You have a garden consisting entirely of grass and weeds. Your garden is described by an n × m grid, with rows numbered 1 to n from top to bottom, and columns 1 to m from left to right. Each cell is identified by a pair (r, c) which means that the cell is located at row r and column c. Each cell may contain either grass or weeds. For example, a 4 × 5 garden may look as follows (empty cells denote grass):

<image>

You have a land-mower with you to mow all the weeds. Initially, you are standing with your lawnmower at the top-left corner of the garden. That is, at cell (1, 1). At any moment of time you are facing a certain direction — either left or right. And initially, you face right.

In one move you can do either one of these:

1) Move one cell in the direction that you are facing.

  * if you are facing right: move from cell (r, c) to cell (r, c + 1)

<image>

  * if you are facing left: move from cell (r, c) to cell (r, c - 1)

<image>

2) Move one cell down (that is, from cell (r, c) to cell (r + 1, c)), and change your direction to the opposite one.

  * if you were facing right previously, you will face left

<image>

  * if you were facing left previously, you will face right

<image>



You are not allowed to leave the garden. Weeds will be mowed if you and your lawnmower are standing at the cell containing the weeds (your direction doesn't matter). This action isn't counted as a move.

What is the minimum number of moves required to mow all the weeds?

Input

The first line contains two integers n and m (1 ≤ n, m ≤ 150) — the number of rows and columns respectively. Then follow n lines containing m characters each — the content of the grid. "G" means that this cell contains grass. "W" means that this cell contains weeds. 

It is guaranteed that the top-left corner of the grid will contain grass.

Output

Print a single number — the minimum number of moves required to mow all the weeds.

Examples

Input

4 5
GWGGW
GGWGG
GWGGG
WGGGG


Output

11


Input

3 3
GWW
WWW
WWG


Output

7


Input

1 1
G


Output

0

Note

For the first example, this is the picture of the initial state of the grid:

<image>

A possible solution is by mowing the weeds as illustrated below:

<image>
import java.io.*;
import java.util.*;
import java.util.Map.*;
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 D();
        solver.solve(1, in, out);
        out.close();
    }
}

interface Task {
    public void solve(int testNumber, InputReader in, OutputWriter out);
}

class A implements Task {
    
    public void solve(int testNumber, InputReader in, OutputWriter out){
        int n=in.readInt(), x, y, ret=0, cap=0;
        while (n-->0) {
            x=in.readInt();
            y=in.readInt();
            cap+=y-x;
            ret=Math.max(ret,  cap);
        }
        out.printLine(ret);
    }
    
}

class B implements Task {
    
    String[] arr;
    int[] dx={-1, 0, 0, 1}, dy={0, -1, 1, 0};
    
    public void solve(int testNumber, InputReader in, OutputWriter out) {
        int n=in.readInt(), m=in.readInt(), ret=0;
        arr=new String[n];
        for (int i=0; i<n; i++) arr[i]=in.next();
        for (int i=0; i<n; i++) for (int j=0; j<m; j++) if (arr[i].charAt(j)=='W') {
            boolean val=false;
            for (int k=0; k<4; k++) {
                int i2=i+dx[k], j2=j+dy[k];
                if (i2>=0 && i2<n && j2>=0 && j2<m && arr[i2].charAt(j2)=='P') val=true;
            }
            if (val) ret++;
        }
        out.printLine(ret);
    }
    
}

class C implements Task {
    
    int[] pai, arr;
    
    public void solve(int testNumber, InputReader in, OutputWriter out){
        int n=in.readInt(), ret=0;
        pai=new int[n+1];
        arr=new int[n+1];
        for (int i=1; i<=n; i++) pai[i]=in.readInt();
        for (int i=1; i<=n; i++) ret=Math.max(ret, f(i));
        out.printLine(ret);
    }
    
    int f(int x) {
        if (arr[x]!=0) return arr[x];
        if (pai[x]==-1) return arr[x]=1;
        return arr[x]=f(pai[x])+1;
    }
    
}

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);
        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 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 Vector {
    public final double x;
    public final double y;
    public final Point point;

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

    public Vector(Point point) {
            this.x = point.x;
            this.y = point.y;
            this.point = point;
    }

    public Vector(Point from, Point to) {
            this(to.x - from.x, to.y - from.y);
    }

    public double angleTo(Vector other) {
            return GeometryUtils.canonicalAngle(other.point.angle() - point.angle());
    }

    public double length() {
            return point.value();
    }

    public double angle() {
            return point.angle();
    }
}

class Point implements Comparable<Point>{
    public static final Point ORIGIN = new Point(0, 0);
    public final double x;
    public final double y;
    
    public int compareTo(Point o2) {
        int value = Double.compare(this.x, o2.x);
        if (value != 0)
            return value;
        return Double.compare(this.y, o2.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 Angle {
    public final Point o;
    public final Point a;
    public final Point b;

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

    public double value() {
        double ab = a.distance(b);
        double ao = a.distance(o);
        double bo = b.distance(o);
        return Math.acos((ao * ao + bo * bo - ab * ab) / (2 * ao * bo));
    }

}

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 D implements Task {
    
    int[] mini, maxi;
    
    public void solve(int testNumber, InputReader in, OutputWriter out){
        int n=in.readInt(), m=in.readInt(), ret=0, x=0, y=-1, i2, j2, f=-1;
        String str;
        mini=new int[n];
        maxi=new int[n];
        for (int i=0; i<n; i++) {
            str=in.next();
            mini[i]=1000;
            maxi[i]=-1000;
            for (int j=0; j<m; j++) if (str.charAt(j)=='W') {
                mini[i]=Math.min(mini[i], j);
                maxi[i]=Math.max(maxi[i], j);
                if (f==-1) f=i;
            }
        }
        if (f!=-1) ret+=f;
        for (int i=0; i<n; i++) {
            i2=1000;
            j2=-1000;
            if (i==f && i%2==1) ret+=x=maxi[i];
            for (int j=i+1; j<n; j++) if (mini[j]!=i2 && maxi[j]!=j2) {
                i2=mini[j];
                j2=maxi[j];
                y=j;
                break;
            }
            if (mini[i]!=1000 && maxi[i]!=-1000) {
                ret+=i%2==0?maxi[i]-x:x-mini[i];
                x=i%2==0?maxi[i]:mini[i];
                if (i2!=1000 && j2!=-1000) {
                    ret+=y-i+Math.abs(x-(y%2==0?i2:j2));
                    x=y%2==0?i2:j2;
                }
            }
        }
        out.printLine(ret);
    }
    
}

class E implements Task {
    
    List<List<Integer> > ladj, filhos, familia;
    List<Integer> pilha;
    boolean[] ciclo, vis;
    int[] arr, pai, mapa, parent, pot=new int[100010];
    
    public void solve(int testNumber, InputReader in, OutputWriter out){
        int n=in.readInt(), m=in.readInt(), a, b, c;
        ladj=new ArrayList<List<Integer> >();
        familia=new ArrayList<List<Integer> >();
        filhos=new ArrayList<List<Integer> >();
        ciclo=new boolean[n+1];
        vis=new boolean[n+1];
        arr=new int[n+1];
        pai=new int[n+1];
        mapa=new int[n+1];
        pilha=new ArrayList<Integer>();
        pot[0]=1;
        for (int i=1; i<=100000; i++) pot[i]=pot[i-1]*2%1000000007;
        for (int i=0; i<=n; i++) {
            filhos.add(new ArrayList<Integer>());
            ladj.add(new ArrayList<Integer>());
        }
        for (int i=1; i<=n; i++) {
            pai[i]=i;
            filhos.get(i).add(i);
        }
        while (m-->0) {
            a=in.readInt();
            b=in.readInt();
            ladj.get(a).add(b);
            ladj.get(b).add(a);
        }
        dfs(1, -1);
        for (int i=1; i<=n; i++) if (!ciclo[i] || filhos.get(i).size()>1) {
            familia.add(filhos.get(i));
            mapa[i]=familia.size()-1;
        }
        for (int i=1; i<=n; i++) if (ciclo[i] && filhos.get(i).size()==1) mapa[i]=mapa[pai[i]];
        for (int i=0; i<familia.size(); i++) {
            ciclo[i]=familia.get(i).size()!=1;
        }
        Arrays.fill(vis, false);
        arr[0]=ciclo[0]?1:0;
        parent=new int[familia.size()-1];
        dfs2(0);
        Graph grafo=Graph.createTree(parent);
        LCA lca=new LCA(grafo, 0);
        int k=in.readInt();
        while (k-->0) {
            a=mapa[pai[in.readInt()]];
            b=mapa[pai[in.readInt()]];
            c=lca.getLCA(a, b);
            out.printLine(pot[arr[a]+arr[b]-2*arr[c]+(ciclo[c]?1:0)]);
        }
    }
    
    void dfs(int a, int p) {
        vis[a]=true;
        pilha.add(a);
        for (int b: ladj.get(a)) {
            if (!vis[b]) dfs(b, a);
            else if (b!=p && !ciclo[pai[b]]) {
                ciclo[b]=true;
                for (int i=pilha.size()-1; i>=0 && pilha.get(i)!=b; i--) {
                    pai[pilha.get(i)]=b;
                    ciclo[pilha.get(i)]=true;
                    filhos.get(b).add(pilha.get(i));
                }
            }
        }
        pilha.remove(pilha.size()-1);
    }
    
    void dfs2(int a) {
        vis[a]=true;
        for (int b: familia.get(a)) {
            for (int c: ladj.get(b)) 
                if (!vis[mapa[c]]) {
                    arr[mapa[c]]=arr[a]+(ciclo[mapa[c]]?1:0);
                    parent[mapa[c]-1]=a;
                    dfs2(mapa[c]);
                }
        }
    }
    
}

interface Edge {
    public int getSource();
    public int getDestination();
    public long getWeight();
    public long getCapacity();
    public long getFlow();
    public void pushFlow(long flow);
    public boolean getFlag(int bit);
    public void setFlag(int bit);
    public void removeFlag(int bit);
    public int getTransposedID();
    public Edge getTransposedEdge();
    public int getReverseID();
    public Edge getReverseEdge();
    public int getID();
    public void remove();
    public void restore();
}

class Graph {
    public static final int REMOVED_BIT = 0;

    protected int vertexCount;
    protected int edgeCount;

    private int[] firstOutbound;
    private int[] firstInbound;

    private Edge[] edges;
    private int[] nextInbound;
    private int[] nextOutbound;
    private int[] from;
    private int[] to;
    private long[] weight;
    private long[] capacity;
    private int[] reverseEdge;
    private int[] flags;

    public Graph(int vertexCount) {
        this(vertexCount, vertexCount);
    }

    public Graph(int vertexCount, int edgeCapacity) {
        this.vertexCount = vertexCount;
        firstOutbound = new int[vertexCount];
        Arrays.fill(firstOutbound, -1);

        from = new int[edgeCapacity];
        to = new int[edgeCapacity];
        nextOutbound = new int[edgeCapacity];
        flags = new int[edgeCapacity];
    }

    public static Graph createGraph(int vertexCount, int[] from, int[] to) {
        Graph graph = new Graph(vertexCount, from.length);
        for (int i = 0; i < from.length; i++)
            graph.addSimpleEdge(from[i], to[i]);
        return graph;
    }

    public static Graph createWeightedGraph(int vertexCount, int[] from, int[] to, long[] weight) {
        Graph graph = new Graph(vertexCount, from.length);
        for (int i = 0; i < from.length; i++)
            graph.addWeightedEdge(from[i], to[i], weight[i]);
        return graph;
    }

    public static Graph createFlowGraph(int vertexCount, int[] from, int[] to, long[] capacity) {
        Graph graph = new Graph(vertexCount, from.length * 2);
        for (int i = 0; i < from.length; i++)
            graph.addFlowEdge(from[i], to[i], capacity[i]);
        return graph;
    }

    public static Graph createFlowWeightedGraph(int vertexCount, int[] from, int[] to, long[] weight, long[] capacity) {
        Graph graph = new Graph(vertexCount, from.length * 2);
        for (int i = 0; i < from.length; i++)
            graph.addFlowWeightedEdge(from[i], to[i], weight[i], capacity[i]);
        return graph;
    }

    public static Graph createTree(int[] parent) {
        Graph graph = new Graph(parent.length + 1, parent.length);
        for (int i = 0; i < parent.length; i++)
            graph.addSimpleEdge(parent[i], i + 1);
        return graph;
    }

    public int addEdge(int fromID, int toID, long weight, long capacity, int reverseEdge) {
        ensureEdgeCapacity(edgeCount + 1);
        if (firstOutbound[fromID] != -1)
            nextOutbound[edgeCount] = firstOutbound[fromID];
        else
            nextOutbound[edgeCount] = -1;
        firstOutbound[fromID] = edgeCount;
        if (firstInbound != null) {
            if (firstInbound[toID] != -1)
                nextInbound[edgeCount] = firstInbound[toID];
            else
                nextInbound[edgeCount] = -1;
            firstInbound[toID] = edgeCount;
        }
        this.from[edgeCount] = fromID;
        this.to[edgeCount] = toID;
        if (capacity != 0) {
            if (this.capacity == null)
                this.capacity = new long[from.length];
            this.capacity[edgeCount] = capacity;
        }
        if (weight != 0) {
            if (this.weight == null)
                this.weight = new long[from.length];
            this.weight[edgeCount] = weight;
        }
        if (reverseEdge != -1) {
            if (this.reverseEdge == null) {
                this.reverseEdge = new int[from.length];
                Arrays.fill(this.reverseEdge, 0, edgeCount, -1);
            }
            this.reverseEdge[edgeCount] = reverseEdge;
        }
        if (edges != null)
            edges[edgeCount] = createEdge(edgeCount);
        return edgeCount++;
    }

    protected final GraphEdge createEdge(int id) {
        return new GraphEdge(id);
    }

    public final int addFlowWeightedEdge(int from, int to, long weight, long capacity) {
        if (capacity == 0) {
            return addEdge(from, to, weight, 0, -1);
        } else {
            int lastEdgeCount = edgeCount;
            addEdge(to, from, -weight, 0, lastEdgeCount + entriesPerEdge());
            return addEdge(from, to, weight, capacity, lastEdgeCount);
        }
    }

    protected int entriesPerEdge() {
        return 1;
    }

    public final int addFlowEdge(int from, int to, long capacity) {
        return addFlowWeightedEdge(from, to, 0, capacity);
    }

    public final int addWeightedEdge(int from, int to, long weight) {
        return addFlowWeightedEdge(from, to, weight, 0);
    }

    public final int addSimpleEdge(int from, int to) {
        return addWeightedEdge(from, to, 0);
    }

    public final int vertexCount() {
        return vertexCount;
    }

    public final int edgeCount() {
        return edgeCount;
    }

    protected final int edgeCapacity() {
        return from.length;
    }

    public final Edge edge(int id) {
        initEdges();
        return edges[id];
    }

    public final int firstOutbound(int vertex) {
        int id = firstOutbound[vertex];
        while (id != -1 && isRemoved(id))
            id = nextOutbound[id];
        return id;
    }

    public final int nextOutbound(int id) {
        id = nextOutbound[id];
        while (id != -1 && isRemoved(id))
            id = nextOutbound[id];
        return id;
    }

    public final int firstInbound(int vertex) {
        initInbound();
        int id = firstInbound[vertex];
        while (id != -1 && isRemoved(id))
            id = nextInbound[id];
        return id;
    }

    public final int nextInbound(int id) {
        initInbound();
        id = nextInbound[id];
        while (id != -1 && isRemoved(id))
            id = nextInbound[id];
        return id;
    }

    public final int source(int id) {
        return from[id];
    }

    public final int destination(int id) {
        return to[id];
    }

    public final long weight(int id) {
        if (weight == null)
            return 0;
        return weight[id];
    }

    public final long capacity(int id) {
        if (capacity == null)
            return 0;
        return capacity[id];
    }

    public final long flow(int id) {
        if (reverseEdge == null)
            return 0;
        return capacity[reverseEdge[id]];
    }

    public final void pushFlow(int id, long flow) {
        if (flow == 0)
            return;
        if (flow > 0) {
            if (capacity(id) < flow)
                throw new IllegalArgumentException("Not enough capacity");
        } else {
            if (flow(id) < -flow)
                throw new IllegalArgumentException("Not enough capacity");
        }
        capacity[id] -= flow;
        capacity[reverseEdge[id]] += flow;
    }

    public int transposed(int id) {
        return -1;
    }

    public final int reverse(int id) {
        if (reverseEdge == null)
            return -1;
        return reverseEdge[id];
    }

    public final void addVertices(int count) {
        ensureVertexCapacity(vertexCount + count);
        Arrays.fill(firstOutbound, vertexCount, vertexCount + count, -1);
        if (firstInbound != null)
            Arrays.fill(firstInbound, vertexCount, vertexCount + count, -1);
        vertexCount += count;
    }

    protected final void initEdges() {
        if (edges == null) {
            edges = new Edge[from.length];
            for (int i = 0; i < edgeCount; i++)
                edges[i] = createEdge(i);
        }
    }

    public final void removeVertex(int vertex) {
        int id = firstOutbound[vertex];
        while (id != -1) {
            removeEdge(id);
            id = nextOutbound[id];
        }
        initInbound();
        id = firstInbound[vertex];
        while (id != -1) {
            removeEdge(id);
            id = nextInbound[id];
        }
    }

    private void initInbound() {
        if (firstInbound == null) {
            firstInbound = new int[firstOutbound.length];
            Arrays.fill(firstInbound, 0, vertexCount, -1);
            nextInbound = new int[from.length];
            for (int i = 0; i < edgeCount; i++) {
                nextInbound[i] = firstInbound[to[i]];
                firstInbound[to[i]] = i;
            }
        }
    }

    public final boolean flag(int id, int bit) {
        return (flags[id] >> bit & 1) != 0;
    }

    public final void setFlag(int id, int bit) {
        flags[id] |= 1 << bit;
    }

    public final void removeFlag(int id, int bit) {
        flags[id] &= -1 - (1 << bit);
    }

    public final void removeEdge(int id) {
        setFlag(id, REMOVED_BIT);
    }

    public final void restoreEdge(int id) {
        removeFlag(id, REMOVED_BIT);
    }

    public final boolean isRemoved(int id) {
        return flag(id, REMOVED_BIT);
    }

    public final Iterable<Edge> outbound(final int id) {
        initEdges();
        return new Iterable<Edge>() {
            public Iterator<Edge> iterator() {
                return new EdgeIterator(id, firstOutbound, nextOutbound);
            }
        };
    }

    public final Iterable<Edge> inbound(final int id) {
        initEdges();
        initInbound();
        return new Iterable<Edge>() {
            public Iterator<Edge> iterator() {
                return new EdgeIterator(id, firstInbound, nextInbound);
            }
        };
    }

    protected void ensureEdgeCapacity(int size) {
        if (from.length < size) {
            int newSize = Math.max(size, 2 * from.length);
            if (edges != null)
                edges = resize(edges, newSize);
            from = resize(from, newSize);
            to = resize(to, newSize);
            nextOutbound = resize(nextOutbound, newSize);
            if (nextInbound != null)
                nextInbound = resize(nextInbound, newSize);
            if (weight != null)
                weight = resize(weight, newSize);
            if (capacity != null)
                capacity = resize(capacity, newSize);
            if (reverseEdge != null)
                reverseEdge = resize(reverseEdge, newSize);
            flags = resize(flags, newSize);
        }
    }

    private void ensureVertexCapacity(int size) {
        if (firstOutbound.length < size) {
            int newSize = Math.max(size, 2 * from.length);
            firstOutbound = resize(firstOutbound, newSize);
            if (firstInbound != null)
                firstInbound = resize(firstInbound, newSize);
        }
    }

    protected final int[] resize(int[] array, int size) {
        int[] newArray = new int[size];
        System.arraycopy(array, 0, newArray, 0, array.length);
        return newArray;
    }

    private long[] resize(long[] array, int size) {
        long[] newArray = new long[size];
        System.arraycopy(array, 0, newArray, 0, array.length);
        return newArray;
    }

    private Edge[] resize(Edge[] array, int size) {
        Edge[] newArray = new Edge[size];
        System.arraycopy(array, 0, newArray, 0, array.length);
        return newArray;
    }

    public final boolean isSparse() {
        return vertexCount == 0 || edgeCount * 20 / vertexCount <= vertexCount;
    }

    protected class GraphEdge implements Edge {
        protected int id;

        protected GraphEdge(int id) {
            this.id = id;
        }

        public int getSource() {
            return source(id);
        }

        public int getDestination() {
            return destination(id);
        }

        public long getWeight() {
            return weight(id);
        }

        public long getCapacity() {
            return capacity(id);
        }

        public long getFlow() {
            return flow(id);
        }

        public void pushFlow(long flow) {
            Graph.this.pushFlow(id, flow);
        }

        public boolean getFlag(int bit) {
            return flag(id, bit);
        }

        public void setFlag(int bit) {
            Graph.this.setFlag(id, bit);
        }

        public void removeFlag(int bit) {
            Graph.this.removeFlag(id, bit);
        }

        public int getTransposedID() {
            return transposed(id);
        }

        public Edge getTransposedEdge() {
            int reverseID = getTransposedID();
            if (reverseID == -1)
                return null;
            initEdges();
            return edge(reverseID);
        }

        public int getReverseID() {
            return reverse(id);
        }

        public Edge getReverseEdge() {
            int reverseID = getReverseID();
            if (reverseID == -1)
                return null;
            initEdges();
            return edge(reverseID);
        }

        public int getID() {
            return id;
        }

        public void remove() {
            removeEdge(id);
        }

        public void restore() {
            restoreEdge(id);
        }
    }

    public class EdgeIterator implements Iterator<Edge> {
        private int edgeID;
        private final int[] next;
        private int lastID = -1;

        public EdgeIterator(int id, int[] first, int[] next) {
            this.next = next;
            edgeID = nextEdge(first[id]);
        }

        private int nextEdge(int id) {
            while (id != -1 && isRemoved(id))
                id = next[id];
            return id;
        }

        public boolean hasNext() {
            return edgeID != -1;
        }

        public Edge next() {
            if (edgeID == -1)
                throw new NoSuchElementException();
            lastID = edgeID;
            edgeID = nextEdge(next[lastID]);
            return edges[lastID];
        }

        public void remove() {
            if (lastID == -1)
                throw new IllegalStateException();
            removeEdge(lastID);
            lastID = -1;
        }
    }

}

abstract class IntervalTree {
    protected int size;

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

    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 ReadOnlyIntervalTree extends IntervalTree {
    protected long[] value;
    protected long[] array;

    protected ReadOnlyIntervalTree(long[] array) {
        super(array.length, false);
        this.array = array;
        init();
    }

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

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

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

    @Override
    protected void initLeaf(int root, int index) {
        value[root] = array[index];
    }

    @Override
    protected void updatePostProcess(int root, int left, int right, int from, int to, long delta, int middle) {
        throw new UnsupportedOperationException();
    }

    @Override
    protected void updatePreProcess(int root, int left, int right, int from, int to, long delta, int middle) {
        throw new UnsupportedOperationException();
    }

    @Override
    protected void updateFull(int root, int left, int right, int from, int to, long delta) {
        throw new UnsupportedOperationException();
    }

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

    @Override
    protected void queryPreProcess(int root, int left, int right, int from, int to, int middle) {
    }

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

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

    @Override
    public void update(int from, int to, long delta) {
        throw new UnsupportedOperationException();
    }

    @Override
    protected void update(int root, int left, int right, int from, int to, long delta) {
        throw new UnsupportedOperationException();
    }

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

class LCA {
    private final long[] order;
    private final int[] position;
    private final Graph graph;
    private final IntervalTree lcaTree;
    private final int[] level;

    public LCA(Graph graph) {
        this(graph, 0);
    }

    public LCA(Graph graph, int root) {
        this.graph = graph;
        order = new long[2 * graph.vertexCount() - 1];
        position = new int[graph.vertexCount()];
        level = new int[graph.vertexCount()];
        int[] index = new int[graph.vertexCount()];
        for (int i = 0; i < index.length; i++)
            index[i] = graph.firstOutbound(i);
        int[] last = new int[graph.vertexCount()];
        int[] stack = new int[graph.vertexCount()];
        stack[0] = root;
        int size = 1;
        int j = 0;
        last[root] = -1;
        Arrays.fill(position, -1);
        while (size > 0) {
            int vertex = stack[--size];
            if (position[vertex] == -1)
                position[vertex] = j;
            order[j++] = vertex;
            if (last[vertex] != -1)
                level[vertex] = level[last[vertex]] + 1;
            while (index[vertex] != -1 && last[vertex] == graph.destination(index[vertex]))
                index[vertex] = graph.nextOutbound(index[vertex]);
            if (index[vertex] != -1) {
                stack[size++] = vertex;
                stack[size++] = graph.destination(index[vertex]);
                last[graph.destination(index[vertex])] = vertex;
                index[vertex] = graph.nextOutbound(index[vertex]);
            }
        }
        lcaTree = new ReadOnlyIntervalTree(order) {
            @Override
            protected long joinValue(long left, long right) {
                if (left == -1)
                    return right;
                if (right == -1)
                    return left;
                if (level[((int) left)] < level[((int) right)])
                    return left;
                return right;
            }

            @Override
            protected long neutralValue() {
                return -1;
            }
        };
        lcaTree.init();
    }

    public int getPosition(int vertex) {
        return position[vertex];
    }

    public int getLCA(int first, int second) {
        return (int) lcaTree.query(Math.min(position[first], position[second]), Math.max(position[first], position[second]));
    }

    public int getLevel(int vertex) {
        return level[vertex];
    }

    public int getPathLength(int first, int second) {
        return level[first] + level[second] - 2 * level[getLCA(first, second)];
    }

    private int calculate(int vertex, int last, int currentPosition) {
        if (last != -1)
            level[vertex] = level[last] + 1;
        position[vertex] = currentPosition;
        order[currentPosition++] = vertex;
        for (int i = graph.firstOutbound(vertex); i != -1; i = graph.nextOutbound(i)) {
            int to = graph.destination(i);
            if (to != last) {
                currentPosition = calculate(to, vertex, currentPosition);
                order[currentPosition++] = vertex;
            }
        }
        return currentPosition;
    }
}

class InputReader {

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

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