// 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")); } trait Change { fn chmax(&mut self, x: Self); fn chmin(&mut self, x: Self); } impl Change for T { fn chmax(&mut self, x: T) { if *self < x { *self = x; } } fn chmin(&mut self, x: T) { if *self > x { *self = x; } } } // Tags: bit-dp fn main() { input! { n: usize, abc: [[i64; 3]; n], } const INF: i64 = 1 << 50; let mut dp = vec![vec![[-INF; 3]; 1 << n]; n]; let get = |idx: usize, x: usize| -> (i64, [i64; 2]) { let mut ans = [0; 2]; for i in 1..3 { ans[i - 1] = abc[idx][(x + i) % 3]; } ans.sort(); (abc[idx][x], ans) }; for i in 0..n { for j in 0..3 { let (w, _v) = get(i, j); dp[i][1 << i][j] = w; } } for bits in 1usize..1 << n { if bits.count_ones() <= 1 { continue; } for i in 0..n { if (bits & 1 << i) == 0 { continue; } for j in 0..n { if i == j || (bits & 1 << i) == 0 { continue; } for k in 0..3 { let val = dp[j][bits ^ 1 << i][k]; let (_, w1) = get(j, k); for l in 0..3 { let (v2, w2) = get(i, l); if w1[0] <= w2[0] && w1[1] <= w2[1] { dp[i][bits][l].chmax(val + v2); } } } } } } let mut ans = -INF; for i in 0..n { for bits in 0..1 << n { for k in 0..3 { ans.chmax(dp[i][bits][k]); } } } println!("{}", ans); }