use std::{ collections::{HashMap}, }; #[allow(clippy::many_single_char_names)] fn main() { let n = getline().parse::().unwrap(); let a = getline() .split(' ') .map(|x| x.parse::().unwrap()) .collect::>(); let mut div_map: HashMap = HashMap::new(); let mut edges: Vec<(usize, usize, i64)> = Vec::new(); for i in 0..n { let divs = divisors(a[i]); for d in divs { div_map.entry(d).or_insert_with(Vec::new).push(i); } } for e in &mut div_map { e.1.sort_by_key(|i| a[*i]); let d = *e.0; let u = e.1[0]; for v in e.1 { if u == *v { continue; } edges.push((u, *v, a[u] / d * a[*v])); } } edges.sort_by_key(|e| e.2); let mut ds = Dsu::new(n); let mut ans = 0; for e in edges { if ds.same(e.0, e.1) { continue; } ds.merge(e.0, e.1); ans += e.2; } println!("{}", ans); } fn divisors(x: i64) -> Vec { let mut ret = vec![]; let mut i = 1; while i * i <= x { if x % i == 0 { ret.push(i); if i * i != x { ret.push(x / i); } } i += 1; } ret } fn getline() -> String { let mut buf = String::new(); std::io::stdin().read_line(&mut buf).unwrap(); buf.trim().to_string() } pub struct Dsu { n: usize, // root node: -1 * component size // otherwise: parent parent_or_size: Vec, } impl Dsu { /// Creates a new `Dsu`. /// /// # Constraints /// /// - $0 \leq n \leq 10^8$ /// /// # Complexity /// /// - $O(n)$ pub fn new(size: usize) -> Self { Self { n: size, parent_or_size: vec![-1; size], } } // `\textsc` does not work in KaTeX /// Performs the Uɴɪᴏɴ operation. /// /// # Constraints /// /// - $0 \leq a < n$ /// - $0 \leq b < n$ /// /// # Panics /// /// Panics if the above constraints are not satisfied. /// /// # Complexity /// /// - $O(\alpha(n))$ amortized pub fn merge(&mut self, a: usize, b: usize) -> usize { assert!(a < self.n); assert!(b < self.n); let (mut x, mut y) = (self.leader(a), self.leader(b)); if x == y { return x; } if -self.parent_or_size[x] < -self.parent_or_size[y] { std::mem::swap(&mut x, &mut y); } self.parent_or_size[x] += self.parent_or_size[y]; self.parent_or_size[y] = x as i32; x } /// Returns whether the vertices $a$ and $b$ are in the same connected component. /// /// # Constraints /// /// - $0 \leq a < n$ /// - $0 \leq b < n$ /// /// # Panics /// /// Panics if the above constraint is not satisfied. /// /// # Complexity /// /// - $O(\alpha(n))$ amortized pub fn same(&mut self, a: usize, b: usize) -> bool { assert!(a < self.n); assert!(b < self.n); self.leader(a) == self.leader(b) } /// Performs the Fɪɴᴅ operation. /// /// # Constraints /// /// - $0 \leq a < n$ /// /// # Panics /// /// Panics if the above constraint is not satisfied. /// /// # Complexity /// /// - $O(\alpha(n))$ amortized pub fn leader(&mut self, a: usize) -> usize { assert!(a < self.n); if self.parent_or_size[a] < 0 { return a; } self.parent_or_size[a] = self.leader(self.parent_or_size[a] as usize) as i32; self.parent_or_size[a] as usize } /// Returns the size of the connected component that contains the vertex $a$. /// /// # Constraints /// /// - $0 \leq a < n$ /// /// # Panics /// /// Panics if the above constraint is not satisfied. /// /// # Complexity /// /// - $O(\alpha(n))$ amortized pub fn size(&mut self, a: usize) -> usize { assert!(a < self.n); let x = self.leader(a); -self.parent_or_size[x] as usize } /// Divides the graph into connected components. /// /// The result may not be ordered. /// /// # Complexity /// /// - $O(n)$ pub fn groups(&mut self) -> Vec> { let mut leader_buf = vec![0; self.n]; let mut group_size = vec![0; self.n]; for i in 0..self.n { leader_buf[i] = self.leader(i); group_size[leader_buf[i]] += 1; } let mut result = vec![Vec::new(); self.n]; for i in 0..self.n { result[i].reserve(group_size[i]); } for i in 0..self.n { result[leader_buf[i]].push(i); } result .into_iter() .filter(|x| !x.is_empty()) .collect::>>() } }