Problem: Little Susie loves strings. Today she calculates distances between them. As Susie is a small girl after all, her strings contain only digits zero and one. She uses the definition of Hamming distance:

We will define the distance between two strings s and t of the same length consisting of digits zero and one as the number of positions i, such that si isn't equal to ti. 

As besides everything else Susie loves symmetry, she wants to find for two strings s and t of length n such string p of length n, that the distance from p to s was equal to the distance from p to t.

It's time for Susie to go to bed, help her find such string p or state that it is impossible.

Input

The first line contains string s of length n. 

The second line contains string t of length n.

The length of string n is within range from 1 to 105. It is guaranteed that both strings contain only digits zero and one.

Output

Print a string of length n, consisting of digits zero and one, that meets the problem statement. If no such string exist, print on a single line "impossible" (without the quotes).

If there are multiple possible answers, print any of them.

Examples

Input

0001
1011


Output

0011


Input

000
111


Output

impossible

Note

In the first sample different answers are possible, namely — 0010, 0011, 0110, 0111, 1000, 1001, 1100, 1101.

Solution (in JAVA):

Solution:
import java.io.*;
import java.util.*;
import java.math.*;

public class Main {
	public static void main(String[] args) {
		InputStream inputStream = System.in;
		OutputStream outputStream = System.out;
		InputReader in = new InputReader(inputStream);
		OutputWriter out = new OutputWriter(outputStream);
		Task solver = new Task();
		solver.solve(1, in, out);
		out.close();
	}
}

class Task {

//	public void solve(int testNumber, InputReader in, OutputWriter out) {
//		int n = in.readInt(), m = in.readInt(), idx = 0;
//		boolean flag = m == 200000;
//		List<Pair<IntPair, Integer>> events = new ArrayList<>(), events2 = new ArrayList<>();
//		int[] L = new int[n], R = new int[n], A = new int[m], B = new int[m], C = new int[m], max = new int[m], best = new int[m];
//		IOUtils.readIntArrays(in, L, R);
//		IOUtils.readIntArrays(in, A, B, C);
//		TreapSet<IntPair> set = new TreapSet<>();
//		Set<Integer> used = new TreapSet<>();
//		for (int i = 0; i < n; i++) {
//			events.add(Pair.makePair(new IntPair(L[i], 0), i));
//			events.add(Pair.makePair(new IntPair(R[i], 2), i));
//			events2.add(Pair.makePair(new IntPair(L[i], 1), i));
//			events2.add(Pair.makePair(new IntPair(R[i], 3), i));
//			used.add(L[i]);
//			used.add(R[i]);
//		}
//		for (int i = 0; i < m; i++) {
//			events.add(Pair.makePair(new IntPair(A[i], 1), i));
//			events.add(Pair.makePair(new IntPair(B[i], 3), i));
//			events2.add(Pair.makePair(new IntPair(A[i], 0), i));
//			events2.add(Pair.makePair(new IntPair(B[i], 2), i));
//			used.add(A[i]);
//			used.add(B[i]);
//		}
//		Collections.sort(events);
//		Collections.sort(events2);
//		Collections.reverse(events2);
//		Map<Integer, Integer> map = new EHashMap<>();
//		for (int i : used)
//			map.put(i, idx++);
//		IntervalTree tree = new LongIntervalTree(used.size()) {
//			protected long neutralDelta() {
//				return 0;
//			}
//
//			protected long neutralValue() {
//				return 0;
//			}
//
//			protected long accumulate(long value, long delta, int length) {
//				return value>delta?value:delta;
//			}
//
//			protected long joinValue(long left, long right) {
//				return left > right ? left : right;
//			}
//
//			protected long joinDelta(long was, long delta) {
//				return delta;
//			}
//		};
//		if (!flag) for (Pair<IntPair, Integer> pair : events) {
//			int x = pair.second;
//			if (pair.first.second == 0)
//				set.add(new IntPair(R[x], x));
//			else if (pair.first.second == 1) {
//				if (!set.isEmpty()) {
//					IntPair pairMax = set.last();
//					int length = Math.min(pairMax.first, B[x]) - A[x];
//					if (length > max[x]) {
//						max[x] = length;
//						best[x] = pairMax.second;
//					}
//				}
//			} else if (pair.first.second == 3) {
//				long aux = tree.query(map.get(A[x]), map.get(B[x]));
//				int length = (int) (aux / n), y = (int) (aux % n);
////				if (x == 4620)
////					out.printLine(aux, length, y, A[x], map.get(A[x]), B[x],
////							map.get(B[x]));
//				if (length > max[x]) {
//					max[x] = length;
//					best[x] = y;
//				}
//			} else {
//				tree.update(map.get(L[x]), map.get(L[x]), 1L * (R[x] - L[x])
//						* n + x);
////				if (tree.query(0, used.size()-1)!=1L*(R[x]-L[x])*n+x) out.printLine(x, L[x], R[x], tree.query(0, used.size()-1));
//			}
//		}
//		set.clear();
//		if (!flag) for (Pair<IntPair, Integer> pair : events2) {
//			int x = pair.second;
//			if (pair.first.second == 3)
//				set.add(new IntPair(L[x], x));
//			else if (pair.first.second == 2) {
//				if (!set.isEmpty()) {
//					IntPair pairMin = set.first();
//					int length = B[x] - Math.max(A[x], pairMin.first);
//					if (length > max[x]) {
//						max[x] = length;
//						best[x] = pairMin.second;
//					}
//				}
//			}
//		}
//		long ret = 0;
//		int aux = -1;
//		for (int i = 0; i < m; i++) {
//			long x = 1L * max[i] * C[i];
//			if (x > ret) {
//				ret = x;
//				aux = i;
//			}
//		}
//		out.printLine(ret);
//		if (ret > 0)
//			out.printLine(best[aux] + 1, aux + 1);
////		if (m == 10000)
////			out.printLine(L[78], R[78], A[4620], B[4620], C[4620]);
//	}
	
	public void solve(int testNumber, InputReader in, OutputWriter out) {
		char[] S=in.readString().toCharArray(), T=in.readString().toCharArray(), ret=new char[S.length];
		int dist=0;
		for (int i=0; i<S.length; i++) {
			if (S[i]==T[i]) ret[i]=S[i];
			else {
				dist++;
				ret[i]=dist%2==1?S[i]:T[i];
			}
		}
		if (dist%2==0) out.printLine(ret);
		else out.printLine("impossible");
	}
}

class InputReader {
	private boolean finished = false;

	private InputStream stream;
	private byte[] buf = new byte[1024];
	private int curChar;
	private int numChars;
	private SpaceCharFilter filter;

	public InputReader(InputStream stream) {
		this.stream = stream;
	}

	public int read() {
		if (numChars == -1)
			throw new InputMismatchException();
		if (curChar >= numChars) {
			curChar = 0;
			try {
				numChars = stream.read(buf);
			} catch (IOException e) {
				throw new InputMismatchException();
			}
			if (numChars <= 0)
				return -1;
		}
		return buf[curChar++];
	}

	public int peek() {
		if (numChars == -1)
			return -1;
		if (curChar >= numChars) {
			curChar = 0;
			try {
				numChars = stream.read(buf);
			} catch (IOException e) {
				return -1;
			}
			if (numChars <= 0)
				return -1;
		}
		return buf[curChar];
	}

	public int readInt() {
		int c = read();
		while (isSpaceChar(c))
			c = read();
		int sgn = 1;
		if (c == '-') {
			sgn = -1;
			c = read();
		}
		int res = 0;
		do {
			if (c < '0' || c > '9')
				throw new InputMismatchException();
			res *= 10;
			res += c - '0';
			c = read();
		} while (!isSpaceChar(c));
		return res * sgn;
	}

	public long readLong() {
		int c = read();
		while (isSpaceChar(c))
			c = read();
		int sgn = 1;
		if (c == '-') {
			sgn = -1;
			c = read();
		}
		long res = 0;
		do {
			if (c < '0' || c > '9')
				throw new InputMismatchException();
			res *= 10;
			res += c - '0';
			c = read();
		} while (!isSpaceChar(c));
		return res * sgn;
	}

	public String readString() {
		int c = read();
		while (isSpaceChar(c))
			c = read();
		StringBuilder res = new StringBuilder();
		do {
			if (Character.isValidCodePoint(c))
				res.appendCodePoint(c);
			c = read();
		} while (!isSpaceChar(c));
		return res.toString();
	}

	public boolean isSpaceChar(int c) {
		if (filter != null)
			return filter.isSpaceChar(c);
		return isWhitespace(c);
	}

	public static boolean isWhitespace(int c) {
		return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
	}

	private String readLine0() {
		StringBuilder buf = new StringBuilder();
		int c = read();
		while (c != '\n' && c != -1) {
			if (c != '\r')
				buf.appendCodePoint(c);
			c = read();
		}
		return buf.toString();
	}

	public String readLine() {
		String s = readLine0();
		while (s.trim().length() == 0)
			s = readLine0();
		return s;
	}

	public String readLine(boolean ignoreEmptyLines) {
		if (ignoreEmptyLines)
			return readLine();
		else
			return readLine0();
	}

	public BigInteger readBigInteger() {
		try {
			return new BigInteger(readString());
		} catch (NumberFormatException e) {
			throw new InputMismatchException();
		}
	}

	public char readCharacter() {
		int c = read();
		while (isSpaceChar(c))
			c = read();
		return (char) c;
	}

	public double readDouble() {
		int c = read();
		while (isSpaceChar(c))
			c = read();
		int sgn = 1;
		if (c == '-') {
			sgn = -1;
			c = read();
		}
		double res = 0;
		while (!isSpaceChar(c) && c != '.') {
			if (c == 'e' || c == 'E')
				return res * Math.pow(10, readInt());
			if (c < '0' || c > '9')
				throw new InputMismatchException();
			res *= 10;
			res += c - '0';
			c = read();
		}
		if (c == '.') {
			c = read();
			double m = 1;
			while (!isSpaceChar(c)) {
				if (c == 'e' || c == 'E')
					return res * Math.pow(10, readInt());
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				m /= 10;
				res += (c - '0') * m;
				c = read();
			}
		}
		return res * sgn;
	}

	public boolean isExhausted() {
		int value;
		while (isSpaceChar(value = peek()) && value != -1)
			read();
		return value == -1;
	}

	public String next() {
		return readString();
	}

	public SpaceCharFilter getFilter() {
		return filter;
	}

	public void setFilter(SpaceCharFilter filter) {
		this.filter = filter;
	}

	public interface SpaceCharFilter {
		public boolean isSpaceChar(int ch);
	}
}

class OutputWriter {
	private final PrintWriter writer;

	public OutputWriter(OutputStream outputStream) {
		writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(
				outputStream)));
	}

	public OutputWriter(Writer writer) {
		this.writer = new PrintWriter(writer);
	}

	public void print(char[] array) {
		writer.print(array);
	}

	public void print(Object... objects) {
		for (int i = 0; i < objects.length; i++) {
			if (i != 0)
				writer.print(' ');
			writer.print(objects[i]);
		}
	}

	public void print(int[] array) {
		for (int i = 0; i < array.length; i++) {
			if (i != 0)
				writer.print(' ');
			writer.print(array[i]);
		}
	}

	public void print(long[] array) {
		for (int i = 0; i < array.length; i++) {
			if (i != 0)
				writer.print(' ');
			writer.print(array[i]);
		}
	}

	public void print(Collection<Integer> collection) {
		boolean first = true;
		for (int i : collection) {
			if (first)
				first = false;
			else
				writer.print(' ');
			writer.print(i);
		}
	}

	public void printLine(int[] array) {
		print(array);
		writer.println();
	}

	public void printLine(long[] array) {
		print(array);
		writer.println();
	}

	public void printLine(Collection<Integer> collection) {
		print(collection);
		writer.println();
	}

	public void printLine() {
		writer.println();
	}

	public void printLine(Object... objects) {
		print(objects);
		writer.println();
	}

	public void print(char i) {
		writer.print(i);
	}

	public void printLine(char i) {
		writer.println(i);
	}

	public void printLine(char[] array) {
		writer.println(array);
	}

	public void printFormat(String format, Object... objects) {
		writer.printf(format, objects);
	}

	public void close() {
		writer.close();
	}

	public void flush() {
		writer.flush();
	}

	public void print(long i) {
		writer.print(i);
	}

	public void printLine(long i) {
		writer.println(i);
	}

	public void print(int i) {
		writer.print(i);
	}

	public void printLine(int i) {
		writer.println(i);
	}
}

class Polygon {
	public final Point[] vertices;
	private Segment[] sides;

	public Polygon(Point... vertices) {
		this.vertices = vertices.clone();
	}

	public double square() {
		double sum = 0;
		for (int i = 1; i < vertices.length; i++)
			sum += (vertices[i].x - vertices[i - 1].x)
					* (vertices[i].y + vertices[i - 1].y);
		sum += (vertices[0].x - vertices[vertices.length - 1].x)
				* (vertices[0].y + vertices[vertices.length - 1].y);
		return Math.abs(sum) / 2;
	}

	public Point center() {
		double sx = 0;
		double sy = 0;
		for (Point point : vertices) {
			sx += point.x;
			sy += point.y;
		}
		return new Point(sx / vertices.length, sy / vertices.length);
	}

	public static boolean over(Point a, Point b, Point c) {
		return a.x * (b.y - c.y) + b.x * (c.y - a.y) + c.x * (a.y - b.y) < -GeometryUtils.epsilon;
	}

	private static boolean under(Point a, Point b, Point c) {
		return a.x * (b.y - c.y) + b.x * (c.y - a.y) + c.x * (a.y - b.y) > GeometryUtils.epsilon;
	}

	public static Polygon convexHull(Point[] points) {
		if (points.length == 1)
			return new Polygon(points);
		Arrays.sort(points, new Comparator<Point>() {
			public int compare(Point o1, Point o2) {
				int value = Double.compare(o1.x, o2.x);
				if (value != 0)
					return value;
				return Double.compare(o1.y, o2.y);
			}
		});
		Point left = points[0];
		Point right = points[points.length - 1];
		List<Point> up = new ArrayList<Point>();
		List<Point> down = new ArrayList<Point>();
		for (Point point : points) {
			if (point == left || point == right || !under(left, point, right)) {
				while (up.size() >= 2
						&& under(up.get(up.size() - 2), up.get(up.size() - 1),
								point))
					up.remove(up.size() - 1);
				up.add(point);
			}
			if (point == left || point == right || !over(left, point, right)) {
				while (down.size() >= 2
						&& over(down.get(down.size() - 2),
								down.get(down.size() - 1), point))
					down.remove(down.size() - 1);
				down.add(point);
			}
		}
		Point[] result = new Point[up.size() + down.size() - 2];
		int index = 0;
		for (Point point : up)
			result[index++] = point;
		for (int i = down.size() - 2; i > 0; i--)
			result[index++] = down.get(i);
		return new Polygon(result);
	}

	public boolean contains(Point point) {
		return contains(point, false);
	}

	public boolean contains(Point point, boolean strict) {
		for (Segment segment : sides()) {
			if (segment.contains(point, true))
				return !strict;
		}
		double totalAngle = GeometryUtils.canonicalAngle(Math.atan2(
				vertices[0].y - point.y, vertices[0].x - point.x)
				- Math.atan2(vertices[vertices.length - 1].y - point.y,
						vertices[vertices.length - 1].x - point.x));
		for (int i = 1; i < vertices.length; i++) {
			totalAngle += GeometryUtils.canonicalAngle(Math.atan2(vertices[i].y
					- point.y, vertices[i].x - point.x)
					- Math.atan2(vertices[i - 1].y - point.y, vertices[i - 1].x
							- point.x));
		}
		return Math.abs(totalAngle) > Math.PI;
	}

	public Segment[] sides() {
		if (sides == null) {
			sides = new Segment[vertices.length];
			for (int i = 0; i < vertices.length - 1; i++)
				sides[i] = new Segment(vertices[i], vertices[i + 1]);
			sides[sides.length - 1] = new Segment(
					vertices[vertices.length - 1], vertices[0]);
		}
		return sides;
	}

	public static double triangleSquare(Point a, Point b, Point c) {
		return Math.abs((a.x - b.x) * (a.y + b.y) + (b.x - c.x) * (b.y + c.y)
				+ (c.x - a.x) * (c.y + a.y)) / 2;
	}

	public double perimeter() {
		double result = vertices[0].distance(vertices[vertices.length - 1]);
		for (int i = 1; i < vertices.length; i++)
			result += vertices[i].distance(vertices[i - 1]);
		return result;
	}
}

class Point {
	public static final Point ORIGIN = new Point(0, 0);
	public final double x;
	public final double y;

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

	public Point(double x, double y) {
		this.x = x;
		this.y = y;
	}

	public Line line(Point other) {
		if (equals(other))
			return null;
		double a = other.y - y;
		double b = x - other.x;
		double c = -a * x - b * y;
		return new Line(a, b, c);
	}

	@Override
	public boolean equals(Object o) {
		if (this == o)
			return true;
		if (o == null || getClass() != o.getClass())
			return false;

		Point point = (Point) o;

		return Math.abs(x - point.x) <= GeometryUtils.epsilon
				&& Math.abs(y - point.y) <= GeometryUtils.epsilon;
	}

	@Override
	public int hashCode() {
		int result;
		long temp;
		temp = x != +0.0d ? Double.doubleToLongBits(x) : 0L;
		result = (int) (temp ^ (temp >>> 32));
		temp = y != +0.0d ? Double.doubleToLongBits(y) : 0L;
		result = 31 * result + (int) (temp ^ (temp >>> 32));
		return result;
	}

	public double distance(Point other) {
		return GeometryUtils.fastHypot(x - other.x, y - other.y);
	}

	public double distance(Line line) {
		return Math.abs(line.a * x + line.b * y + line.c);
	}

	public double value() {
		return GeometryUtils.fastHypot(x, y);
	}

	public double angle() {
		return Math.atan2(y, x);
	}

	public static Point readPoint(InputReader in) {
		double x = in.readDouble();
		double y = in.readDouble();
		return new Point(x, y);
	}

	public Point rotate(double angle) {
		double nx = x * Math.cos(angle) - y * Math.sin(angle);
		double ny = y * Math.cos(angle) + x * Math.sin(angle);
		return new Point(nx, ny);
	}
}

class Segment {
	public final Point a;
	public final Point b;
	private double distance = Double.NaN;
	private Line line = null;

	public Segment(Point a, Point b) {
		this.a = a;
		this.b = b;
	}

	public double length() {
		if (Double.isNaN(distance))
			distance = a.distance(b);
		return distance;
	}

	public double distance(Point point) {
		double length = length();
		double left = point.distance(a);
		if (length < GeometryUtils.epsilon)
			return left;
		double right = point.distance(b);
		if (left * left > right * right + length * length)
			return right;
		if (right * right > left * left + length * length)
			return left;
		return point.distance(line());
	}

	public Point intersect(Segment other, boolean includeEnds) {
		Line line = line();
		Line otherLine = other.a.line(other.b);
		if (line.parallel(otherLine))
			return null;
		Point intersection = line.intersect(otherLine);
		if (contains(intersection, includeEnds)
				&& other.contains(intersection, includeEnds))
			return intersection;
		else
			return null;
	}

	public boolean contains(Point point, boolean includeEnds) {
		if (a.equals(point) || b.equals(point))
			return includeEnds;
		if (a.equals(b))
			return false;
		Line line = line();
		if (!line.contains(point))
			return false;
		Line perpendicular = line.perpendicular(a);
		double aValue = perpendicular.value(a);
		double bValue = perpendicular.value(b);
		double pointValue = perpendicular.value(point);
		return aValue < pointValue && pointValue < bValue
				|| bValue < pointValue && pointValue < aValue;
	}

	public Line line() {
		if (line == null)
			line = a.line(b);
		return line;
	}

	public Point middle() {
		return new Point((a.x + b.x) / 2, (a.y + b.y) / 2);
	}

	public Point[] intersect(Circle circle) {
		Point[] result = line().intersect(circle);
		if (result.length == 0)
			return result;
		if (result.length == 1) {
			if (contains(result[0], true))
				return result;
			return new Point[0];
		}
		if (contains(result[0], true)) {
			if (contains(result[1], true))
				return result;
			return new Point[] { result[0] };
		}
		if (contains(result[1], true))
			return new Point[] { result[1] };
		return new Point[0];
	}

	public Point intersect(Line line) {
		Line selfLine = line();
		Point intersect = selfLine.intersect(line);
		if (intersect == null)
			return null;
		if (contains(intersect, true))
			return intersect;
		return null;
	}

	public double distance(Segment other) {
		Line line = line();
		Line otherLine = other.line();
		Point p = line == null || otherLine == null ? null : line
				.intersect(otherLine);
		if (p != null && contains(p, true) && other.contains(p, true))
			return 0;
		return Math.min(Math.min(other.distance(a), other.distance(b)),
				Math.min(distance(other.a), distance(other.b)));
	}
}

class GeometryUtils {
	public static double epsilon = 1e-8;

	public static double fastHypot(double... x) {
		if (x.length == 0)
			return 0;
		else if (x.length == 1)
			return Math.abs(x[0]);
		else {
			double sumSquares = 0;
			for (double value : x)
				sumSquares += value * value;
			return Math.sqrt(sumSquares);
		}
	}

	public static double fastHypot(double x, double y) {
		return Math.sqrt(x * x + y * y);
	}

	public static double fastHypot(double[] x, double[] y) {
		if (x.length == 0)
			return 0;
		else if (x.length == 1)
			return Math.abs(x[0] - y[0]);
		else {
			double sumSquares = 0;
			for (int i = 0; i < x.length; i++) {
				double diff = x[i] - y[i];
				sumSquares += diff * diff;
			}
			return Math.sqrt(sumSquares);
		}
	}

	public static double fastHypot(int[] x, int[] y) {
		if (x.length == 0)
			return 0;
		else if (x.length == 1)
			return Math.abs(x[0] - y[0]);
		else {
			double sumSquares = 0;
			for (int i = 0; i < x.length; i++) {
				double diff = x[i] - y[i];
				sumSquares += diff * diff;
			}
			return Math.sqrt(sumSquares);
		}
	}

	public static double missileTrajectoryLength(double v, double angle,
			double g) {
		return (v * v * Math.sin(2 * angle)) / g;
	}

	public static double sphereVolume(double radius) {
		return 4 * Math.PI * radius * radius * radius / 3;
	}

	public static double triangleSquare(double first, double second,
			double third) {
		double p = (first + second + third) / 2;
		return Math.sqrt(p * (p - first) * (p - second) * (p - third));
	}

	public static double canonicalAngle(double angle) {
		while (angle > Math.PI)
			angle -= 2 * Math.PI;
		while (angle < -Math.PI)
			angle += 2 * Math.PI;
		return angle;
	}

	public static double positiveAngle(double angle) {
		while (angle > 2 * Math.PI - GeometryUtils.epsilon)
			angle -= 2 * Math.PI;
		while (angle < -GeometryUtils.epsilon)
			angle += 2 * Math.PI;
		return angle;
	}
}

class Line {
	public final double a;
	public final double b;
	public final double c;

	public Line(Point p, double angle) {
		a = Math.sin(angle);
		b = -Math.cos(angle);
		c = -p.x * a - p.y * b;
	}

	public Line(double a, double b, double c) {
		double h = GeometryUtils.fastHypot(a, b);
		this.a = a / h;
		this.b = b / h;
		this.c = c / h;
	}

	public Point intersect(Line other) {
		if (parallel(other))
			return null;
		double determinant = b * other.a - a * other.b;
		double x = (c * other.b - b * other.c) / determinant;
		double y = (a * other.c - c * other.a) / determinant;
		return new Point(x, y);
	}

	public boolean parallel(Line other) {
		return Math.abs(a * other.b - b * other.a) < GeometryUtils.epsilon;
	}

	public boolean contains(Point point) {
		return Math.abs(value(point)) < GeometryUtils.epsilon;
	}

	public Line perpendicular(Point point) {
		return new Line(-b, a, b * point.x - a * point.y);
	}

	public double value(Point point) {
		return a * point.x + b * point.y + c;
	}

	public Point[] intersect(Circle circle) {
		double distance = distance(circle.center);
		if (distance > circle.radius + GeometryUtils.epsilon)
			return new Point[0];
		Point intersection = intersect(perpendicular(circle.center));
		if (Math.abs(distance - circle.radius) < GeometryUtils.epsilon)
			return new Point[] { intersection };
		double shift = Math.sqrt(circle.radius * circle.radius - distance
				* distance);
		return new Point[] {
				new Point(intersection.x + shift * b, intersection.y - shift
						* a),
				new Point(intersection.x - shift * b, intersection.y + shift
						* a) };
	}

	public double distance(Point center) {
		return Math.abs(value(center));
	}

	@Override
	public boolean equals(Object o) {
		if (this == o)
			return true;
		if (o == null || getClass() != o.getClass())
			return false;

		Line line = (Line) o;

		if (!parallel(line))
			return false;
		if (Math.abs(a * line.c - c * line.a) > GeometryUtils.epsilon
				|| Math.abs(b * line.c - c * line.b) > GeometryUtils.epsilon)
			return false;

		return true;
	}
}

class Circle {
	public final Point center;
	public final double radius;

	public Circle(Point center, double radius) {
		this.center = center;
		this.radius = radius;
	}

	public boolean contains(Point point) {
		return center.distance(point) < radius + GeometryUtils.epsilon;
	}

	public boolean strictContains(Point point) {
		return center.distance(point) < radius - GeometryUtils.epsilon;
	}

	public Point[] findTouchingPoints(Point point) {
		double distance = center.distance(point);
		if (distance < radius - GeometryUtils.epsilon)
			return new Point[0];
		if (distance < radius + GeometryUtils.epsilon)
			return new Point[] { point };
		Circle power = new Circle(point, Math.sqrt((distance - radius)
				* (distance + radius)));
		return intersect(power);
	}

	public Point[] intersect(Circle other) {
		double distance = center.distance(other.center);
		if (distance > radius + other.radius + GeometryUtils.epsilon
				|| Math.abs(radius - other.radius) > distance
						+ GeometryUtils.epsilon)
			return new Point[0];
		double p = (radius + other.radius + distance) / 2;
		double height = 2
				* Math.sqrt(p * (p - radius) * (p - other.radius)
						* (p - distance)) / distance;
		double l1 = Math.sqrt(radius * radius - height * height);
		double l2 = Math.sqrt(other.radius * other.radius - height * height);
		if (radius * radius + distance * distance < other.radius * other.radius)
			l1 = -l1;
		if (radius * radius > distance * distance + other.radius * other.radius)
			l2 = -l2;
		Point middle = new Point((center.x * l2 + other.center.x * l1)
				/ (l1 + l2), (center.y * l2 + other.center.y * l1) / (l1 + l2));
		Line line = center.line(other.center).perpendicular(middle);
		return line.intersect(this);
	}
}

class Pair<U, V> implements Comparable<Pair<U, V>> {
	public final U first;
	public final V second;

	public static <U, V> Pair<U, V> makePair(U first, V second) {
		return new Pair<U, V>(first, second);
	}

	private Pair(U first, V second) {
		this.first = first;
		this.second = second;
	}

	public boolean equals(Object o) {
		if (this == o)
			return true;
		if (o == null || getClass() != o.getClass())
			return false;

		Pair pair = (Pair) o;

		return !(first != null ? !first.equals(pair.first) : pair.first != null)
				&& !(second != null ? !second.equals(pair.second)
						: pair.second != null);

	}

	public int hashCode() {
		int result = first != null ? first.hashCode() : 0;
		result = 31 * result + (second != null ? second.hashCode() : 0);
		return result;
	}

	public String toString() {
		return "(" + first + "," + second + ")";
	}

	public int compareTo(Pair<U, V> o) {
		int value = ((Comparable<U>) first).compareTo(o.first);
		if (value != 0)
			return value;
		return ((Comparable<V>) second).compareTo(o.second);
	}
}

class IntPair implements Comparable<IntPair> {
	public final int first, second;

	public IntPair(int first, int second) {
		this.first = first;
		this.second = second;
	}

	@Override
	public String toString() {
		return "(" + first + "," + second + ")";
	}

	@Override
	public boolean equals(Object o) {
		if (this == o)
			return true;
		if (o == null || getClass() != o.getClass())
			return false;

		IntPair intPair = (IntPair) o;

		return first == intPair.first && second == intPair.second;

	}

	@Override
	public int hashCode() {
		int result = first;
		result = 31 * result + second;
		return result;
	}

	public int compareTo(IntPair o) {
		if (first < o.first)
			return -1;
		if (first > o.first)
			return 1;
		if (second < o.second)
			return -1;
		if (second > o.second)
			return 1;
		return 0;
	}
}

class IOUtils {

	public static void readIntArrays(InputReader in, int[]... arrays) {
		for (int i = 0; i < arrays[0].length; i++) {
			for (int j = 0; j < arrays.length; j++)
				arrays[j][i] = in.readInt();
		}
	}

}

class TreapSet<K> implements NavigableSet<K> {
	protected static final Random rnd = new Random(239);

	protected final Node nullNode;
	protected final Comparator<? super K> comparator;
	protected Node root;
	private final K from;
	private final K to;
	private final boolean fromInclusive;
	private final boolean toInclusive;

	public TreapSet() {
		this((Comparator<? super K>) null);
	}

	public TreapSet(Comparator<? super K> comparator) {
		this(null, null, false, false, comparator, null, null);
	}

	protected TreapSet(K from, K to, boolean fromInclusive,
			boolean toInclusive, Comparator<? super K> comparator, Node root,
			Node nullNode) {
		this.comparator = comparator;
		this.from = from;
		this.to = to;
		this.fromInclusive = fromInclusive;
		this.toInclusive = toInclusive;
		if (nullNode == null)
			nullNode = new NullNode();
		if (root == null)
			root = nullNode;
		this.root = root;
		this.nullNode = nullNode;
	}

	public boolean addAll(Iterable<? extends K> collection) {
		boolean result = false;
		for (K element : collection)
			result |= add(element);
		return result;
	}

	public K lower(K k) {
		Node target = root.lower(k);
		if (target == nullNode)
			return null;
		if (belongs(target.key))
			return target.key;
		return null;
	}

	private boolean belongs(K key) {
		int valueFrom = compare(from, key);
		int valueTo = compare(key, to);
		return (valueFrom < 0 || valueFrom == 0 && fromInclusive)
				&& (valueTo < 0 || valueTo == 0 && toInclusive);
	}

	public K floor(K k) {
		Node target = root.floor(k);
		if (target == nullNode)
			return null;
		if (belongs(target.key))
			return target.key;
		return null;
	}

	public K ceiling(K k) {
		Node target = root.ceil(k);
		if (target == nullNode)
			return null;
		if (belongs(target.key))
			return target.key;
		return null;
	}

	public K higher(K k) {
		Node target = root.higher(k);
		if (target == nullNode)
			return null;
		if (belongs(target.key))
			return target.key;
		return null;
	}

	public K pollFirst() {
		K first = first();
		if (first == null)
			throw new NoSuchElementException();
		root.erase(first);
		return first;
	}

	public K pollLast() {
		K last = last();
		if (last == null)
			throw new NoSuchElementException();
		root.erase(last);
		return last;
	}

	public int size() {
		if (from == null && to == null)
			return root.size;
		if (from == null) {
			Node to = toInclusive ? root.floor(this.to) : root.lower(this.to);
			if (to == nullNode)
				return 0;
			return root.indexOf(to) + 1;
		}
		if (to == null) {
			Node from = fromInclusive ? root.ceil(this.from) : root
					.higher(this.from);
			if (from == nullNode)
				return 0;
			return root.size - root.indexOf(from);
		}
		Node from = fromInclusive ? root.ceil(this.from) : root
				.higher(this.from);
		if (from == nullNode || !belongs(from.key))
			return 0;
		Node to = toInclusive ? root.floor(this.to) : root.lower(this.to);
		return root.indexOf(to) - root.indexOf(from) + 1;
	}

	public boolean isEmpty() {
		return size() == 0;
	}

	public boolean contains(Object o) {
		return belongs((K) o) && root.search((K) o) != nullNode;
	}

	public Iterator<K> iterator() {
		return new Iterator<K>() {
			private K current = first();

			public boolean hasNext() {
				return current != null;
			}

			public K next() {
				K result = current;
				current = higher(current);
				return result;
			}

			public void remove() {
				TreapSet.this.remove(current);
			}
		};
	}

	public Object[] toArray() {
		Object[] array = new Object[size()];
		int index = 0;
		for (K key : this)
			array[index++] = key;
		return array;
	}

	public <T> T[] toArray(T[] a) {
		if (a.length < size())
			throw new IllegalArgumentException();
		int index = 0;
		for (K key : this)
			a[index++] = (T) key;
		return a;
	}

	public boolean add(K k) {
		if (k == null)
			throw new NullPointerException();
		if (contains(k))
			return false;
		root = root.insert(createNode(k));
		return true;
	}

	protected Node createNode(K k) {
		return new Node(k, rnd.nextLong());
	}

	public boolean remove(Object o) {
		if (!contains(o))
			return false;
		// noinspection unchecked
		root = root.erase((K) o);
		return true;
	}

	public boolean containsAll(Collection<?> c) {
		for (Object o : c) {
			if (!contains(o))
				return false;
		}
		return true;
	}

	public boolean addAll(Collection<? extends K> c) {
		return addAll((Iterable<? extends K>) c);
	}

	public boolean retainAll(Collection<?> c) {
		List<K> toRemove = new ArrayList<K>();
		for (K key : this) {
			if (!c.contains(key))
				toRemove.add(key);
		}
		return removeAll(toRemove);
	}

	public boolean removeAll(Collection<?> c) {
		boolean result = false;
		for (Object o : c)
			result |= remove(o);
		return result;
	}

	public void clear() {
		retainAll(Collections.<Object> emptySet());
	}

	public NavigableSet<K> descendingSet() {
		throw new UnsupportedOperationException();
	}

	public Iterator<K> descendingIterator() {
		return new Iterator<K>() {
			private K current = last();

			public boolean hasNext() {
				return current != null;
			}

			public K next() {
				K result = current;
				current = lower(current);
				return result;
			}

			public void remove() {
				TreapSet.this.remove(current);
			}
		};
	}

	public NavigableSet<K> subSet(K fromElement, boolean fromInclusive,
			K toElement, boolean toInclusive) {
		return new TreapSet<K>(fromElement, toElement, fromInclusive,
				toInclusive, comparator, root, nullNode);
	}

	public NavigableSet<K> headSet(K toElement, boolean inclusive) {
		return subSet(null, false, toElement, inclusive);
	}

	public NavigableSet<K> tailSet(K fromElement, boolean inclusive) {
		return subSet(fromElement, inclusive, null, false);
	}

	public Comparator<? super K> comparator() {
		return comparator;
	}

	public SortedSet<K> subSet(K fromElement, K toElement) {
		return subSet(fromElement, true, toElement, false);
	}

	public SortedSet<K> headSet(K toElement) {
		return subSet(null, false, toElement, false);
	}

	public SortedSet<K> tailSet(K fromElement) {
		return tailSet(fromElement, true);
	}

	public K first() {
		if (isEmpty())
			return null;
		if (from == null)
			return root.first().key;
		if (fromInclusive)
			return ceiling(from);
		return higher(from);
	}

	public K last() {
		if (isEmpty())
			return null;
		if (to == null)
			return root.last().key;
		if (toInclusive)
			return floor(to);
		return lower(to);
	}

	protected int compare(K first, K second) {
		if (first == null || second == null)
			return -1;
		if (comparator != null)
			return comparator.compare(first, second);
		// noinspection unchecked
		return ((Comparable<? super K>) first).compareTo(second);
	}

	protected class Node {
		protected final K key;
		protected final long priority;
		protected Node left;
		protected Node right;
		protected int size;

		protected Node(K key, long priority) {
			this.key = key;
			this.priority = priority;
			left = nullNode;
			right = nullNode;
			size = 1;
		}

		protected Object[] split(K key) {
			if (compare(key, this.key) < 0) {
				Object[] result = left.split(key);
				left = (Node) result[1];
				result[1] = this;
				updateSize();
				return result;
			}
			Object[] result = right.split(key);
			right = (Node) result[0];
			result[0] = this;
			updateSize();
			return result;
		}

		protected void updateSize() {
			size = left.size + right.size + 1;
		}

		protected Node insert(Node node) {
			if (node.priority > priority) {
				Object[] result = split(node.key);
				node.left = (Node) result[0];
				node.right = (Node) result[1];
				node.updateSize();
				return node;
			}
			if (compare(node.key, this.key) < 0) {
				left = left.insert(node);
				updateSize();
				return this;
			}
			right = right.insert(node);
			updateSize();
			return this;
		}

		protected Node merge(Node left, Node right) {
			if (left == nullNode)
				return right;
			if (right == nullNode)
				return left;
			if (left.priority > right.priority) {
				left.right = left.right.merge(left.right, right);
				left.updateSize();
				return left;
			}
			right.left = right.left.merge(left, right.left);
			right.updateSize();
			return right;
		}

		protected Node erase(K key) {
			int value = compare(key, this.key);
			if (value == 0)
				return merge(left, right);
			if (value < 0) {
				left = left.erase(key);
				updateSize();
				return this;
			}
			right = right.erase(key);
			updateSize();
			return this;
		}

		protected Node lower(K key) {
			if (compare(key, this.key) <= 0)
				return left.lower(key);
			Node result = right.lower(key);
			if (result == nullNode)
				return this;
			return result;
		}

		protected Node floor(K key) {
			if (compare(key, this.key) < 0)
				return left.floor(key);
			Node result = right.floor(key);
			if (result == nullNode)
				return this;
			return result;
		}

		protected Node higher(K key) {
			if (compare(key, this.key) >= 0)
				return right.higher(key);
			Node result = left.higher(key);
			if (result == nullNode)
				return this;
			return result;
		}

		protected Node ceil(K key) {
			if (compare(key, this.key) > 0)
				return right.ceil(key);
			Node result = left.ceil(key);
			if (result == nullNode)
				return this;
			return result;
		}

		protected Node first() {
			if (left == nullNode)
				return this;
			return left.first();
		}

		protected Node last() {
			if (right == nullNode)
				return this;
			return right.last();
		}

		protected Node search(K key) {
			int value = compare(key, this.key);
			if (value == 0)
				return this;
			if (value < 0)
				return left.search(key);
			return right.search(key);
		}

		public int indexOf(Node node) {
			if (this == node)
				return left.size;
			if (compare(node.key, this.key) > 0)
				return left.size + 1 + right.indexOf(node);
			return left.indexOf(node);
		}

	}

	private class NullNode extends Node {
		private Object[] splitResult = new Object[2];

		private NullNode() {
			super(null, Long.MIN_VALUE);
			left = this;
			right = this;
			size = 0;
		}

		protected Object[] split(K key) {
			splitResult[0] = splitResult[1] = this;
			return splitResult;
		}

		protected Node insert(Node node) {
			return node;
		}

		protected Node erase(K key) {
			return this;
		}

		protected Node lower(K key) {
			return this;
		}

		protected Node floor(K key) {
			return this;
		}

		protected Node higher(K key) {
			return this;
		}

		protected Node ceil(K key) {
			return this;
		}

		protected Node first() {
			throw new NoSuchElementException();
		}

		protected Node last() {
			throw new NoSuchElementException();
		}

		protected void updateSize() {
		}

		protected Node search(K key) {
			return this;
		}

	}
}

class EHashMap<E, V> extends AbstractMap<E, V> {
	private static final int[] shifts = new int[10];

	private int size;
	private HashEntry<E, V>[] data;
	private int capacity;
	private Set<Entry<E, V>> entrySet;

	static {
		Random random = new Random(System.currentTimeMillis());
		for (int i = 0; i < 10; i++)
			shifts[i] = 1 + 3 * i + random.nextInt(3);
	}

	public EHashMap() {
		this(4);
	}

	private void setCapacity(int size) {
		capacity = Integer.highestOneBit(4 * size);
		// noinspection unchecked
		data = new HashEntry[capacity];
	}

	public EHashMap(int maxSize) {
		setCapacity(maxSize);
		entrySet = new AbstractSet<Entry<E, V>>() {
			public Iterator<Entry<E, V>> iterator() {
				return new Iterator<Entry<E, V>>() {
					private HashEntry<E, V> last = null;
					private HashEntry<E, V> current = null;
					private HashEntry<E, V> base = null;
					private int lastIndex = -1;
					private int index = -1;

					public boolean hasNext() {
						if (current == null) {
							for (index++; index < capacity; index++) {
								if (data[index] != null) {
									base = current = data[index];
									break;
								}
							}
						}
						return current != null;
					}

					public Entry<E, V> next() {
						if (!hasNext())
							throw new NoSuchElementException();
						last = current;
						lastIndex = index;
						current = current.next;
						if (base.next != last)
							base = base.next;
						return last;
					}

					public void remove() {
						if (last == null)
							throw new IllegalStateException();
						size--;
						if (base == last)
							data[lastIndex] = last.next;
						else
							base.next = last.next;
					}
				};
			}

			public int size() {
				return size;
			}
		};
	}

	public Set<Entry<E, V>> entrySet() {
		return entrySet;
	}

	public void clear() {
		Arrays.fill(data, null);
		size = 0;
	}

	private int index(Object o) {
		return getHash(o.hashCode()) & (capacity - 1);
	}

	private int getHash(int h) {
		int result = h;
		for (int i : shifts)
			result ^= h >>> i;
		return result;
	}

	public V remove(Object o) {
		if (o == null)
			return null;
		int index = index(o);
		HashEntry<E, V> current = data[index];
		HashEntry<E, V> last = null;
		while (current != null) {
			if (current.key.equals(o)) {
				if (last == null)
					data[index] = current.next;
				else
					last.next = current.next;
				size--;
				return current.value;
			}
			last = current;
			current = current.next;
		}
		return null;
	}

	public V put(E e, V value) {
		if (e == null)
			return null;
		int index = index(e);
		HashEntry<E, V> current = data[index];
		if (current != null) {
			while (true) {
				if (current.key.equals(e)) {
					V oldValue = current.value;
					current.value = value;
					return oldValue;
				}
				if (current.next == null)
					break;
				current = current.next;
			}
		}
		if (current == null)
			data[index] = new HashEntry<E, V>(e, value);
		else
			current.next = new HashEntry<E, V>(e, value);
		size++;
		if (2 * size > capacity) {
			HashEntry<E, V>[] oldData = data;
			setCapacity(size);
			for (HashEntry<E, V> entry : oldData) {
				while (entry != null) {
					HashEntry<E, V> next = entry.next;
					index = index(entry.key);
					entry.next = data[index];
					data[index] = entry;
					entry = next;
				}
			}
		}
		return null;
	}

	public V get(Object o) {
		if (o == null)
			return null;
		int index = index(o);
		HashEntry<E, V> current = data[index];
		while (current != null) {
			if (current.key.equals(o))
				return current.value;
			current = current.next;
		}
		return null;
	}

	public boolean containsKey(Object o) {
		if (o == null)
			return false;
		int index = index(o);
		HashEntry<E, V> current = data[index];
		while (current != null) {
			if (current.key.equals(o))
				return true;
			current = current.next;
		}
		return false;
	}

	public int size() {
		return size;
	}

	private static class HashEntry<E, V> implements Entry<E, V> {
		private final E key;
		private V value;
		private HashEntry<E, V> next;

		private HashEntry(E key, V value) {
			this.key = key;
			this.value = value;
		}

		public E getKey() {
			return key;
		}

		public V getValue() {
			return value;
		}

		public V setValue(V value) {
			V oldValue = this.value;
			this.value = value;
			return oldValue;
		}
	}
}

abstract class IntervalTree {
	protected int size;

	public IntervalTree(int size, boolean shouldInit) {
		this.size = size;
		int nodeCount = Math.max(1, Integer.highestOneBit(size) << 2);
		initData(size, nodeCount);
		if (shouldInit)
			init();
	}

	protected abstract void initData(int size, int nodeCount);

	protected abstract void initAfter(int root, int left, int right, int middle);

	protected abstract void initBefore(int root, int left, int right, int middle);

	protected abstract void initLeaf(int root, int index);

	protected abstract void updatePostProcess(int root, int left, int right,
			int from, int to, long delta, int middle);

	protected abstract void updatePreProcess(int root, int left, int right,
			int from, int to, long delta, int middle);

	protected abstract void updateFull(int root, int left, int right, int from,
			int to, long delta);

	protected abstract long queryPostProcess(int root, int left, int right,
			int from, int to, int middle, long leftResult, long rightResult);

	protected abstract void queryPreProcess(int root, int left, int right,
			int from, int to, int middle);

	protected abstract long queryFull(int root, int left, int right, int from,
			int to);

	protected abstract long emptySegmentResult();

	public void init() {
		if (size == 0)
			return;
		init(0, 0, size - 1);
	}

	private void init(int root, int left, int right) {
		if (left == right) {
			initLeaf(root, left);
		} else {
			int middle = (left + right) >> 1;
			initBefore(root, left, right, middle);
			init(2 * root + 1, left, middle);
			init(2 * root + 2, middle + 1, right);
			initAfter(root, left, right, middle);
		}
	}

	public void update(int from, int to, long delta) {
		update(0, 0, size - 1, from, to, delta);
	}

	protected void update(int root, int left, int right, int from, int to,
			long delta) {
		if (left > to || right < from)
			return;
		if (left >= from && right <= to) {
			updateFull(root, left, right, from, to, delta);
			return;
		}
		int middle = (left + right) >> 1;
		updatePreProcess(root, left, right, from, to, delta, middle);
		update(2 * root + 1, left, middle, from, to, delta);
		update(2 * root + 2, middle + 1, right, from, to, delta);
		updatePostProcess(root, left, right, from, to, delta, middle);
	}

	public long query(int from, int to) {
		return query(0, 0, size - 1, from, to);
	}

	protected long query(int root, int left, int right, int from, int to) {
		if (left > to || right < from)
			return emptySegmentResult();
		if (left >= from && right <= to)
			return queryFull(root, left, right, from, to);
		int middle = (left + right) >> 1;
		queryPreProcess(root, left, right, from, to, middle);
		long leftResult = query(2 * root + 1, left, middle, from, to);
		long rightResult = query(2 * root + 2, middle + 1, right, from, to);
		return queryPostProcess(root, left, right, from, to, middle,
				leftResult, rightResult);
	}
}

abstract class LongIntervalTree extends IntervalTree {
	protected long[] value;
	protected long[] delta;

	protected LongIntervalTree(int size) {
		this(size, true);
	}

	public LongIntervalTree(int size, boolean shouldInit) {
		super(size, shouldInit);
	}

	protected void initData(int size, int nodeCount) {
		value = new long[nodeCount];
		delta = new long[nodeCount];
	}

	protected abstract long joinValue(long left, long right);

	protected abstract long joinDelta(long was, long delta);

	protected abstract long accumulate(long value, long delta, int length);

	protected abstract long neutralValue();

	protected abstract long neutralDelta();

	protected long initValue(int index) {
		return neutralValue();
	}

	protected void initAfter(int root, int left, int right, int middle) {
		value[root] = joinValue(value[2 * root + 1], value[2 * root + 2]);
		delta[root] = neutralDelta();
	}

	protected void initBefore(int root, int left, int right, int middle) {
	}

	protected void initLeaf(int root, int index) {
		value[root] = initValue(index);
		delta[root] = neutralDelta();
	}

	protected void updatePostProcess(int root, int left, int right, int from,
			int to, long delta, int middle) {
		value[root] = joinValue(value[2 * root + 1], value[2 * root + 2]);
	}

	protected void updatePreProcess(int root, int left, int right, int from,
			int to, long delta, int middle) {
		pushDown(root, left, middle, right);
	}

	protected void pushDown(int root, int left, int middle, int right) {
		value[2 * root + 1] = accumulate(value[2 * root + 1], delta[root],
				middle - left + 1);
		value[2 * root + 2] = accumulate(value[2 * root + 2], delta[root],
				right - middle);
		delta[2 * root + 1] = joinDelta(delta[2 * root + 1], delta[root]);
		delta[2 * root + 2] = joinDelta(delta[2 * root + 2], delta[root]);
		delta[root] = neutralDelta();
	}

	protected void updateFull(int root, int left, int right, int from, int to,
			long delta) {
		value[root] = accumulate(value[root], delta, right - left + 1);
		this.delta[root] = joinDelta(this.delta[root], delta);
	}

	protected long queryPostProcess(int root, int left, int right, int from,
			int to, int middle, long leftResult, long rightResult) {
		return joinValue(leftResult, rightResult);
	}

	protected void queryPreProcess(int root, int left, int right, int from,
			int to, int middle) {
		pushDown(root, left, middle, right);
	}

	protected long queryFull(int root, int left, int right, int from, int to) {
		return value[root];
	}

	protected long emptySegmentResult() {
		return neutralValue();
	}
}