Problem: Takahashi has a water bottle with the shape of a rectangular prism whose base is a square of side a~\mathrm{cm} and whose height is b~\mathrm{cm}. (The thickness of the bottle can be ignored.)

We will pour x~\mathrm{cm}^3 of water into the bottle, and gradually tilt the bottle around one of the sides of the base.

When will the water be spilled? More formally, find the maximum angle in which we can tilt the bottle without spilling any water.

Constraints

* All values in input are integers.
* 1 \leq a \leq 100
* 1 \leq b \leq 100
* 1 \leq x \leq a^2b

Input

Input is given from Standard Input in the following format:


a b x


Output

Print the maximum angle in which we can tilt the bottle without spilling any water, in degrees. Your output will be judged as correct when the absolute or relative error from the judge's output is at most 10^{-6}.

Examples

Input

2 2 4


Output

45.0000000000


Input

12 21 10


Output

89.7834636934


Input

3 1 8


Output

4.2363947991

Solution (in JAVA):

Solution:
import java.io.*;
import java.nio.CharBuffer;
import java.util.NoSuchElementException;

public class Main {

    private static double EPSILON = 1e-9;

    public static void main(String[] args) {
        SimpleScanner scanner = new SimpleScanner(System.in);
        PrintWriter writer = new PrintWriter(System.out);

        int a = scanner.nextInt();
        int b = scanner.nextInt();
        int x = scanner.nextInt();
        int full = a * a * b;
        double half = full / 2.0;
        double ans;
        if (x >= half) {
            double l = 0;
            double r = b;
            while (l < r - EPSILON) {
                double mid = (l + r) / 2;
                if ((b + mid) * a * a / 2 < x)
                    l = mid;
                else
                    r = mid;
            }
            ans = Math.toDegrees(Math.atan((b - l) / a));
        } else {
            double l = 0;
            double r = a;
            while (l < r - EPSILON) {
                double mid = (l + r) / 2;
                if ((b * mid) * a / 2 < x)
                    l = mid;
                else
                    r = mid;
            }
            ans = Math.toDegrees(Math.atan(b / l));
        }

        writer.println(ans);

        writer.close();
    }

    private static class SimpleScanner {

        private static final int BUFFER_SIZE = 10240;

        private Readable in;
        private CharBuffer buffer;
        private boolean eof;

        SimpleScanner(InputStream in) {
            this.in = new BufferedReader(new InputStreamReader(in));
            buffer = CharBuffer.allocate(BUFFER_SIZE);
            buffer.limit(0);
            eof = false;
        }


        private char read() {
            if (!buffer.hasRemaining()) {
                buffer.clear();
                int n;
                try {
                    n = in.read(buffer);
                } catch (IOException e) {
                    n = -1;
                }
                if (n <= 0) {
                    eof = true;
                    return '\0';
                }
                buffer.flip();
            }
            return buffer.get();
        }

        private void checkEof() {
            if (eof)
                throw new NoSuchElementException();
        }

        private char nextChar() {
            checkEof();
            char b = read();
            checkEof();
            return b;
        }

        private String next() {
            char b;
            do {
                b = read();
                checkEof();
            } while (Character.isWhitespace(b));
            StringBuilder sb = new StringBuilder();
            do {
                sb.append(b);
                b = read();
            } while (!eof && !Character.isWhitespace(b));
            return sb.toString();
        }

        private int nextInt() {
            return Integer.parseInt(next());
        }

        private long nextLong() {
            return Long.parseLong(next());
        }

        private double nextDouble() {
            return Double.parseDouble(next());
        }
    }
}