Once Vasya and Petya assembled a figure of m cubes, each of them is associated with a number between 0 and m - 1 (inclusive, each number appeared exactly once). Let's consider a coordinate system such that the OX is the ground, and the OY is directed upwards. Each cube is associated with the coordinates of its lower left corner, these coordinates are integers for each cube.

The figure turned out to be stable. This means that for any cube that is not on the ground, there is at least one cube under it such that those two cubes touch by a side or a corner. More formally, this means that for the cube with coordinates (x, y) either y = 0, or there is a cube with coordinates (x - 1, y - 1), (x, y - 1) or (x + 1, y - 1).

Now the boys want to disassemble the figure and put all the cubes in a row. In one step the cube is removed from the figure and being put to the right of the blocks that have already been laid. The guys remove the cubes in such order that the figure remains stable. To make the process more interesting, the guys decided to play the following game. The guys take out the cubes from the figure in turns. It is easy to see that after the figure is disassembled, the integers written on the cubes form a number, written in the m-ary positional numerical system (possibly, with a leading zero). Vasya wants the resulting number to be maximum possible, and Petya, on the contrary, tries to make it as small as possible. Vasya starts the game.

Your task is to determine what number is formed after the figure is disassembled, if the boys play optimally. Determine the remainder of the answer modulo 109 + 9.

Input

The first line contains number m (2 ≤ m ≤ 105).

The following m lines contain the coordinates of the cubes xi, yi ( - 109 ≤ xi ≤ 109, 0 ≤ yi ≤ 109) in ascending order of numbers written on them. It is guaranteed that the original figure is stable.

No two cubes occupy the same place.

Output

In the only line print the answer to the problem.

Examples

Input

3
2 1
1 0
0 1


Output

19


Input

5
0 0
0 1
0 2
0 3
0 4


Output

2930
import static java.lang.Math.*;
import java.util.*;
import java.io.*;

public class B {

	
	public void solve() throws Exception {
		
		int m = nextInt();
		PairII[] coords = new PairII[m];
		TreeMap<PairII, Integer> all = new TreeMap<PairII, Integer>();
		for (int i=0; i<m; ++i) {
			coords[i] = new PairII(nextInt(), nextInt());
			all.put(new PairII(coords[i].x, coords[i].y), i);
		}
		
		TreeMap<PairII, TreeSet<PairII>> under = new TreeMap<PairII, TreeSet<PairII>>();
		for (PairII coord: all.keySet()) under.put(coord, new TreeSet<PairII>()); 
		for (PairII coord: all.keySet()) {
			for (PairII u: getNeighbours(coord, false, all)) {
				under.get(coord).add(u);
			}
		}
		
		TreeSet<Integer> readyMax = new TreeSet<Integer>();
		for (PairII coord: all.keySet()) {
			if (canRemove(coord, under, all)) readyMax.add(all.get(coord));
		}
		
		long res = 0;
		boolean max = true;
		
		while (!readyMax.isEmpty()) {
			
			PairII coord = coords[max ? readyMax.last() : readyMax.first()];
			max = !max;
			res = (res*m + all.get(coord)) % 1000000009;
			
			readyMax.remove(all.get(coord));
			all.remove(coord);
			under.remove(coord);
			
			List<PairII> over = getNeighbours(coord, true, all);
			for (PairII o: over) under.get(o).remove(coord);
			for (PairII o: over) for (PairII u: getNeighbours(o, false, all)) {
				if (readyMax.contains(all.get(u)) && !canRemove(u, under, all)) readyMax.remove(all.get(u));
			}
			
			for (PairII u: getNeighbours(coord, false, all)) {
				if (all.containsKey(u) && canRemove(u, under, all) && !readyMax.contains(all.get(u))) {
					readyMax.add(all.get(u));
				}
			}
		}
		
		println(res);
		
	}
	
	private List<PairII> getNeighbours(PairII coord, boolean over, TreeMap<PairII, Integer> all) {
		List<PairII> res = new LinkedList<PairII>();
		for (int i=-1; i<=1; ++i) {
			PairII c = new PairII(coord.x+i, coord.y + (over ? 1 : -1));
			if (all.containsKey(c)) res.add(c);
		}
		return res;
	}
	
	private boolean canRemove(PairII coord, TreeMap<PairII, TreeSet<PairII>> under, TreeMap<PairII, Integer> all) {
		for (PairII o: getNeighbours(coord, true, all)) {
			if (under.containsKey(o) && under.get(o).size()<=1) {
				return false;
			}
		}
		return true;
	}
	
	static class PairII implements Comparable<PairII> {
		public final int x,y;
		public PairII(int x, int y) {
			this.x = x; this.y = y;
		}
		@Override
		public int hashCode() {
			final int prime = 31;
			int result = 1;
			result = prime * result + x;
			result = prime * result + y;
			return result;
		}
		@Override
		public boolean equals(Object obj) {
			if (this == obj) return true;
			if (obj == null || getClass() != obj.getClass()) return false;
			PairII other = (PairII) obj;
			return x == other.x && y == other.y;
		}
		@Override
		public int compareTo(PairII o) {
			if (x == o.x) {
				if (y == o.y) return 0;
				return y > o.y ? 1 : -1;
			}
			return x > o.x ? 1 : -1;
		}
		@Override
		public String toString() {
			return "(" + Integer.toString(x) + "," + Integer.toString(y) + ")";
		}
	}

	

	////////////////////////////////////////////////////////////////////////////
	
	boolean showDebug = true;
	static boolean useFiles = false;
	static String inFile = "input.txt";
	static String outFile = "output.txt";

	double EPS = 1e-7;
	int INF = Integer.MAX_VALUE;
	long INFL = Long.MAX_VALUE;
	double INFD = Double.MAX_VALUE;

	
	int absPos(int num) {
		return num<0 ? 0:num;
	}
	long absPos(long num) {
		return num<0 ? 0:num;
	}
	double absPos(double num) {
		return num<0 ? 0:num;
	}
	
	int min(int... nums) {
		int r = nums[0];
		for (int i=1; i<nums.length; ++i)
			if (nums[i]<r) r=nums[i];
		return r;
	}
	int max(int... nums) {
		int r = nums[0];
		for (int i=1; i<nums.length; ++i)
			if (nums[i]>r) r=nums[i];
		return r;
	}
	long minL(long... nums) {
		long r = nums[0];
		for (int i=1; i<nums.length; ++i)
			if (nums[i]<r) r=nums[i];
		return r;
	}
	long maxL(long... nums) {
		long r = nums[0];
		for (int i=1; i<nums.length; ++i)
			if (nums[i]>r) r=nums[i];
		return r;
	}
	double minD(double... nums) {
		double r = nums[0];
		for (int i=1; i<nums.length; ++i)
			if (nums[i]<r) r=nums[i];
		return r;
	}
	double maxD(double... nums) {
		double r = nums[0];
		for (int i=1; i<nums.length; ++i)
			if (nums[i]>r) r=nums[i];
		return r;
	}
	
	long sumArr(int[] arr) {
		long res = 0;
		for (int i=0; i<arr.length; ++i)
			res+=arr[i];
		return res;
	}
	long sumArr(long[] arr) {
		long res = 0;
		for (int i=0; i<arr.length; ++i)
			res+=arr[i];
		return res;
	}
	double sumArr(double[] arr) {
		double res = 0;
		for (int i=0; i<arr.length; ++i)
			res+=arr[i];
		return res;
	}

	long partsFitCnt(long partSize, long wholeSize) {
		return (partSize+wholeSize-1)/partSize;
	}

	boolean odd(long num) {
		return (num&1)==1;
	}
	
	boolean hasBit(int num, int pos) {
		return (num&(1<<pos))>0;
	}

	boolean isLetter(char c) {
		return (c>='a' && c<='z') || (c>='A' && c<='Z');
	}
	boolean isLowercase(char c) {
		return (c>='a' && c<='z');
	}
	boolean isUppercase(char c) {
		return (c>='A' && c<='Z');
	}
	boolean isDigit(char c) {
		return (c>='0' && c<='9');
	}
	
	boolean charIn(String chars, String s) {
		if (s==null) return false;
		if (chars==null || chars.equals("")) return true;
		for (int i=0; i<s.length(); ++i)
			for (int j=0; j<chars.length(); ++j)
				if (chars.charAt(j)==s.charAt(i)) return true;
		return false;
	}
	
	String stringn(String s, int n) {
		if (n<1 || s==null) return "";
		StringBuilder sb = new StringBuilder(s.length()*n);
		for (int i=0; i<n; ++i) sb.append(s);
		return sb.toString();
	}
	String str(Object o) {
		if (o==null) return "";
		return o.toString();
	}


	long timer = System.currentTimeMillis();
	void startTimer() {
		timer = System.currentTimeMillis();
	}
	void stopTimer() {
		System.err.println("time: "+(System.currentTimeMillis()-timer)/1000.0);
	}


	static class InputReader {
		private byte[] buf;
		private int bufPos = 0, bufLim = -1;
		private InputStream stream;
		public InputReader(InputStream stream, int size) {
			buf = new byte[size];
			this.stream = stream;
		}
		private void fillBuf() throws IOException {
			bufLim = stream.read(buf);
			bufPos = 0;
		}
		char read() throws IOException {
			if (bufPos>=bufLim) fillBuf(); 
			return (char)buf[bufPos++];
		}
		boolean hasInput() throws IOException {
			if (bufPos>=bufLim) fillBuf();
			return bufPos<bufLim;
		}
	}
	
	static InputReader inputReader;
	static BufferedWriter outputWriter;

	char nextChar() throws IOException {
		return inputReader.read();
	}
	char nextNonWhitespaceChar() throws IOException {
		char c = inputReader.read();
		while (c<=' ') c=inputReader.read();
		return c;
	}
	String nextWord() throws IOException {
		StringBuilder sb = new StringBuilder();
		char c = inputReader.read();
		while (c<=' ') c=inputReader.read();
		while (c>' ') {
			sb.append(c);
			c = inputReader.read();
		}
		return new String(sb);
	}
	String nextLine() throws IOException {
		StringBuilder sb = new StringBuilder();
		char c = inputReader.read();
		while (c<=' ') c=inputReader.read();
		while (c!='\n' && c!='\r') {
			sb.append(c);
			c = inputReader.read();
		}
		return new String(sb);
	}
	int nextInt() throws IOException {
		int r = 0;
		char c = nextNonWhitespaceChar();
		boolean neg = false;
		if (c=='-') neg=true;
		else r=c-48;
		c = nextChar();
		while (c>='0' && c<='9') {
			r*=10;
			r+=c-48;
			c=nextChar();
		}
		return neg ? -r:r;
	}
	long nextLong() throws IOException {
		long r = 0;
		char c = nextNonWhitespaceChar();
		boolean neg = false;
		if (c=='-') neg=true;
		else r = c-48;
		c = nextChar();
		while (c>='0' && c<='9') {
			r*=10L;
			r+=c-48L;
			c=nextChar();
		}
		return neg ? -r:r;
	}
	double nextDouble() throws NumberFormatException, IOException {
		return Double.parseDouble(nextWord());
	}
	int[] nextArr(int size) throws NumberFormatException, IOException {
		int[] arr = new int[size];
		for (int i=0; i<size; ++i)
			arr[i] = nextInt();
		return arr;
	}
	long[] nextArrL(int size) throws NumberFormatException, IOException {
		long[] arr = new long[size];
		for (int i=0; i<size; ++i)
			arr[i] = nextLong();
		return arr;
	}
	double[] nextArrD(int size) throws NumberFormatException, IOException {
		double[] arr = new double[size];
		for (int i=0; i<size; ++i)
			arr[i] = nextDouble();
		return arr;
	}
	String[] nextArrS(int size) throws NumberFormatException, IOException {
		String[] arr = new String[size];
		for (int i=0; i<size; ++i)
			arr[i] = nextWord();
		return arr;
	}
	char[] nextArrCh(int size) throws IOException {
		char[] arr = new char[size];
		for (int i=0; i<size; ++i)
			arr[i] = nextNonWhitespaceChar();
		return arr;
	}
	char[][] nextArrCh(int rows, int columns) throws IOException {
		char[][] arr = new char[rows][columns];
		for (int i=0; i<rows; ++i)
			for (int j=0; j<columns; ++j)
				arr[i][j] = nextNonWhitespaceChar();
		return arr;
	}
	char[][] nextArrChBorders(int rows, int columns, char border) throws IOException {
		char[][] arr = new char[rows+2][columns+2];
		for (int i=1; i<=rows; ++i)
			for (int j=1; j<=columns; ++j)
				arr[i][j] = nextNonWhitespaceChar();
		for (int i=0; i<columns+2; ++i) {
			arr[0][i] = border;
			arr[rows+1][i] = border;
		}
		for (int i=0; i<rows+2; ++i) {
			arr[i][0] = border;
			arr[i][columns+1] = border;
		}
		return arr;
	}

	void printf(String format, Object... args) throws IOException {
		outputWriter.write(String.format(format, args));
	}
	void print(Object o) throws IOException {
		outputWriter.write(o.toString());
	}
	void println(Object o) throws IOException {
		outputWriter.write(o.toString());
		outputWriter.newLine();
	}
	void print(Object... o) throws IOException {
		for (int i=0; i<o.length; ++i) {
			if (i!=0) outputWriter.write(' ');
			outputWriter.write(o[i].toString());
		}
	}
	void println(Object... o) throws IOException {
		print(o);
		outputWriter.newLine();
	}
	void printn(Object o, int n) throws IOException {
		String s = o.toString();
		for (int i=0; i<n; ++i) {
			outputWriter.write(s);
			if (i!=n-1) outputWriter.write(' ');
		}
	}
	void printnln(Object o, int n) throws IOException {
		printn(o, n);
		outputWriter.newLine();
	}
	void printArr(int[] arr) throws IOException {
		for (int i=0; i<arr.length; ++i) {
			if (i!=0) outputWriter.write(' ');
			outputWriter.write(Integer.toString(arr[i]));
		}
	}
	void printArr(long[] arr) throws IOException {
		for (int i=0; i<arr.length; ++i) {
			if (i!=0) outputWriter.write(' ');
			outputWriter.write(Long.toString(arr[i]));
		}
	}
	void printArr(double[] arr) throws IOException {
		for (int i=0; i<arr.length; ++i) {
			if (i!=0) outputWriter.write(' ');
			outputWriter.write(Double.toString(arr[i]));
		}
	}
	void printArr(String[] arr) throws IOException {
		for (int i=0; i<arr.length; ++i) {
			if (i!=0) outputWriter.write(' ');
			outputWriter.write(arr[i]);
		}
	}
	void printlnArr(int[] arr) throws IOException {
		printArr(arr);
		outputWriter.newLine();
	}
	void printlnArr(long[] arr) throws IOException {
		printArr(arr);
		outputWriter.newLine();
	}
	void printlnArr(double[] arr) throws IOException {
		printArr(arr);
		outputWriter.newLine();
	}
	void printlnArr(String[] arr) throws IOException {
		printArr(arr);
		outputWriter.newLine();
	}
	void halt(Object... o) throws IOException {
		if (o.length!=0) println(o);
		outputWriter.flush(); outputWriter.close();
		System.exit(0);
	}
	
	void debug(Object... o) {
		if (showDebug) System.err.println(Arrays.deepToString(o));
	}


	public static void main(String[] args) throws Exception {
		Locale.setDefault(Locale.US);
		if (!useFiles) {
			inputReader = new InputReader(System.in, 1<<16);
			outputWriter = new BufferedWriter(new OutputStreamWriter(System.out), 1<<16);
		} else {
			inputReader = new InputReader(new FileInputStream(new File(inFile)), 1<<16);
			outputWriter = new BufferedWriter(new OutputStreamWriter(new FileOutputStream(new File(outFile))), 1<<16);
		}
		new B().solve();
		outputWriter.flush(); outputWriter.close();
	}
}
