Problem:
Score: 500 points

Problem Statement

We have caught N sardines. The deliciousness and fragrantness of the i-th sardine is A_i and B_i, respectively.

We will choose one or more of these sardines and put them into a cooler. However, two sardines on bad terms cannot be chosen at the same time.

The i-th and j-th sardines (i \neq j) are on bad terms if and only if A_i \cdot A_j + B_i \cdot B_j = 0.

In how many ways can we choose the set of sardines to put into the cooler? Since the count can be enormous, print it modulo 1000000007.

Constraints

All values in input are integers.

1 \leq N \leq 2 \times 10^5

-10^{18} \leq A_i, B_i \leq 10^{18}

Input

Input is given from Standard Input in the following format:

N
A_1 B_1
:
A_N B_N

Output

Print the count modulo 1000000007.

Sample Input 1

3
1 2
-1 1
2 -1

Sample Output 1

5

There are five ways to choose the set of sardines, as follows:

The 1-st

The 1-st and 2-nd

The 2-nd

The 2-nd and 3-rd

The 3-rd

Sample Input 2

10
3 2
3 2
-1 1
2 -1
-3 -9
-8 12
7 7
8 1
8 2
8 4

Sample Output 2

479

Solution in Java (OpenJDK 11.0.6) (judge verdict: Wrong Answer)


import java.util.HashMap;
import java.util.HashSet;
import java.util.Map;
import java.util.Set;

public class Main {

  private static void solve() {
    int n = ni();

    Map<String, Long> map = new HashMap<>();

    for (int i = 0; i < n; i++) {
      long a = nl();
      long b = nl();

      if (a == 0 && b == 0) {
      } else {

        long gcd = gcd(Math.abs(a), Math.abs(b));
        a /= gcd;
        b /= gcd;

        if (a < 0) {
          a = -a;
          b = -b;
        }
        if (a == 0 && b < 0) {
          a = 0;
          b = -b;
        }
        String key = a + "," + b;
        map.putIfAbsent(key, 0L);
        map.put(key, map.get(key) + 1);
      }
    }
    int mod = (int) 1e9 + 7;

    long ret = 1;

    Set<String> used = new HashSet<>();
    for (Map.Entry<String, Long> entry : map.entrySet()) {
      String key = entry.getKey();
      if (used.contains(key)) {
        continue;
      }
      long x = entry.getValue();

      String[] elem = key.split(",");
      long a = Long.parseLong(elem[1]);
      long b = -Long.parseLong(elem[0]);

      if (a < 0) {
        a = -a;
        b = -b;
      }
      if (a == 0 && b < 0) {
        a = 0;
        b = -b;
      }
      String key1 = a + "," + b;


      long y = 0;
      if (map.containsKey(key1)) {
        y += map.get(key1);
      }

      long z = pow(2, y, mod) + pow(2, x, mod) - 1 + mod;
      z %= mod;

      ret *= z;
      ret %= mod;

      used.add(key);
      used.add(key1);
    }

    System.out.println((ret - 1 + mod) % mod);

  }

  public static long pow(long a, long n, long mod) {
    // a %= mod;
    long ret = 1;
    int x = 63 - Long.numberOfLeadingZeros(n);
    for (; x >= 0; x--) {
      ret = ret * ret % mod;
      if (n << 63 - x < 0)
        ret = ret * a % mod;
    }
    return ret;
  }


  public static long gcd(long a, long b) {
    while (b > 0) {
      long c = a;
      a = b;
      b = c % b;
    }
    return a;
  }


  public static void main(String[] args) {
    new Thread(null, new Runnable() {
      @Override
      public void run() {
        long start = System.currentTimeMillis();
        String debug = args.length > 0 ? args[0] : null;
        if (debug != null) {
          try {
            is = java.nio.file.Files.newInputStream(java.nio.file.Paths.get(debug));
          } catch (Exception e) {
            throw new RuntimeException(e);
          }
        }
        reader = new java.io.BufferedReader(new java.io.InputStreamReader(is), 32768);
        solve();
        out.flush();
        tr((System.currentTimeMillis() - start) + "ms");
      }
    }, "", 64000000).start();
  }

  private static java.io.InputStream is = System.in;
  private static java.io.PrintWriter out = new java.io.PrintWriter(System.out);
  private static java.util.StringTokenizer tokenizer = null;
  private static java.io.BufferedReader reader;

  public static String next() {
    while (tokenizer == null || !tokenizer.hasMoreTokens()) {
      try {
        tokenizer = new java.util.StringTokenizer(reader.readLine());
      } catch (Exception e) {
        throw new RuntimeException(e);
      }
    }
    return tokenizer.nextToken();
  }

  private static double nd() {
    return Double.parseDouble(next());
  }

  private static long nl() {
    return Long.parseLong(next());
  }

  private static int[] na(int n) {
    int[] a = new int[n];
    for (int i = 0; i < n; i++)
      a[i] = ni();
    return a;
  }

  private static char[] ns() {
    return next().toCharArray();
  }

  private static long[] nal(int n) {
    long[] a = new long[n];
    for (int i = 0; i < n; i++)
      a[i] = nl();
    return a;
  }

  private static int[][] ntable(int n, int m) {
    int[][] table = new int[n][m];
    for (int i = 0; i < n; i++) {
      for (int j = 0; j < m; j++) {
        table[i][j] = ni();
      }
    }
    return table;
  }

  private static int[][] nlist(int n, int m) {
    int[][] table = new int[m][n];
    for (int i = 0; i < n; i++) {
      for (int j = 0; j < m; j++) {
        table[j][i] = ni();
      }
    }
    return table;
  }

  private static int ni() {
    return Integer.parseInt(next());
  }

  private static void tr(Object... o) {
    if (is != System.in)
      System.out.println(java.util.Arrays.deepToString(o));
  }
}