Problem: One day, as Sherlock Holmes was tracking down one very important criminal, he found a wonderful painting on the wall. This wall could be represented as a plane. The painting had several concentric circles that divided the wall into several parts. Some parts were painted red and all the other were painted blue. Besides, any two neighboring parts were painted different colors, that is, the red and the blue color were alternating, i. e. followed one after the other. The outer area of the wall (the area that lied outside all circles) was painted blue. Help Sherlock Holmes determine the total area of red parts of the wall.

Let us remind you that two circles are called concentric if their centers coincide. Several circles are called concentric if any two of them are concentric.

Input

The first line contains the single integer n (1 ≤ n ≤ 100). The second line contains n space-separated integers ri (1 ≤ ri ≤ 1000) — the circles' radii. It is guaranteed that all circles are different.

Output

Print the single real number — total area of the part of the wall that is painted red. The answer is accepted if absolute or relative error doesn't exceed 10 - 4.

Examples

Input

1
1


Output

3.1415926536


Input

3
1 4 2


Output

40.8407044967

Note

In the first sample the picture is just one circle of radius 1. Inner part of the circle is painted red. The area of the red part equals π × 12 = π.

In the second sample there are three circles of radii 1, 4 and 2. Outside part of the second circle is painted blue. Part between the second and the third circles is painted red. Part between the first and the third is painted blue. And, finally, the inner part of the first circle is painted red. Overall there are two red parts: the ring between the second and the third circles and the inner part of the first circle. Total area of the red parts is equal (π × 42 - π × 22) + π × 12 = π × 12 + π = 13π

Solution (in JAVA):

Solution:
import java.io.BufferedWriter;
import java.io.FileInputStream;
import java.io.FileWriter;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStreamWriter;
import java.io.PrintWriter;
import java.math.BigDecimal;
import java.util.Arrays;
import java.util.Locale;

public class B157 
{
	public static void main(String[] args) throws IOException 
	{
		setStandardIO();
		//setFileIO("test");		
		
		int n = nextInt();
		int tab[] = new int[n];
		for (int i = 0; i < n; i++) 
			tab[i] = nextInt();
		
		Arrays.sort(tab);
		
		double res = 0;
		for (int i = n - 1, k = 0; i >= 0; i--,k++) 
			if (k % 2 == 0) res += Math.PI * tab[i] * tab[i];
			else res -= Math.PI * tab[i] * tab[i];
		
		println(res);
		flush();
	}

	// ~ -----------------------------------------------------------------------
	// ~ - Auxiliary code ------------------------------------------------------
	// ~ -----------------------------------------------------------------------
	static InputStream in;
	static PrintWriter out;

	/**
	 * Simple buffered reader class. Reads if buffer is empty. Try to fill up
	 * whole buffer.
	 */
	public static class SimpleBufferedInputStream extends InputStream 
	{
		// ~ Static fields / Initializers --------------------------------------
		private static int defaultCharBufferSize = 16384;
		private InputStream in;
		byte[] buffer;
		int pos = 0;
		int len = 0;
		
		// ~ Constructors ------------------------------------------------------
		public SimpleBufferedInputStream(InputStream in) {
			this(in, defaultCharBufferSize);
		}

		public SimpleBufferedInputStream(InputStream in, int size) {
			this.in = in;
			this.buffer = new byte[size];
		}
	    
		// ~ Methods -----------------------------------------------------------
		@Override
		public int read() throws IOException {
			if (pos < len)
				return buffer[pos++];
			
			len = in.read(buffer);
			if (len == -1)
				return len;
			
			pos = 0;
			if (len <= 0)
				return -1;
			
			return buffer[pos++];
		}
	}

	public static void setStandardIO() {
		in = new SimpleBufferedInputStream(System.in);
		out = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));
	}

	public static void setFileIO(String fileName) throws IOException {
		in = new SimpleBufferedInputStream(new FileInputStream(fileName + ".in"));
 		out = new PrintWriter(new BufferedWriter(new FileWriter(fileName + ".out")));
	}

	public static int skipWhitespaces() throws IOException {
		int c;
		for (;;) {
			c = in.read();
			if (c == -1) throw new IOException();
			if (!isWhitespace(c)) break;
		}	
		
		return c;
	}
	
	public static int skipNewLines() throws IOException {
		int c;
		for (;;) {
			c = in.read();
			if (c == -1) throw new IOException();
			if (!isNewLine(c)) break;
		}	
		
		return c;
	}

	public static boolean isNewLine(int c) {
		return c == '\n' || c == '\r' ? true : false;
	}

	public static boolean isWhitespace(int c) {
		return c == ' ' || c == '\n' || c == '\r' || c == '\t' ? true : false;
	}
	
	public static int nextNoWhitespace() throws IOException {
		int c = in.read();
		if (c == -1 || isWhitespace(c)) return -1;
		
		return c;
	}

	public static int nextNoNewLine() throws IOException {
		int c = in.read();
		if (c == -1 || isNewLine(c)) return -1;
		
		return c;
	}

	public static long nextLong() throws IOException {
		int c;
		for (;;) {
			c = in.read();
			if (!isWhitespace(c)) break;
			if (c == -1) throw new RuntimeException();
		}	

		boolean neg = false;
		long val = 0;
		if (c == '-')
			neg = true;
		else 
			val = c - '0';
		
		for (;;) {
			c = in.read();
			if (isWhitespace(c) || c == -1) 
				break;
			
			val = val * 10 + (c - '0');
		}

		if (neg) 
			return -val;
		
		return val;
	}

	public static int nextInt() throws IOException {
		int c;
		for (;;) {
			c = in.read();
			if (!isWhitespace(c)) break;
			if (c == -1) throw new RuntimeException();
		}	
		
		boolean neg = false;		
		int val = 0;
		if (c == '-')
			neg = true;
		else 
			val = c - '0';
		
		for (;;) {
			c = in.read();
			if (isWhitespace(c) || c == -1) 
				break;
			
			val = val * 10 + (c - '0');
		}

		if (neg) 
			return -val;
		
		return val;
	}

	public static byte nextByte() throws IOException {
		return (byte) nextInt();
	}

	public static String nextLine() throws IOException {
		int c = (char) skipNewLines();
		
		StringBuilder sb = new StringBuilder();
		sb.append((char) c);
		
		for (;;) {
			c = nextNoNewLine();
			if (c == -1)
				break;
			
			sb.append((char) c);
		}

		return sb.toString();
	}

	public static String nextString() throws IOException {
		int c = (char) skipWhitespaces();
		
		StringBuilder sb = new StringBuilder();
		sb.append((char) c);
		
		for (;;) {
			c = nextNoWhitespace();
			if (c == -1)
				break;
			
			sb.append((char) c);
		}

		return sb.toString();
	}

	public static double nextDouble() throws IOException {
		return Double.parseDouble(nextString());
	}	
	
	public static BigDecimal nextBigDecimal() throws IOException {
		return new BigDecimal(nextString());
	}
	
	public static void flush() {
		out.flush();
	}

	public static void println(Object object) {
		out.println(object);
	}

	public static void print(Object object) {
		out.print(object);
	}

	public static void println(double d, int precision) {
		String s = "%1$." + precision + "f";
		out.format(Locale.ENGLISH, s, d);
		out.println();
	}

	public static void println(BigDecimal d, int precision) {
		String s = "%1$." + precision + "f";
		out.format(Locale.ENGLISH, s, d);
		out.println();
	}
}