usize = sc.next(b'\n'); let mut a = vec![Value(0usize); 1 << n]; let mut b = vec![Value(0usize); 1 << n]; for a in a.iter_mut().chain(b.iter_mut()) { for i in 0..32 { let x = sc.next::(if i == 31 { b'\n' } else { b' ' }); a.0 |= x << i; } } bitwise_transform(&mut a, |a, b| *a = *a + *b); bitwise_transform(&mut b, |a, b| *a = *a + *b); let mut c = subset_convolution(&a, &b); bitwise_transform(&mut c, |a, b| *a = *a + *b); use std::fmt::*; let mut s = String::new(); for c in c { for i in 0..63 { let p = c.0 >> i & 1; write!(&mut s, "{} ", p).ok(); } s.pop(); s.push('\n'); } print!("{}", s); }