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.*;
import java.io.*;
import java.math.*;
public class Main implements Runnable {
	static boolean DEBUG;
	public static void main(String[] args) {
		DEBUG = args.length > 0 && args[0].equals("-DEBUG");
		new Thread(null, new Main(), "", 1 << 31).start();
	}

	public void run() {
		Solver solver = new Solver();
		solver.solve();
		solver.exit();
	}

	static class FastScanner {
		private final InputStream in = System.in;
		private final byte[] buffer = new byte[1024];
		private int pointer = 0;
		private int buflen = 0;
		private boolean hasNextByte() {
			if(pointer < buflen) return true;
			else {
				pointer = 0;
				try {
					buflen = in.read(buffer);
				}catch (IOException e) {
					e.printStackTrace();
				}
				return buflen > 0;
			}
		}
		private int readByte() { if(hasNextByte()) return buffer[pointer ++]; else return -1; }
		private boolean isPrintableChar(int c) { return isPrintableChar(c, false); }
		private boolean isPrintableChar(int c, boolean includingSpace) { return (includingSpace ? 32 : 33) <= c && c <= 126; }
		private void skipUnprintable() { skipUnprintable(false); }
		private void skipUnprintable(boolean includingSpace) { while(hasNextByte() && !isPrintableChar(buffer[pointer], includingSpace)) pointer++; }
		private boolean hasNext() { return hasNext(false); }
		private boolean hasNext(boolean includingSpace) { skipUnprintable(includingSpace); return hasNextByte(); }
		private StringBuilder sb = new StringBuilder();
		public String next() { return next(false); }
		public String next(boolean includingSpace) {
			if(!hasNext(includingSpace)) throw new NoSuchElementException();
			sb.setLength(0);
			int b = readByte();
			while(isPrintableChar(b, includingSpace)) {
				sb.appendCodePoint(b);
				b = readByte();
			}
			return sb.toString();
		}
		public long nextLong() {
			if(!hasNext()) throw new NoSuchElementException();
			long n = 0;
			boolean minus = false;
			int b = readByte();
			if(b == '-') {
				minus = true;
				b = readByte();
			}
			if(b < '0' || '9' < b) throw new NumberFormatException();
			while(true) {
				if('0' <= b && b <= '9') n = n * 10 + b - '0';
				else if(b == -1 || !isPrintableChar(b)) return minus ? -n : n;
				else throw new NumberFormatException();
				b = readByte();
			}
		}
	}

	static class Solver {
		FastScanner sc = new FastScanner();
		public Solver() { }

		String ns() { return ns(false); }
		String ns(boolean includingSpace) { return sc.next(includingSpace); }
		String[] ns(int n) { return ns(n, false); }
		String[] ns(int n, boolean includingSpace) {
			String a[] = new String[n];
			for(int i = 0; i < n; i ++) a[i] = ns(includingSpace);
			return a;
		}
		String[][] ns(int n, int m) { return ns(n, m, false); }
		String[][] ns(int n, int m, boolean includingSpace) {
			String a[][] = new String[n][m];
			for(int i = 0; i < n; i ++) a[i] = ns(m, includingSpace);
			return a;
		}
		char nc() { return ns().charAt(0); }
		char[] nc(int n) {
			String str = ns();
			if(n < 0) n = str.length();
			char a[] = new char[n];
			for(int i = 0; i < n; i ++) a[i] = str.charAt(i);
			return a;
		}
		char[][] nc(int n, int m) {
			char a[][] = new char[n][m];
			for(int i = 0; i < n; i ++) a[i] = nc(m);
			return a;
		}
		boolean[] nb(int n, char t) {
			char c[] = nc(-1);
			if(n < 0) n = c.length;
			boolean a[] = new boolean[n];
			for(int i = 0; i < n; i ++) a[i] = c[i] == t;
			return a;
		}
		boolean[][] nb(int n, int m, char t) {
			boolean a[][] = new boolean[n][m];
			for(int i = 0; i < n; i ++) a[i] = nb(m, t);
			return a;
		}
		int ni() { return Math.toIntExact(sc.nextLong()); }
		int[] ni(int n) {
			int a[] = new int[n];
			for(int i = 0; i < n; i ++) a[i] = ni();
			return a;
		}
		int[][] ni(int n, int m) {
			int a[][] = new int[n][m];
			for(int i = 0; i < n; i ++) a[i] = ni(m);
			return a;
		}
		long nl() { return sc.nextLong(); }
		long[] nl(int n) {
			long a[] = new long[n];
			for(int i = 0; i < n; i ++) a[i] = nl();
			return a;
		}
		long[][] nl(int n, int m) {
			long a[][] = new long[n][m];
			for(int i = 0; i < n; i ++) a[i] = nl(m);
			return a;
		}
		double nd() { return Double.parseDouble(sc.next()); }
		double[] nd(int n) {
			double a[] = new double[n];
			for(int i = 0; i < n; i ++) a[i] = nd();
			return a;
		}
		double[][] nd(int n, int m) {
			double a[][] = new double[n][m];
			for(int i = 0; i < n; i ++) a[i] = nd(m);
			return a;
		}


		String booleanToString(boolean b) { return b ? "#" : "."; }

		PrintWriter out = new PrintWriter(System.out);
		PrintWriter err = new PrintWriter(System.err);
		StringBuilder sb4prtln = new StringBuilder();
		void prt() { out.print(""); }
		<T> void prt(T a) { out.print(a); }
		void prtln() { out.println(""); }
		<T> void prtln(T a) { out.println(a); }
		void prtln(int... a) {
			sb4prtln.setLength(0);
			for(int element : a) sb4prtln.append(element+" ");
			prtln(sb4prtln.toString().trim());
		}
		void prtln(long... a) {
			sb4prtln.setLength(0);
			for(long element : a) sb4prtln.append(element+" ");
			prtln(sb4prtln.toString().trim());
		}
		void prtln(double... a) {
			sb4prtln.setLength(0);
			for(double element : a) sb4prtln.append(element+" ");
			prtln(sb4prtln.toString().trim());
		}
		void prtln(String... a) {
			sb4prtln.setLength(0);
			for(String element : a) sb4prtln.append(element+" ");
			prtln(sb4prtln.toString().trim());
		}
		void prtln(char... a) {
			sb4prtln.setLength(0);
			for(char element : a) sb4prtln.append(element);
			prtln(sb4prtln.toString());
		}
		void prtln(boolean... a) {
			sb4prtln.setLength(0);
			for(boolean element : a) sb4prtln.append(booleanToString(element));
			prtln(sb4prtln.toString());
		}
		void prtln(int[][] a) { for(int[] element : a) prtln(element); }
		void prtln(long[][] a) { for(long[] element : a) prtln(element); }
		void prtln(double[][] a) { for(double[] element : a) prtln(element); }
		void prtln(String[][] a) { for(String[] element : a) prtln(element); }
		void prtln(char[][] a) { for(char[] element : a) prtln(element); }
		void prtln(boolean[][] a) { for(boolean[] element : a) prtln(element); }

		String errconvert(int a) { return isINF(a) ? "_" : String.valueOf(a); }
		String errconvert(long a) { return isINF(a) ? "_" : String.valueOf(a); }
		void errprt(int a) { if(DEBUG) err.print(errconvert(a)); }
		void errprt(long a) { if(DEBUG) err.print(errconvert(a)); }
		void errprt() { if(DEBUG) err.print(""); }
		<T> void errprt(T a) { if(DEBUG) err.print(a); }
		void errprt(boolean a) { if(DEBUG) errprt(booleanToString(a)); }
		void errprtln() { if(DEBUG) err.println(""); }
		void errprtln(int a) { if(DEBUG) err.println(errconvert(a)); }
		void errprtln(long a) { if(DEBUG) err.println(errconvert(a)); }
		<T> void errprtln(T a) { if(DEBUG) err.println(a); }
		void errprtln(boolean a) { if(DEBUG) errprtln(booleanToString(a)); }
		void errprtln(int... a) {
			if(DEBUG) {
				sb4prtln.setLength(0);
				for(int element : a) sb4prtln.append(errconvert(element)+" ");
				errprtln(sb4prtln.toString().trim());
			}
		}
		void errprtln(long... a) {
			if(DEBUG) {
				sb4prtln.setLength(0);
				for(long element : a) sb4prtln.append(errconvert(element)+" ");
				errprtln(sb4prtln.toString().trim());
			}
		}
		void errprtln(double... a) {
			if(DEBUG) {
				sb4prtln.setLength(0);
				for(double element : a) sb4prtln.append(element+" ");
				errprtln(sb4prtln.toString().trim());
			}
		}
		void errprtln(String... a) {
			if(DEBUG) {
				sb4prtln.setLength(0);
				for(String element : a) sb4prtln.append(element+" ");
				errprtln(sb4prtln.toString().trim());
			}
		}
		void errprtln(char... a) {
			if(DEBUG) {
				sb4prtln.setLength(0);
				for(char element : a) sb4prtln.append(element);
				errprtln(sb4prtln.toString());
			}
		}
		void errprtln(boolean... a) {
			if(DEBUG) {
				sb4prtln.setLength(0);
				for(boolean element : a) sb4prtln.append(booleanToString(element));
				errprtln(sb4prtln.toString());
			}
		}
		void errprtln(Object[] a) { if(DEBUG) for(Object element : a) errprtln(element); }
		void errprtln(int[][] a) { if(DEBUG) for(int[] element : a) errprtln(element); }
		void errprtln(long[][] a) { if(DEBUG) for(long[] element : a) errprtln(element); }
		void errprtln(double[][] a) { if(DEBUG) for(double[] element : a) errprtln(element); }
		void errprtln(String[][] a) { if(DEBUG) for(String[] element : a) errprtln(element); }
		void errprtln(char[][] a) { if(DEBUG) for(char[] element : a) errprtln(element); }
		void errprtln(boolean[][] a) { if(DEBUG) for(boolean[] element : a) errprtln(element); }
		void errprtln(Object[][] a) { if(DEBUG) for(Object element : a) { errprtln(element); errprtln(); } }

		void reply(boolean b) { prtln(b ? "Yes" : "No"); }
		void REPLY(boolean b) { prtln(b ? "YES" : "NO"); }

		void flush() { out.flush(); if(DEBUG) err.flush(); }
		void assertion(boolean b) { if(!b) throw new AssertionError(); }

		void exit() { flush(); System.exit(0); }
		<T> void exit(T a) { prtln(a); exit(); }
		void exit(int... a) { prtln(a); exit(); }
		void exit(long... a) { prtln(a); exit(); }
		void exit(double... a) { prtln(a); exit(); }
		void exit(String... a) { prtln(a); exit(); }
		void exit(char... a) { prtln(a); exit(); }
		void exit(boolean... a) { prtln(a); exit(); }
		void exit(int[][] a) { prtln(a); exit(); }
		void exit(long[][] a) { prtln(a); exit(); }
		void exit(double[][] a) { prtln(a); exit(); }
		void exit(String[][] a) { prtln(a); exit(); }
		void exit(char[][] a) { prtln(a); exit(); }
		void exit(boolean[][] a) { prtln(a); exit(); }


		long INF = (long)1e18 + 7;
		boolean isPlusINF(long a) { return a > INF / 10; }
		boolean isMinusINF(long a) { return isPlusINF(- a); }
		boolean isINF(long a) { return isPlusINF(a) || isMinusINF(a); }
		int I_INF = (int)1e9 + 7;
		boolean isPlusINF(int a) { return a > I_INF / 10; }
		boolean isMinusINF(int a) { return isPlusINF(- a); }
		boolean isINF(int a) { return isPlusINF(a) || isMinusINF(a); }


		int min(int a, int b) { return Math.min(a, b); }
		long min(long a, long b) { return Math.min(a, b); }
		double min(double a, double b) { return Math.min(a, b); }
		<T extends Comparable<T>> T min(T a, T b) { return a.compareTo(b) <= 0 ? a : b; }
		int min(int... x) {
			int min = x[0];
			for(int val : x) min = min(min, val);
			return min;
		}
		long min(long... x) {
			long min = x[0];
			for(long val : x) min = min(min, val);
			return min;
		}
		double min(double... x) {
			double min = x[0];
			for(double val : x) min = min(min, val);
			return min;
		}
		int max(int a, int b) { return Math.max(a, b); }
		long max(long a, long b) { return Math.max(a, b); }
		double max(double a, double b) { return Math.max(a, b); }
		<T extends Comparable<T>> T max(T a, T b) { return a.compareTo(b) >= 0 ? a : b; }
		int max(int... x) {
			int max = x[0];
			for(int val : x) max = max(max, val);
			return max;
		}
		long max(long... x) {
			long max = x[0];
			for(long val : x) max = max(max, val);
			return max;
		}
		double max(double... x) {
			double max = x[0];
			for(double val : x) max = max(max, val);
			return max;
		}
		long sum(int... a) {
			long sum = 0;
			for(int element : a) sum += element;
			return sum;
		}
		long sum(long... a) {
			long sum = 0;
			for(long element : a) sum += element;
			return sum;
		}
		double sum(double... a) {
			double sum = 0;
			for(double element : a) sum += element;
			return sum;
		}
		long sum(boolean... a) {
			long sum = 0;
			for(boolean element : a) sum += element ? 1 : 0;
			return sum;
		}
		long[] sums(int[] a) {
			long sum[] = new long[a.length + 1];
			sum[0] = 0;
			for(int i = 0; i < a.length; i ++) sum[i + 1] = sum[i] + a[i];
			return sum;
		}
		long[] sums(long[] a) {
			long sum[] = new long[a.length + 1];
			sum[0] = 0;
			for(int i = 0; i < a.length; i ++) sum[i + 1] = sum[i] + a[i];
			return sum;
		}
		double[] sums(double[] a) {
			double sum[] = new double[a.length + 1];
			sum[0] = 0;
			for(int i = 0; i < a.length; i ++) sum[i + 1] = sum[i] + a[i];
			return sum;
		}
		long[] sums(boolean[] a) {
			long sum[] = new long[a.length + 1];
			sum[0] = 0;
			for(int i = 0; i < a.length; i ++) sum[i + 1] = sum[i] + (a[i] ? 1 : 0);
			return sum;
		}
		long[][] sums(int[][] a) {
			long sum[][] = new long[a.length + 1][a[0].length + 1];
			fill(sum, 0);
			for(int i = 0; i < a.length; i ++) {
				for(int j = 0; j < a[i].length; j ++) {
					sum[i + 1][j + 1] = sum[i + 1][j] + sum[i][j + 1] - sum[i][j] + a[i][j];
				}
			}
			return sum;
		}
		long[][] sums(long[][] a) {
			long sum[][] = new long[a.length + 1][a[0].length + 1];
			fill(sum, 0);
			for(int i = 0; i < a.length; i ++) {
				for(int j = 0; j < a[i].length; j ++) {
					sum[i + 1][j + 1] = sum[i + 1][j] + sum[i][j + 1] - sum[i][j] + a[i][j];
				}
			}
			return sum;
		}
		double[][] sums(double[][] a) {
			double sum[][] = new double[a.length + 1][a[0].length + 1];
			fill(sum, 0);
			for(int i = 0; i < a.length; i ++) {
				for(int j = 0; j < a[i].length; j ++) {
					sum[i + 1][j + 1] = sum[i + 1][j] + sum[i][j + 1] - sum[i][j] + a[i][j];
				}
			}
			return sum;
		}
		long[][] sums(boolean[][] a) {
			long sum[][] = new long[a.length + 1][a[0].length + 1];
			fill(sum, 0);
			for(int i = 0; i < a.length; i ++) {
				for(int j = 0; j < a[i].length; j ++) {
					sum[i + 1][j + 1] = sum[i + 1][j] + sum[i][j + 1] - sum[i][j] + (a[i][j] ? 1 : 0);
				}
			}
			return sum;
		}
		int constrain(int x, int l, int r) { return min(max(x, min(l, r)), max(l, r)); }
		long constrain(long x, long l, long r) { return min(max(x, min(l, r)), max(l, r)); }
		double constrain(double x, double l, double r) { return min(max(x, min(l, r)), max(l, r)); }
		int abs(int x) { return x >= 0 ? x : - x; }
		long abs(long x) { return x >= 0 ? x : - x; }
		double abs(double x) { return x >= 0 ? x : - x; }
		int signum(int x) { return x > 0 ? 1 : x < 0 ? -1 : 0; }
		int signum(long x) { return x > 0 ? 1 : x < 0 ? -1 : 0; }
		int signum(double x) { return x > 0 ? 1 : x < 0 ? -1 : 0; }
		long round(double x) { return Math.round(x); }
		long floor(double x) { return (long)Math.floor(x); }
		int divfloor(int a, int b) { return signum(a) == signum(b) ? a / b : - divceil(abs(a), abs(b)); }
		long divfloor(long a, long b) { return signum(a) == signum(b) ? a / b : - divceil(abs(a), abs(b)); }
		long ceil(double x) { return (long)Math.ceil(x); }
		int divceil(int a, int b) { return a >= 0 && b > 0 ? (a + b - 1) / b
											: a < 0 && b < 0 ? divceil(abs(a), abs(b))
											: - divfloor(abs(a), abs(b)); }
		long divceil(long a, long b) { return a >= 0 && b > 0 ? (a + b - 1) / b
											: a < 0 && b < 0 ? divceil(abs(a), abs(b))
											: - divfloor(abs(a), abs(b)); }
		double sqrt(int x) { return Math.sqrt((double)x); }
		double sqrt(long x) { return Math.sqrt((double)x); }
		double sqrt(double x) { return Math.sqrt(x); }
		long fact(int n) {
			long ans = 1;
			for(int i = 1; i <= n; i ++) ans = Math.multiplyExact(ans, i);
			return ans;
		}
		double pow(double x, double y) { return Math.pow(x, y); }
		long pow(long x, long y) {
			long ans = 1;
			for(; y > 0; y /= 2) {
				if(y % 2 != 0) ans = Math.multiplyExact(ans, x);
				x = Math.multiplyExact(x, x);
			}
			return ans;
		}
		int gcd(int a, int b) {
			while(true) {
				if(b == 0) return a;
				int tmp = a;
				a = b;
				b = tmp % b;
			}
		}
		long gcd(long a, long b) {
			while(true) {
				if(b == 0) return a;
				long tmp = a;
				a = b;
				b = tmp % b;
			}
		}
		long lcm(long a, long b) { return a / gcd(a, b) * b; }
		int gcd(int... a) {
			int gcd = 0;
			for(int i = 0; i < a.length; i ++) gcd = gcd(gcd, a[i]);
			return gcd;
		}
		long gcd(long... a) {
			long gcd = 0;
			for(int i = 0; i < a.length; i ++) gcd = gcd(gcd, a[i]);
			return gcd;
		}
		double random() { return Math.random(); }
		int random(int max) { return (int)floor(random() * max); }
		long random(long max) { return floor(random() * max); }
		int random(int min, int max) { return random(max - min) + max; }
		long random(long min, long max) { return random(max - min) + max; }

		boolean isUpper(char a) { return a >= 'A' && a <= 'Z'; }
		boolean isLower(char a) { return a >= 'a' && a <= 'z'; }
		int upperToInt(char a) { return a - 'A'; }
		int lowerToInt(char a) { return a - 'a'; }
		int numToInt(char a) { return a - '0'; }
		int charToInt(char a) { return a >= 'a' ? lowerToInt(a) : a >= 'A' ? upperToInt(a) : numToInt(a); }
		char intToUpper(int a) { return (char)(a + 'A'); }
		char intToLower(int a) { return (char)(a + 'a'); }
		char intToNum(int a) { return (char)(a + '0'); }
		int[] charToInt(char[] a) {
			int array[] = new int[a.length];
			for(int i = 0; i < a.length; i ++) array[i] = charToInt(a[i]);
			return array;
		}

		long[] div(long a) {
			List<Long> divList = new ArrayList<Long>();
			for(long i = 1; i * i <= a; i ++) {
				if(a % i == 0) {
					divList.add(i);
					if(i * i != a) divList.add(a / i);
				}
			}
			long div[] = new long[divList.size()];
			for(int i = 0; i < divList.size(); i ++) div[i] = divList.get(i);
			Arrays.sort(div);
			return div;
		}

		long[][] factor(long a) {
			List<Long> factorList = new ArrayList<Long>();
			List<Long> degreeList = new ArrayList<Long>();
			for(long i = 2; i * i <= a; i ++) {
				if(a % i == 0) {
					long count = 0;
					while(a % i == 0) { a /= i; count ++; }
					factorList.add(i);
					degreeList.add(count);
				}
			}
			if(a > 1) { factorList.add(a); degreeList.add(1L); }
			long factor[][] = new long[factorList.size()][2];
			for(int i = 0; i < factorList.size(); i ++) {
				factor[i][0] = factorList.get(i);
				factor[i][1] = degreeList.get(i);
			}
			Arrays.sort(factor, (sort1, sort2) -> Long.compare(sort1[0], sort2[0]));
			return factor;
		}

		boolean isPrime(long x) {
			boolean ok = x > 1;
			for(long i = 2; i * i <= x; i ++) {
				ok &= x % i != 0;
				if(!ok) return ok;
			}
			return ok;
		}
		boolean[] prime(int num) {
			boolean prime[] = new boolean[num];
			fill(prime, true);
			if(num > 0) prime[0] = false;
			if(num > 1) prime[1] = false;
			for(int i = 2; i < num; i ++) if(prime[i]) for(int j = 2; i * j < num; j ++) prime[i * j] = false;
			return prime;
		}

		long[][] countElements(long[] a, boolean sort) {
			int len = a.length;
			long array[] = new long[len];
			for(int i = 0; i < len; i ++) array[i] = a[i];
			if(sort) Arrays.sort(array);
			List<Long> elem = new ArrayList<Long>();
			List<Long> cnt = new ArrayList<Long>();
			long tmp = 1;
			for(int i = 1; i <= len; i ++) {
				if(i == len || array[i] != array[i - 1]) {
					elem.add(array[i - 1]);
					cnt.add(tmp);
					tmp = 1;
				}else tmp ++;
			}
			long counts[][] = new long[elem.size()][2];
			for(int i = 0; i < elem.size(); i ++) {
				counts[i][0] = elem.get(i);
				counts[i][1] = cnt.get(i);
			}
			return counts;
		}
		long[][] countElements(String str, boolean sort) {
			int len = str.length();
			char array[] = str.toCharArray();
			if(sort) Arrays.sort(array);
			List<Long> elem = new ArrayList<Long>();
			List<Long> cnt = new ArrayList<Long>();
			long tmp = 1;
			for(int i = 1; i <= len; i ++) {
				if(i == len || array[i] != array[i - 1]) {
					elem.add((long)array[i - 1]);
					cnt.add(tmp);
					tmp = 1;
				}else tmp ++;
			}
			long counts[][] = new long[elem.size()][2];
			for(int i = 0; i < elem.size(); i ++) {
				counts[i][0] = elem.get(i);
				counts[i][1] = cnt.get(i);
			}
			return counts;
		}

		int[] baseConvert(long x, int n, int len) {
			int digit[] = new int[len];
			int i = 0;
			long tmp = x;
			while(tmp > 0 && i < len) { digit[i ++] = (int)(tmp % n); tmp /= n; }
			return digit;
		}
		int[] baseConvert(long x, int n) {
			long tmp = x;
			int len = 0;
			while(tmp > 0) { tmp /= n; len ++; }
			return baseConvert(x, n, len);
		}
		int[] baseConvert(int x, int n, int len) {
			int digit[] = new int[len];
			int i = 0;
			int tmp = x;
			while(tmp > 0 && i < len) { digit[i ++] = (int)(tmp % n); tmp /= n; }
			return digit;
		}
		int[] baseConvert(int x, int n) {
			int tmp = x;
			int len = 0;
			while(tmp > 0) { tmp /= n; len ++; }
			return baseConvert(x, n, len);
		}
		long[] baseConvert(long x, long n, int len) {
			long digit[] = new long[len];
			int i = 0;
			long tmp = x;
			while(tmp > 0 && i < len) { digit[i ++] = tmp % n; tmp /= n; }
			return digit;
		}
		long[] baseConvert(long x, long n) {
			long tmp = x;
			int len = 0;
			while(tmp > 0) { tmp /= n; len ++; }
			return baseConvert(x, n, len);
		}

		int numDigits(long a) { return Long.toString(a).length(); }
		long bitFlag(int a) { return 1L << (long)a; }
		boolean isFlagged(long x, int a) { return (x & bitFlag(a)) != 0; }

		long countString(String str, String a) { return (str.length() - str.replace(a, "").length()) / a.length(); }
		long countStringAll(String str, String a) { return str.length() - str.replaceAll(a, "").length(); }


		String reverse(String str) { return (new StringBuilder(str)).reverse().toString(); }
		void reverse(String[] array) { for(int i = 0; i < array.length / 2; i ++) swap(array, i, array.length - i - 1); }
		void reverse(int[] array) { for(int i = 0; i < array.length / 2; i ++) swap(array, i, array.length - i - 1); }
		void reverse(long[] array) { for(int i = 0; i < array.length / 2; i ++) swap(array, i, array.length - i - 1); }
		void reverse(double[] array) { for(int i = 0; i < array.length / 2; i ++) swap(array, i, array.length - i - 1); }
		void reverse(char[] array) { for(int i = 0; i < array.length / 2; i ++) swap(array, i, array.length - i - 1); }
		void reverse(boolean[] array) { for(int i = 0; i < array.length / 2; i ++) swap(array, i, array.length - i - 1); }
		<T> void reverse(T[] array) { for(int i = 0; i < array.length / 2; i ++) swap(array, i, array.length - i - 1); }
		void fill(int[] array, int x) { Arrays.fill(array, x); }
		void fill(long[] array, long x) { Arrays.fill(array, x); }
		void fill(double[] array, double x) { Arrays.fill(array, x); }
		void fill(char[] array, char x) { Arrays.fill(array, x); }
		void fill(boolean[] array, boolean x) { Arrays.fill(array, x); }
		void fill(int[][] array, int x) { for(int[] a : array) fill(a, x); }
		void fill(long[][] array, long x) { for(long[] a : array) fill(a, x); }
		void fill(double[][] array, double x) { for(double[] a : array) fill(a, x); }
		void fill(char[][] array, char x) { for(char[] a : array) fill(a, x); }
		void fill(boolean[][] array, boolean x) { for(boolean[] a : array) fill(a, x); }
		void fill(int[][][] array, int x) { for(int[][] a : array) fill(a, x); }
		void fill(long[][][] array, long x) { for(long[][] a : array) fill(a, x); }
		void fill(double[][][] array, double x) { for(double[][] a : array) fill(a, x); }
		void fill(char[][][] array, char x) { for(char[][] a : array) fill(a, x); }
		void fill(boolean[][][] array, boolean x) { for(boolean[][] a : array) fill(a, x); }

		int[] resize(int[] array, int m, int x) {
			int resized[] = new int[m];
			for(int i = max(0, - x); i < array.length && i + x < m; i ++) resized[i + x] = array[i];
			return resized;
		}
		long[] resize(long[] array, int m, int x) {
			long resized[] = new long[m];
			for(int i = max(0, - x); i < array.length && i + x < m; i ++) resized[i + x] = array[i];
			return resized;
		}
		double[] resize(double[] array, int m, int x) {
			double resized[] = new double[m];
			for(int i = max(0, - x); i < array.length && i + x < m; i ++) resized[i + x] = array[i];
			return resized;
		}
		char[] resize(char[] array, int m, int x) {
			char resized[] = new char[m];
			for(int i = max(0, - x); i < array.length && i + x < m; i ++) resized[i + x] = array[i];
			return resized;
		}
		boolean[] resize(boolean[] array, int m, int x) {
			boolean resized[] = new boolean[m];
			for(int i = max(0, - x); i < array.length && i + x < m; i ++) resized[i + x] = array[i];
			return resized;
		}
		Object[] resize(Object[] array, int m, int x) {
			Object resized[] = new Object[m];
			for(int i = max(0, - x); i < array.length && i + x < m; i ++) resized[i + x] = array[i];
			return resized;
		}

		void shuffleArray(int[] array){
			for(int i = 0; i < array.length; i ++){
				int tmp = array[i];
				int randomPos = random(i, array.length);
				array[i] = array[randomPos];
				array[randomPos] = tmp;
			}
		}
		void shuffleArray(long[] array){
			for(int i = 0; i < array.length; i ++){
				long tmp = array[i];
				int randomPos = random(i, array.length);
				array[i] = array[randomPos];
				array[randomPos] = tmp;
			}
		}
		void shuffleArray(double[] array){
			for(int i = 0; i < array.length; i ++){
				double tmp = array[i];
				int randomPos = random(i, array.length);
				array[i] = array[randomPos];
				array[randomPos] = tmp;
			}
		}

		void swap(String[] array, int i, int j) {
			String tmp = array[i];
			array[i] = array[j];
			array[j] = tmp;
		}
		void swap(int[] array, int i, int j) {
			int tmp = array[i];
			array[i] = array[j];
			array[j] = tmp;
		}
		void swap(long[] array, int i, int j) {
			long tmp = array[i];
			array[i] = array[j];
			array[j] = tmp;
		}
		void swap(double[] array, int i, int j) {
			double tmp = array[i];
			array[i] = array[j];
			array[j] = tmp;
		}
		void swap(char[] array, int i, int j) {
			char tmp = array[i];
			array[i] = array[j];
			array[j] = tmp;
		}
		void swap(boolean[] array, int i, int j) {
			boolean tmp = array[i];
			array[i] = array[j];
			array[j] = tmp;
		}
		<T> void swap(T[] array, int i, int j) {
			T tmp = array[i];
			array[i] = array[j];
			array[j] = tmp;
		}

		int[] compress(int[] a) {
			int num = a.length;
			Set<Integer> ss = new TreeSet<>();
			for(int i = 0; i < num; i ++) ss.add(a[i]);
			int compressed[] = new int[ss.size()];
			int j = 0;
			for(Integer x : ss) compressed[j ++] = x;
			for(int i = 0; i < num; i ++) a[i] = lowerBound(compressed, a[i]);
			return compressed;
		}
		long[] compress(long[] a) {
			int num = a.length;
			Set<Long> ss = new TreeSet<>();
			for(int i = 0; i < num; i ++) ss.add(a[i]);
			long compressed[] = new long[ss.size()];
			int j = 0;
			for(Long x : ss) compressed[j ++] = x;
			for(int i = 0; i < num; i ++) a[i] = lowerBound(compressed, a[i]);
			return compressed;
		}
		double[] compress(double[] a) {
			int num = a.length;
			Set<Double> ss = new TreeSet<>();
			for(int i = 0; i < num; i ++) ss.add(a[i]);
			double compressed[] = new double[ss.size()];
			int j = 0;
			for(Double x : ss) compressed[j ++] = x;
			for(int i = 0; i < num; i ++) a[i] = lowerBound(compressed, a[i]);
			return compressed;
		}


		int lowerBound(int[] array, int key) {
			return BS(array, key, true, true, true);
		}
		int lowerBound(int[] array, int key, int ng, int ok) {
			return BS(array, key, true, true, true, ng, ok);
		}
		int upperBound(int[] array, int key) {
			return BS(array, key, true, true, false);
		}
		int upperBound(int[] array, int key, int ng, int ok) {
			return BS(array, key, true, true, false, ng, ok);
		}
		int cntBS(int[] array, int key, boolean ascending, boolean greater, boolean equals) {
			return BS(array, key, ascending, greater, equals, true);
		}
		int cntBS(int[] array, int key, boolean ascending, boolean greater, boolean equals, int ng, int ok) {
			return BS(array, key, ascending, greater, equals, true, ng, ok);
		}
		int BS(int[] array, int key, boolean ascending, boolean greater, boolean equals) {
			return BS(array, key, ascending, greater, equals, false);
		}
		int BS(int[] array, int key, boolean ascending, boolean greater, boolean equals, int ng, int ok) {
			return BS(array, key, ascending, greater, equals, false, ng, ok);
		}
		int BS(int[] array, int key, boolean ascending, boolean greater, boolean equals, boolean count) {
			int ng = ascending ^ greater ? array.length : -1;
			int ok = ascending ^ greater ? -1 : array.length;
			return BS(array, key, ascending, greater, equals, count, ng, ok);
		}
		int BS(int[] array, int key, boolean ascending, boolean greater, boolean equals, boolean count, int ng, int ok) {
			int index = binarySearch(array, key, greater, equals, ng, ok);
			return count ? (int)abs(ok - index) : index;
		}
		int binarySearch(int[] array, int key, boolean greater, boolean equals, int ng, int ok) {
			while (abs(ok - ng) > 1) {
				int mid = (ok + ng) / 2;
				if(isOKforBinarySearch(array, mid, key, greater, equals)) {
					ok = mid;
				}else {
					ng = mid;
				}
			}
			return ok;
		}
		boolean isOKforBinarySearch(int[] array, int index, int key, boolean greater, boolean equals) {
			return (array[index] > key && greater)
				|| (array[index] < key && !greater)
				|| (array[index] == key && equals);
		}
		int lowerBound(long[] array, long key) {
			return BS(array, key, true, true, true);
		}
		int lowerBound(long[] array, long key, int ng, int ok) {
			return BS(array, key, true, true, true, ng, ok);
		}
		int upperBound(long[] array, long key) {
			return BS(array, key, true, true, false);
		}
		int upperBound(long[] array, long key, int ng, int ok) {
			return BS(array, key, true, true, false, ng, ok);
		}
		int cntBS(long[] array, long key, boolean ascending, boolean greater, boolean equals) {
			return BS(array, key, ascending, greater, equals, true);
		}
		int cntBS(long[] array, long key, boolean ascending, boolean greater, boolean equals, int ng, int ok) {
			return BS(array, key, ascending, greater, equals, true, ng, ok);
		}
		int BS(long[] array, long key, boolean ascending, boolean greater, boolean equals) {
			return BS(array, key, ascending, greater, equals, false);
		}
		int BS(long[] array, long key, boolean ascending, boolean greater, boolean equals, int ng, int ok) {
			return BS(array, key, ascending, greater, equals, false, ng, ok);
		}
		int BS(long[] array, long key, boolean ascending, boolean greater, boolean equals, boolean count) {
			int ng = ascending ^ greater ? array.length : -1;
			int ok = ascending ^ greater ? -1 : array.length;
			return BS(array, key, ascending, greater, equals, count, ng, ok);
		}
		int BS(long[] array, long key, boolean ascending, boolean greater, boolean equals, boolean count, int ng, int ok) {
			int index = binarySearch(array, key, greater, equals, ng, ok);
			return count ? (int)abs(ok - index) : index;
		}
		int binarySearch(long[] array, long key, boolean greater, boolean equals, int ng, int ok) {
			while (abs(ok - ng) > 1) {
				int mid = (ok + ng) / 2;
				if(isOKforBinarySearch(array, mid, key, greater, equals)) {
					ok = mid;
				}else {
					ng = mid;
				}
			}
			return ok;
		}
		boolean isOKforBinarySearch(long[] array, int index, long key, boolean greater, boolean equals) {
			return (array[index] > key && greater)
				|| (array[index] < key && !greater)
				|| (array[index] == key && equals);
		}
		int lowerBound(double[] array, double key) {
			return BS(array, key, true, true, true);
		}
		int lowerBound(double[] array, double key, int ng, int ok) {
			return BS(array, key, true, true, true, ng, ok);
		}
		int upperBound(double[] array, double key) {
			return BS(array, key, true, true, false);
		}
		int upperBound(double[] array, double key, int ng, int ok) {
			return BS(array, key, true, true, false, ng, ok);
		}
		int cntBS(double[] array, double key, boolean ascending, boolean greater, boolean equals) {
			return BS(array, key, ascending, greater, equals, true);
		}
		int cntBS(double[] array, double key, boolean ascending, boolean greater, boolean equals, int ng, int ok) {
			return BS(array, key, ascending, greater, equals, true, ng, ok);
		}
		int BS(double[] array, double key, boolean ascending, boolean greater, boolean equals) {
			return BS(array, key, ascending, greater, equals, false);
		}
		int BS(double[] array, double key, boolean ascending, boolean greater, boolean equals, int ng, int ok) {
			return BS(array, key, ascending, greater, equals, false, ng, ok);
		}
		int BS(double[] array, double key, boolean ascending, boolean greater, boolean equals, boolean count) {
			int ng = ascending ^ greater ? array.length : -1;
			int ok = ascending ^ greater ? -1 : array.length;
			return BS(array, key, ascending, greater, equals, count, ng, ok);
		}
		int BS(double[] array, double key, boolean ascending, boolean greater, boolean equals, boolean count, int ng, int ok) {
			int index = binarySearch(array, key, greater, equals, ng, ok);
			return count ? (int)abs(ok - index) : index;
		}
		int binarySearch(double[] array, double key, boolean greater, boolean equals, int ng, int ok) {
			while (abs(ok - ng) > 1) {
				int mid = (ok + ng) / 2;
				if(isOKforBinarySearch(array, mid, key, greater, equals)) {
					ok = mid;
				}else {
					ng = mid;
				}
			}
			return ok;
		}
		boolean isOKforBinarySearch(double[] array, int index, double key, boolean greater, boolean equals) {
			return (array[index] > key && greater)
				|| (array[index] < key && !greater)
				|| (array[index] == key && equals);
		}
		<T> int lowerBound(T[] array, T key, Comparator<? super T> c) {
			return BS(array, key, true, true, true, c);
		}
		<T> int lowerBound(T[] array, T key, int ng, int ok, Comparator<? super T> c) {
			return BS(array, key, true, true, true, ng, ok, c);
		}
		<T> int upperBound(T[] array, T key, Comparator<? super T> c) {
			return BS(array, key, true, true, false, c);
		}
		<T> int upperBound(T[] array, T key, int ng, int ok, Comparator<? super T> c) {
			return BS(array, key, true, true, false, ng, ok, c);
		}
		<T> int cntBS(T[] array, T key, boolean ascending, boolean greater, boolean equals, Comparator<? super T> c) {
			return BS(array, key, ascending, greater, equals, true, c);
		}
		<T> int cntBS(T[] array, T key, boolean ascending, boolean greater, boolean equals, int ng, int ok, Comparator<? super T> c) {
			return BS(array, key, ascending, greater, equals, true, ng, ok, c);
		}
		<T> int BS(T[] array, T key, boolean ascending, boolean greater, boolean equals, Comparator<? super T> c) {
			return BS(array, key, ascending, greater, equals, false, c);
		}
		<T> int BS(T[] array, T key, boolean ascending, boolean greater, boolean equals, int ng, int ok, Comparator<? super T> c) {
			return BS(array, key, ascending, greater, equals, false, ng, ok, c);
		}
		<T> int BS(T[] array, T key, boolean ascending, boolean greater, boolean equals, boolean count, Comparator<? super T> c) {
			int ng = ascending ^ greater ? array.length : -1;
			int ok = ascending ^ greater ? -1 : array.length;
			return BS(array, key, ascending, greater, equals, count, ng, ok, c);
		}
		<T> int BS(T[] array, T key, boolean ascending, boolean greater, boolean equals, boolean count, int ng, int ok, Comparator<? super T> c) {
			int index = binarySearch(array, key, greater, equals, ng, ok, c);
			return count ? (int)abs(ok - index) : index;
		}
		<T> int binarySearch(T[] array, T key, boolean greater, boolean equals, int ng, int ok, Comparator<? super T> c) {
			while (abs(ok - ng) > 1) {
				int mid = (ok + ng) / 2;
				if(isOKforBinarySearch(array, mid, key, greater, equals, c)) {
					ok = mid;
				}else {
					ng = mid;
				}
			}
			return ok;
		}
		<T> boolean isOKforBinarySearch(T[] array, int index, T key, boolean greater, boolean equals, Comparator<? super T> c) {
			int compare = c.compare(array[index], key);
			return (compare > 0 && greater)
				|| (compare < 0 && !greater)
				|| (compare == 0 && equals);
		}


		// mods
		final long MOD = (long)1e9 + 7; // 998244353;
		long mod(long i) { i %= MOD; return i + (i < 0 ? MOD : 0); }
		void mod(long[] a) { for(int i = 0; i < a.length; i ++) a[i] = mod(a[i]); }
		void mod(long[][] a) { for(int i = 0; i < a.length; i ++) mod(a[i]); }
		void mod(long[][][] a) { for(int i = 0; i < a.length; i ++) mod(a[i]); }

		long pow_m(long x, long y) {
			long ans = 1;
			for(; y > 0; y /= 2) {
				if(y % 2 != 0) ans = mod(ans * x);
				x = mod(x * x);
			}
			return ans;
		}
		long[] pows_m(long x, int max) {
			long pow[] = new long[max + 1];
			pow[0] = 1;
			for(int i = 0; i < max; i ++) pow[i + 1] = mod(pow[i] * x);
			return pow;
		}
		long fact_m(int n) {
			long ans = 1;
			for(int i = 1; i <= n; i ++) ans = mod(ans * i);
			return ans;
		}

		final int MAX_INV_SIZE = 100_100;
		Map<Long, Long> invMap = new HashMap<>();
		long inv(long x) {
			x = mod(x);
			if(invMap.containsKey(x)) return invMap.get(x);
			if(invMap.size() >= MAX_INV_SIZE) return calInv(x);
			invMap.put(x, calInv(x));
			return invMap.get(x);
		}
		long calInv(long x) { return pow_m(x, MOD - 2); }

		final int MAX_FACT = 5_000_100;
		long fact[];
		long invFact[];
		boolean isFactPrepared = false;
		Map<Integer, long[]> factMap;
		void prepareFact() {
			fact = new long[MAX_FACT];
			fill(fact, 0);
			invFact = new long[MAX_FACT];
			fill(invFact, 0);
			fact[0] = 1;
			int maxIndex = min(MAX_FACT, (int)MOD);
			for(int i = 1; i < maxIndex; i ++) fact[i] = mod(fact[i - 1] * i);
			invFact[maxIndex - 1] = inv(fact[maxIndex - 1]);
			for(int i = maxIndex - 1; i > 0; i --) invFact[i - 1] = mod(invFact[i] * i);

			factMap = new HashMap<>();
			isFactPrepared = true;
		}

		long P(int n, int r) {
			if(!isFactPrepared) { prepareFact(); }
			if(n < 0 || r < 0 || n < r) { return 0; }
			if(n >= MAX_FACT) {
				if(!factMap.containsKey(n)) {
					long largeFact[] = new long[MAX_FACT];
					factMap.put(n, largeFact);
					fill(largeFact, -INF);
					largeFact[0] = 1;
				}
				long largeFact[] = factMap.get(n);
				int i = r;
				while(isINF(largeFact[i])) i --;
				for(; i < r; i ++) largeFact[i + 1] = mod(largeFact[i] * (n - i));
				return largeFact[r];
			}
			return mod(fact[n] * invFact[n - r]);
		}
		long C(int n, int r) {
			if(!isFactPrepared) prepareFact();
			if(n < 0 || r < 0 || n < r) return 0;
			return mod(P(n, r) * invFact[r]);
		}
		long H(int n, int r) { return C((n - 1) + r, r); }


		// grid
		class Grids {
			int h;
			int w;
			Grid[][] gs;
			Grid[] gi;
			Grids(int h, int w) {
				this.h = h;
				this.w = w;
				gs = new Grid[h][w];
				gi = new Grid[h * w];
				for(int i = 0; i < h; i ++) {
					for(int j = 0; j < w; j ++) {
						gs[i][j] = new Grid(i, j, h, w);
						gi[gs[i][j].i] = gs[i][j];
					}
				}
			}

			void init(boolean[][] b) {
				for(int i = 0; i < h; i ++) for(int j = 0; j < w; j ++) gs[i][j].b = b[i][j];
			}
			void init(long[][] val) {
				for(int i = 0; i < h; i ++) for(int j = 0; j < w; j ++) gs[i][j].val = val[i][j];
			}

			Grid get(int x, int y) { return isValid(x, y, h, w) ? gs[x][y] : null; }
			Grid get(int i) { return get(i / w, i % w); }

			int dx[] = {0, -1, 1, 0, 0, -1, 1, -1, 1};
			int dy[] = {0, 0, 0, -1, 1, -1, -1, 1, 1};
			Grid next(int x, int y, int i) { return next(gs[x][y], i); }
			Grid next(Grid g, int i) {
				return isValid(g.x + dx[i], g.y + dy[i], g.h, g.w)
					? gs[g.x + dx[i]][g.y + dy[i]]
					: null;
			}
		}
		class Grid implements Comparable<Grid> {
			int x;
			int y;
			int h;
			int w;
			int i;
			boolean b;
			long val;

			Grid() {  }
			Grid(int x, int y, int h, int w) { init(x, y, h, w, false, 0); }
			Grid(int x, int y, int h, int w, boolean b) { init(x, y, h, w, b, 0); }
			Grid(int x, int y, int h, int w, long val) { init(x, y, h, w, false, val); }
			Grid(int x, int y, int h, int w, boolean b, long val) { init(x, y, h, w, b, val); }

			void init(int x, int y, int h, int w, boolean b, long val) {
				this.x = x;
				this.y = y;
				this.h = h;
				this.w = w;
				this.b = b;
				this.val = val;
				this.i = x * w + y;
			}

			@Override
			public String toString() { return "("+x+", "+y+")"+" "+booleanToString(b)+" "+val; }

			@Override
			public int hashCode() { return Objects.hash(x, y, h, w, b, val); }

			@Override
			public boolean equals(Object obj) {
				if(this == obj) return true;
				if(obj == null) return false;
				if(this.getClass() != obj.getClass()) return false;
				Grid that = (Grid) obj;
				if(this.x != that.x) return false;
				if(this.y != that.y) return false;
				if(this.h != that.h) return false;
				if(this.w != that.w) return false;
				if(this.b != that.b) return false;
				if(this.val != that.val) return false;
				return true;
			}

			@Override
			public int compareTo(Grid that) {
				int c = Long.compare(this.val, that.val);
				if(c == 0) c = Integer.compare(this.x, that.x);
				if(c == 0) c = Integer.compare(this.y, that.y);
				return c;
			}
		}

		boolean isValid(int x, int y, int h, int w) { return x >= 0 && x < h && y >= 0 && y < w; }
		boolean isValid(Grid g) { return isValid(g.x, g.y, g.h, g.w); }

		// graph
		class Graph {
			int numNode;
			int numEdge;
			boolean directed;
			Edge edges[];
			Node nodes[];
			Node reversedNodes[];

			Graph(int numNode, int numEdge, boolean directed) {
				this.numNode = numNode;
				this.numEdge = numEdge;
				this.directed = directed;
				nodes = new Node[numNode];
				reversedNodes = new Node[numNode];
				for(int i = 0; i < numNode; i ++) {
					nodes[i] = new Node(i);
					reversedNodes[i] = new Node(i);
				}
			}

			void init(Edge[] edges) {
				this.edges = edges;
				for(Edge edge : edges) {
					nodes[edge.source].add(edge.target, edge.cost);
					if(directed) reversedNodes[edge.target].add(edge.source, edge.cost);
					else nodes[edge.target].add(edge.source, edge.cost);
				}
			}

			void clearNodes() {
				for(Node n : nodes) n.clear();
				for(Node n : reversedNodes) n.clear();
			}
		}

		class Node extends ArrayList<Edge> {
			int id;

			Node(int id) { this.id = id; }
			void add(int target, long cost) { add(new Edge(id, target, cost)); }
		}

		class Edge implements Comparable<Edge> {
			int source;
			int target;
			long cost;
			Edge(int source, int target, long cost) {
				this.source = source;
				this.target = target;
				this.cost = cost;
			}


			@Override
			public String toString() { return source+" - "+cost+" -> "+target; }

			@Override
			public int hashCode() { return Objects.hash(source, target, cost); }

			@Override
			public boolean equals(Object obj) {
				if(this == obj) return true;
				if(obj == null) return false;
				if(this.getClass() != obj.getClass()) return false;
				Edge that = (Edge) obj;
				if(this.source != that.source) return false;
				if(this.target != that.target) return false;
				if(this.cost != that.cost) return false;
				return true;
			}

			@Override
			public int compareTo(Edge that) {
				int c = Long.compare(this.cost, that.cost);
				if(c == 0) c = Integer.compare(this.source, that.source);
				if(c == 0) c = Integer.compare(this.target, that.target);
				return c;
			}
		}


public void solve() {
	int num = ni();
	PairLL a[] = new PairLL[num];
	for(int i = 0; i < num; i ++) {
		a[i] = new PairLL(nl(), nl());
	}
	Map<Long, Long> hm = new HashMap<>();
	MultiSet<PairLL> ms = new MultiSet<>();
	for(int i = 0; i < num; i ++) {
		ms.add(a[i]);
	}
	errprtln(a);
	long ans = 1;
	long pow_2[] = pows_m(2, num + 10);
	long cnt0 = ms.count(new PairLL(0, 0));
	ms.remove(new PairLL(0, 0));
	for(PairLL crt : a) {
		PairLL normal = new PairLL(crt.b, - crt.a);
		errprtln(ms.count(crt), ms.count(normal));
		ans *= pow_2[(int)ms.count(crt)] + pow_2[(int)ms.count(normal)] - 1;
		ans = mod(ans);
		ms.remove(crt);
		ms.remove(normal);
	}
	ans --;
	ans = mod(ans);
	prtln(ans);
}

public class MultiSet<K> extends HashMap<K, Long> {
	public Long add(K key) { return update(key, 1); }
	public Long erase(K key) { return update(key, -1); }
	public Long update(K key, long value) {
		Long prv = get(key);
		long crt = convert(prv) + value;
		if(crt < 0) throw new NoSuchElementException();
		else if(crt == 0) remove(key);
		else put(key, crt);
		return prv;
	}
	public long count(K key) { return convert(get(key)); }

	private long convert(Long value) { return value == null ? 0 : value; }
}

class PairLL implements Comparable<PairLL> {
	long a = 0;
	long b = 0;
	PairLL(long a, long b) {
		long gcd = gcd(a, b);
		if(gcd != 0) {
			a /= gcd;
			b /= gcd;
		}
		if(a < 0) {
			a *= -1;
			b *= -1;
		}
		this.a = a;
		this.b = b;
	}

	@Override
	public String toString() { return "("+a+", "+b+")"; }

	@Override
	public int hashCode() { return Objects.hash(a, b); }

	@Override
	public boolean equals(Object obj) {
		if(this == obj) return true;
		if(obj == null) return false;
		if(this.getClass() != obj.getClass()) return false;
		PairLL that = (PairLL) obj;
		if(this.a != that.a) return false;
		if(this.b != that.b) return false;
		return true;
	}

	@Override
	public int compareTo(PairLL that) {
		int c = Long.compare(this.a, that.a);
		if(c == 0) c = Long.compare(this.b, that.b);
		return c;
	}
}

	}
}