Problem: One day a bear lived on the Oxy axis. He was afraid of the dark, so he couldn't move at night along the plane points that aren't lit. One day the bear wanted to have a night walk from his house at point (l, 0) to his friend's house at point (r, 0), along the segment of length (r - l). Of course, if he wants to make this walk, he needs each point of the segment to be lit. That's why the bear called his friend (and yes, in the middle of the night) asking for a very delicate favor.

The Oxy axis contains n floodlights. Floodlight i is at point (xi, yi) and can light any angle of the plane as large as ai degree with vertex at point (xi, yi). The bear asked his friend to turn the floodlights so that he (the bear) could go as far away from his house as possible during the walking along the segment. His kind friend agreed to fulfill his request. And while he is at it, the bear wonders: what is the furthest he can go away from his house? Hep him and find this distance.

Consider that the plane has no obstacles and no other light sources besides the floodlights. The bear's friend cannot turn the floodlights during the bear's walk. Assume that after all the floodlights are turned in the correct direction, the bear goes for a walk and his friend goes to bed.

Input

The first line contains three space-separated integers n, l, r (1 ≤ n ≤ 20; - 105 ≤ l ≤ r ≤ 105). The i-th of the next n lines contain three space-separated integers xi, yi, ai ( - 1000 ≤ xi ≤ 1000; 1 ≤ yi ≤ 1000; 1 ≤ ai ≤ 90) — the floodlights' description. 

Note that two floodlights can be at the same point of the plane.

Output

Print a single real number — the answer to the problem. The answer will be considered correct if its relative or absolute error doesn't exceed 10 - 6.

Examples

Input

2 3 5
3 1 45
5 1 45


Output

2.000000000


Input

1 0 1
1 1 30


Output

0.732050808


Input

1 0 1
1 1 45


Output

1.000000000


Input

1 0 2
0 2 90


Output

2.000000000

Note

In the first sample, one of the possible solutions is: 

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In the second sample, a single solution is: 

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In the third sample, a single solution is: 

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Solution (in JAVA):

Solution:
import java.io.IOException;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.List;
import java.util.Scanner;

public class Main {

    public static void main(final String[] args) throws IOException {
        try(Scanner scan = new Scanner(System.in);
            PrintWriter print = new PrintWriter(System.out)) {
            final int n = scan.nextInt();
            final int l = scan.nextInt();
            final int r = scan.nextInt();
            final Floodlight[] floodlights = new Floodlight[n];
            for(int i = 0; i < n; ++i) {
                final int x = scan.nextInt();
                final int y = scan.nextInt();
                final double angle = scan.nextInt() / 180. * Math.PI;
                floodlights[i] = new Floodlight(x, y, angle);
            }
            print.println(calcMaxBeginSeg(l, r, floodlights));
        }
    }

    public static double calcMaxBeginSeg(final int left, final int right, final Floodlight[] floodlights) {
        if(right <= left) return 0.;
        final int n = floodlights.length;
        double maxLitRight[] = new double[1 << n];
        maxLitRight[0] = left;
        for(int mask = 1; mask < 1 << n; ++mask) {
            double result = left;
            for(int i = 0; i < n; ++i) {
                if(((mask >> i) & 1) == 1) {
                    result = Math.max(result, extendLitSeg(maxLitRight[mask ^ (1 << i)], floodlights[i], right));
                }
            }
            maxLitRight[mask] = result;
        }
        return maxLitRight[(1 << n) - 1] - left;
    }

    private static double extendLitSeg(final double left, final Floodlight light, final double maxRight) {
        if(left >= maxRight) return left;
        if(light.y <= 0.) throw new RuntimeException("light.y must be > 0");
        final double startAngle = Math.atan((left - light.getX()) / light.getY());
        final double endAngle = startAngle + light.angle;
        if(endAngle >= Math.PI / 2.) return maxRight;
        return Math.min(maxRight, light.getX() + light.getY() * Math.tan(endAngle));
    }

    public static class Floodlight {
        private final int x;
        private final int y;
        private final double angle;

        public Floodlight(final int x, final int y, final double angle) {
            this.x = x;
            this.y = y;
            this.angle = angle;
        }

        public int getX() {
            return x;
        }

        public int getY() {
            return y;
        }

        public double getAngle() {
            return angle;
        }
    }

    public static class NumberUtils {
        public static interface Factorizer {
            List<Integer> factorize(int number);
        }

        /**
         * thread safe Factorizer
         */
        public static Factorizer createSmallNumberFactorizer(final int upperBound) {
            return new SmallNumberFactorizer(upperBound);
        }

        /**
         * thread safe
         */
        private static class SmallNumberFactorizer implements Factorizer {
            private int[] divisors;
            private final int upperBound;
            private boolean prepared = false;

            /**
             * lazy
             * time complexity O(n * log(n) * log(log(n))
             * memory complexity O(n)
             */
            public SmallNumberFactorizer(final int upperBound) {
                this.upperBound = upperBound;
            }

            private synchronized void prepare() {
                divisors = new int[upperBound];
                Arrays.fill(divisors, 0);
                for(int i = 2; i * i < upperBound; ++i) {
                    if(divisors[i] == 0) {
                        for(int j = i * i; j < upperBound; j += i) {
                            if(divisors[j] == 0) {
                                divisors[j] = i;
                            }
                        }
                    }
                }
                prepared = true;
            }

            /**
             * complexity O(result)
             */
            public List<Integer> factorize(int number) {
                synchronized (this) {
                    if(!prepared) {
                        prepare();
                    }
                }
                final List<Integer> result = CollectionFactory.createArrayList();
                if(number < 2) return result;
                if(number >= upperBound) throw new RuntimeException("number should be less than upper bound");
                while(divisors[number] > 0) {
                    result.add(divisors[number]);
                    number /= divisors[number];
                }
                result.add(number);
                return result;
            }
        }
    }

    public static class CollectionFactory {
        public static<T> List<T> createArrayList() {
            return new ArrayList<>();
        }

        public static<T> List<T> createArrayList(final int capacity) {
            return new ArrayList<>(capacity);
        }
    }

    public static class CollectionUtils {
        public static<T> List<T> unique(final List<T> list) {
            final List<T> result = CollectionFactory.createArrayList();
            T p = null;
            for(T elem : list) {
                if(!elem.equals(p)) {
                    result.add(elem);
                    p = elem;
                }
            }
            return result;
        }

        public static<T extends Comparable<T>> T max(final List<T> list, final T lowerBound) {
            T result = lowerBound;
            for(T elem : list) {
                if(elem.compareTo(result) > 0) {
                    result = elem;
                }
            }
            return result;
        }
    }

}