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.

Examples

Input

3
1 2
-1 1
2 -1


Output

5


Input

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


Output

479

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

      if (a == 0 && b == 0) {
        zero++;
      } 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 + zero - 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));
  }
}

