// 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),* )) => { ($(read_value!($next, $t)),*) }; ($next:expr, [ $t:tt ; $len:expr ]) => { (0..$len).map(|_| read_value!($next, $t)).collect::>() }; ($next:expr, $t:ty) => ($next().parse::<$t>().expect("Parse error")); } /// Verified by https://atcoder.jp/contests/abc198/submissions/21774342 mod mod_int { use std::ops::*; pub trait Mod: Copy { fn m() -> i64; } #[derive(Copy, Clone, Hash, PartialEq, Eq, PartialOrd, Ord)] pub struct ModInt { pub x: i64, phantom: ::std::marker::PhantomData } impl ModInt { // x >= 0 pub fn new(x: i64) -> Self { ModInt::new_internal(x % M::m()) } fn new_internal(x: i64) -> Self { ModInt { x: x, phantom: ::std::marker::PhantomData } } pub fn pow(self, mut e: i64) -> Self { debug_assert!(e >= 0); let mut sum = ModInt::new_internal(1); let mut cur = self; while e > 0 { if e % 2 != 0 { sum *= cur; } cur *= cur; e /= 2; } sum } #[allow(dead_code)] pub fn inv(self) -> Self { self.pow(M::m() - 2) } } impl>> Add for ModInt { type Output = Self; fn add(self, other: T) -> Self { let other = other.into(); let mut sum = self.x + other.x; if sum >= M::m() { sum -= M::m(); } ModInt::new_internal(sum) } } impl>> Sub for ModInt { type Output = Self; fn sub(self, other: T) -> Self { let other = other.into(); let mut sum = self.x - other.x; if sum < 0 { sum += M::m(); } ModInt::new_internal(sum) } } impl>> Mul for ModInt { type Output = Self; fn mul(self, other: T) -> Self { ModInt::new(self.x * other.into().x % M::m()) } } impl>> AddAssign for ModInt { fn add_assign(&mut self, other: T) { *self = *self + other; } } impl>> SubAssign for ModInt { fn sub_assign(&mut self, other: T) { *self = *self - other; } } impl>> MulAssign for ModInt { fn mul_assign(&mut self, other: T) { *self = *self * other; } } impl Neg for ModInt { type Output = Self; fn neg(self) -> Self { ModInt::new(0) - self } } impl ::std::fmt::Display for ModInt { fn fmt(&self, f: &mut ::std::fmt::Formatter) -> ::std::fmt::Result { self.x.fmt(f) } } impl From for ModInt { fn from(x: i64) -> Self { Self::new(x) } } } // mod mod_int macro_rules! define_mod { ($struct_name: ident, $modulo: expr) => { #[derive(Copy, Clone, PartialEq, Eq, PartialOrd, Ord, Hash)] struct $struct_name {} impl mod_int::Mod for $struct_name { fn m() -> i64 { $modulo } } } } const MOD: i64 = 1_000_000_007; define_mod!(PP, MOD); type MInt = mod_int::ModInt; type Coord = i64; // the type of coordinates fn arg_sort(xy: &mut [(Coord, Coord, i32)]) { fn half((x, y, _): (Coord, Coord, i32)) -> i32 { assert_ne!((x, y), (0, 0)); if y >= 0 { if x > 0 || y > 0 { 1 } else { 2 } } else { 2 } } xy.sort_unstable_by(|&a, &b| { half(a).cmp(&half(b)).then_with( || 0.cmp(&(a.0 * b.1 - a.1 * b.0)) .then_with(|| a.2.cmp(&b.2))) }); } fn calc(a: Vec<(i64, i64)>) -> MInt { let n = a.len(); let mut b = vec![]; for (x, y) in a { b.push((x, y, 0)); b.push((-x, -y, 1)); } arg_sort(&mut b); let mut acc_x = vec![MInt::new(0); 3 * n + 1]; let mut acc_y = vec![MInt::new(0); 3 * n + 1]; let mut tot = MInt::new(0); for i in 0..3 * n { let (x, y) = if b[i % (2 * n)].2 == 0 { (MOD + b[i % (2 * n)].0, MOD + b[i % (2 * n)].1) } else { (0, 0) }; acc_x[i + 1] = acc_x[i] + x; acc_y[i + 1] = acc_y[i] + y; } for i in 0..2 * n { if b[i].2 != 0 { continue; } let p = acc_x[i + n] - acc_x[i]; let q = acc_y[i + n] - acc_y[i]; tot += q * (MOD + b[i].0) - p * (MOD + b[i].1); } tot } // Tags: counting, area-of-triangles, sort-by-argument fn main() { input! { n: usize, xy: [(i64, i64); n], } let mut tot = MInt::new(0); for i in 0..n { let (x, y) = xy[i]; let v: Vec<_> = xy[i + 1..].iter().map(|&(a, b)| (a - x, b - y)) .filter(|&p| p != (0, 0)).collect(); tot += calc(v); } println!("{}", tot); }