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| 1 | +// https://atcoder.jp/contests/abc168/tasks/abc168_e |
| 2 | +// |
| 3 | +// 以下のクレートを使用。 |
| 4 | +// - `maplit` |
| 5 | +// - `num` |
| 6 | +// - `num-rational` |
| 7 | +// - `proconio` |
| 8 | + |
| 9 | +use maplit::hashmap; |
| 10 | +use num::{rational::Ratio, One, Signed as _}; |
| 11 | +use proconio::input; |
| 12 | +use std::{ |
| 13 | + fmt, |
| 14 | + iter::Product, |
| 15 | + ops::{Add, Mul, Sub}, |
| 16 | +}; |
| 17 | + |
| 18 | +fn main() { |
| 19 | + // `proconio::input!`。 |
| 20 | + // |
| 21 | + // https://docs.rs/proconio/0.3.6/proconio/macro.input.html |
| 22 | + input! { |
| 23 | + n: usize, |
| 24 | + abs: [(i64, i64); n], |
| 25 | + } |
| 26 | + |
| 27 | + // 有理数として`num_rational::Ratio<i64>`を使う。 |
| 28 | + // |
| 29 | + // https://docs.rs/num-rational/0.2.4/num_rational/struct.Ratio.html |
| 30 | + |
| 31 | + let mut zeros = 0; |
| 32 | + let mut horz = 0; |
| 33 | + let mut vert = 0; |
| 34 | + let mut others = hashmap!(); |
| 35 | + |
| 36 | + for (a, b) in abs { |
| 37 | + match (a.signum(), b.signum()) { |
| 38 | + (0, 0) => zeros += 1, |
| 39 | + (1, 0) | (-1, 0) => horz += 1, |
| 40 | + (0, 1) | (0, -1) => vert += 1, |
| 41 | + _ => *others.entry(Ratio::new(a, b)).or_insert(0) += 1usize, |
| 42 | + } |
| 43 | + } |
| 44 | + |
| 45 | + let ans = others |
| 46 | + .iter() |
| 47 | + .map(|(grad, &num1)| { |
| 48 | + // `Ratio::recip`で逆元を得ることができる。 |
| 49 | + // |
| 50 | + // https://docs.rs/num-rational/0.2.4/num_rational/struct.Ratio.html#method.recip |
| 51 | + let num2 = *others.get(&-grad.recip()).unwrap_or(&0); |
| 52 | + if grad.is_negative() && num2 > 0 { |
| 53 | + Zp::unchecked(1) |
| 54 | + } else { |
| 55 | + xor_combinations(num1, num2) |
| 56 | + } |
| 57 | + }) |
| 58 | + .product::<Zp>() |
| 59 | + * xor_combinations(horz, vert) |
| 60 | + + Zp::unchecked(zeros) |
| 61 | + - Zp::unchecked(1); |
| 62 | + println!("{}", ans); |
| 63 | +} |
| 64 | + |
| 65 | +fn xor_combinations(a: usize, b: usize) -> Zp { |
| 66 | + return pow2(a) + pow2(b) - Zp::unchecked(1); |
| 67 | + |
| 68 | + fn pow2(exp: usize) -> Zp { |
| 69 | + num::pow(Zp::unchecked(2), exp) |
| 70 | + } |
| 71 | +} |
| 72 | + |
| 73 | +const P: usize = 1_000_000_007; |
| 74 | + |
| 75 | +#[derive(Clone, Copy, Debug)] |
| 76 | +struct Zp { |
| 77 | + repr: usize, |
| 78 | +} |
| 79 | + |
| 80 | +impl Zp { |
| 81 | + fn new(val: usize) -> Self { |
| 82 | + Self { repr: val % P } |
| 83 | + } |
| 84 | + |
| 85 | + fn unchecked(repr: usize) -> Self { |
| 86 | + Self { repr } |
| 87 | + } |
| 88 | +} |
| 89 | + |
| 90 | +impl One for Zp { |
| 91 | + fn one() -> Self { |
| 92 | + Self::unchecked(1) |
| 93 | + } |
| 94 | +} |
| 95 | + |
| 96 | +impl fmt::Display for Zp { |
| 97 | + fn fmt(&self, fmt: &mut fmt::Formatter) -> fmt::Result { |
| 98 | + fmt::Display::fmt(&self.repr, fmt) |
| 99 | + } |
| 100 | +} |
| 101 | + |
| 102 | +impl Add for Zp { |
| 103 | + type Output = Self; |
| 104 | + |
| 105 | + fn add(self, rhs: Self) -> Self { |
| 106 | + Self::new(self.repr + rhs.repr) |
| 107 | + } |
| 108 | +} |
| 109 | + |
| 110 | +impl Sub for Zp { |
| 111 | + type Output = Self; |
| 112 | + |
| 113 | + fn sub(self, rhs: Self) -> Self { |
| 114 | + Self::new(P + self.repr - rhs.repr) |
| 115 | + } |
| 116 | +} |
| 117 | + |
| 118 | +impl Mul for Zp { |
| 119 | + type Output = Self; |
| 120 | + |
| 121 | + fn mul(self, rhs: Self) -> Self { |
| 122 | + Self::new(self.repr * rhs.repr) |
| 123 | + } |
| 124 | +} |
| 125 | + |
| 126 | +impl Product for Zp { |
| 127 | + fn product<I: Iterator<Item = Self>>(iter: I) -> Self { |
| 128 | + iter.fold(Self::unchecked(1), Mul::mul) |
| 129 | + } |
| 130 | +} |
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