// https://qiita.com/tanakh/items/0ba42c7ca36cd29d0ac8 macro_rules! input { ($($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 ; $len:expr ]) => { (0..$len).map(|_| read_value!($next, $t)).collect::>() }; ($next:expr, $t:ty) => ($next().parse::<$t>().expect("Parse error")); } // Verified by https://atcoder.jp/contests/arc084/submissions/3935443 #[derive(Clone)] struct BitSet { size: usize, buf: Vec, } impl BitSet { // size should be a multiple of bit-size of usize. fn new(size: usize) -> Self { let w = 8 * std::mem::size_of::(); assert_eq!(size & (w - 1), 0); let count = size / w; BitSet { size: size, buf: vec![0; count], } } #[allow(unused)] fn set(&mut self, idx: usize, val: bool) { debug_assert!(idx < self.size); let w = 8 * std::mem::size_of::(); let idx0 = idx / w; let idx1 = idx & (w - 1); if val { self.buf[idx0] |= 1 << idx1; } else { self.buf[idx0] &= !(1 << idx1); } } #[allow(unused)] fn get(&self, idx: usize) -> bool { let w = 8 * std::mem::size_of::(); debug_assert!(idx < self.size); let idx0 = idx / w; let idx1 = idx & (w - 1); (self.buf[idx0] >> idx1 & 1) == 1 } #[allow(unused)] fn shl(&self, val: usize) -> Self { if val >= self.size { return Self::new(self.size); } let w = 8 * std::mem::size_of::(); let count = self.size / w; let sh0 = val / w; let sh1 = val & (w - 1); let mut ans = Self::new(self.size); if sh1 == 0 { for i in 0..count - sh0 { ans.buf[i + sh0] = self.buf[i]; } } else { ans.buf[sh0] = self.buf[0] << sh1; for i in 1..count - sh0 { ans.buf[i + sh0] = self.buf[i] << sh1 | self.buf[i - 1] >> (w - sh1); } } ans } // Verified by: https://www.hackerrank.com/contests/yfkpo4/challenges/e-strange-clock/submissions/code/1357435235 #[allow(unused)] fn shr(&self, val: usize) -> Self { if val >= self.size { return Self::new(self.size); } let w = 8 * std::mem::size_of::(); let count = self.size / w; let sh0 = val / w; let sh1 = val & (w - 1); let mut ans = Self::new(self.size); if sh1 == 0 { for i in 0..count - sh0 { ans.buf[i] = self.buf[i + sh0]; } } else { for i in 0..count - sh0 - 1 { ans.buf[i] = self.buf[i + sh0] >> sh1 | self.buf[i + sh0 + 1] << (w - sh1); } ans.buf[count - sh0 - 1] = self.buf[count - 1] >> sh1; } ans } #[allow(unused)] fn msb(&self) -> Option { let w = 8 * std::mem::size_of::(); let count = self.size / w; for i in (0..count).rev() { let v = self.buf[i]; if v != 0 { return Some(w * i + w - 1 - v.leading_zeros() as usize); } } None } } // TODO reference is not allowed as rhs impl std::ops::BitXorAssign for BitSet { fn bitxor_assign(&mut self, other: BitSet) { debug_assert_eq!(self.size, other.size); for i in 0..self.buf.len() { self.buf[i] ^= other.buf[i]; } } } impl std::ops::BitOrAssign for BitSet { fn bitor_assign(&mut self, other: BitSet) { debug_assert_eq!(self.size, other.size); for i in 0..self.buf.len() { self.buf[i] |= other.buf[i]; } } } // https://yukicoder.me/problems/no/1876 (3) // ナップサック問題で、それぞれの重みについてそれを実現する方法の総数の偶奇だけが分かれば良いことに注意すると、bitset で O(N \sum_i A_i/w)。 // Similar problems: https://atcoder.jp/contests/agc020/tasks/agc020_c fn main() { input! { n: usize, a: [usize; n], } const W: usize = 4_000_064; let mut bs = BitSet::new(W); bs.set(0, true); for a in a { let tmp = bs.shl(a); bs ^= tmp; } let mut ans = 0; for i in 0..W { if bs.get(i) { ans ^= i; } } println!("{}", ans); }