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.text.DecimalFormat;
import java.util.*;
import java.util.regex.Matcher;
import java.util.regex.Pattern;

import javax.swing.text.Position;

import org.xml.sax.HandlerBase;

import java.io.*;
import java.math.BigDecimal;
import java.math.BigInteger;
import java.math.MathContext;

import static java.lang.Math.*;
import static java.util.Arrays.*;
import static java.util.Arrays.fill;
import static java.util.Collections.*;

import java.awt.Point;
import java.awt.geom.Point2D;

public class Main {
	public static void main(String[] args) throws Exception {
		InputReader in = new InputReader(System.in);
		PrintWriter out = new PrintWriter(System.out);
		TaskA solver = new TaskA();
		solver.solve(1, in, out);
		out.close();
	}

	static class TaskA {
		public int[] dx = { 1, 0, -1, 0, -1, -1, 1, 1 }, dy = { 0, 1, 0, -1, -1, 1, -1, 1 };
		int MAX = (int) (1e9 + 7);

		// GCD && LCM
		long gcd(long a, long b) {
			return b == 0 ? a : gcd(b, a % b);
		}

		long lcm(long a, long b) {
			return a * (b / gcd(a, b));
		}

		// REverse a String
		String rev(String s) {
			return new StringBuilder(s).reverse().toString();
		}

		boolean isprime[] = new boolean[1000015];
		ArrayList<Integer> al = new ArrayList<>();

		void sieve() {
			Arrays.fill(isprime, true);
			boolean visited[] = new boolean[1000015];
			isprime[0] = false;
			isprime[1] = false;
			for (int i = 2; i * i <= 1000015; i++) {
				visited[i] = true;
				for (int j = i * i; j < 1000015; j += i) {
					if (!visited[j]) {
						visited[j] = true;
						isprime[j] = false;
					}
				}
			}
			for (int i = 2; i < 1000012; i++)
				if (isprime[i])
					al.add(i);
		}
 
		public void solve(int testNumber, InputReader in, PrintWriter out) throws IOException {
			int n = in.nextInt();
			int[] a = in.readintArray(n);
			sort(a);
			double area = 0,r1=0,r2=0;
			for(int i = n-1; i>=0; i--){
				if(i>=1){
					r1 = a[i]; r2 = a[i-1];
				}
				else{
					r1 = a[i] ; r2 = 0;
				}
				area += PI*(r1*r1 - r2*r2);
				//out.println(r1+" "+r2);
				i--;
			}
			out.print(area);
		}
		
		public int res(int q,int pos,int pet){
			if(pos==q)
				return pet;
			if(pos>q)
				return Integer.MAX_VALUE;
			return min(res(q, pos+1, pet+1),res(q, 2*pos, pet+2));
		}
	}


	static class InputReader {
		private byte[] buf = new byte[8000];
		private int index;
		private int total;
		private InputStream in;
		// BufferedReader br = new BufferedReader(new
		// InputStreamReader(System.in));

		public InputReader(InputStream stream) {
			in = stream;
		}

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

		public long nextLong() {
			long integer = 0;
			int n = scan();
			while (isWhiteSpace(n))
				n = scan();
			int neg = 1;
			if (n == '-') {
				neg = -1;
				n = scan();
			}
			while (!isWhiteSpace(n)) {
				if (n >= '0' && n <= '9') {
					integer *= 10;
					integer += n - '0';
					n = scan();
				} else
					throw new InputMismatchException();
			}
			return neg * integer;
		}

		private int nextInt() {
			int integer = 0;
			int n = scan();
			while (isWhiteSpace(n))
				n = scan();
			int neg = 1;
			if (n == '-') {
				neg = -1;
				n = scan();
			}
			while (!isWhiteSpace(n)) {
				if (n >= '0' && n <= '9') {
					integer *= 10;
					integer += n - '0';
					n = scan();
				} else
					throw new InputMismatchException();
			}
			return neg * integer;
		}

		public double nextDouble() {
			double doubll = 0;
			int n = scan();
			int neg = 1;
			while (isWhiteSpace(n))
				n = scan();
			if (n == '-') {
				neg = -1;
				n = scan();
			}
			while (!isWhiteSpace(n) && n != '.') {
				if (n >= '0' && n <= '9') {
					doubll *= 10;
					doubll += n - '0';
					n = scan();
				}
			}
			if (n == '.') {
				n = scan();
				double temp = 1;
				while (!isWhiteSpace(n)) {
					if (n >= '0' && n <= '9') {
						temp /= 10;
						doubll += (n - '0') * temp;
						n = scan();
					}
				}
			}
			return neg * doubll;
		}

		private float nextFloat() {
			float doubll = 0;
			int n = scan();
			int neg = 1;
			while (isWhiteSpace(n))
				n = scan();
			if (n == '-') {
				neg = -1;
				n = scan();
			}
			while (!isWhiteSpace(n) && n != '.') {
				if (n >= '0' && n <= '9') {
					doubll *= 10;
					doubll += n - '0';
					n = scan();
				}
			}
			if (n == '.') {
				n = scan();
				double temp = 1;
				while (!isWhiteSpace(n)) {
					if (n >= '0' && n <= '9') {
						temp /= 10;
						doubll += (n - '0') * temp;
						n = scan();
					}
				}
			}
			return neg * doubll;
		}

		public String next() {
			StringBuilder sb = new StringBuilder();
			int n = scan();
			while (isWhiteSpace(n))
				n = scan();
			while (!isWhiteSpace(n)) {
				sb.append((char) n);
				n = scan();
			}
			return sb.toString();
		}

		public String nextLine() {
			int n = scan();
			while (isWhiteSpace(n))
				n = scan();
			StringBuilder res = new StringBuilder();
			do {
				res.appendCodePoint(n);
				n = scan();
			} while (!isEndOfLine(n));
			return res.toString();
		}

		public boolean isWhiteSpace(int n) {
			if (n == ' ' || n == '\n' || n == '\r' || n == '\t' || n == -1)
				return true;
			return false;
		}

		private boolean isEndOfLine(int c) {
			return c == '\n' || c == '\r' || c == -1;
		}

		/*
		 * /// Input module
		 * 
		 * public int nextInt() { return scanInt(); }
		 * 
		 * public long nextLong() { return scanlong(); }
		 * 
		 * public double nextDouble() { return scandouble(); }
		 * 
		 * public float nextFloat() { return scanfloat(); }
		 * 
		 * public String next() { return scanstring(); }
		 * 
		 * public String nextLine() throws IOException { return scan_nextLine();
		 * }
		 */
		public int[] readintArray(int size) {
			int[] array = new int[size];
			for (int i = 0; i < size; i++) {
				array[i] = nextInt();
			}
			return array;
		}

		public Integer[] readIntegerArray(int size) {
			Integer[] array = new Integer[size];
			for (int i = 0; i < size; i++) {
				array[i] = nextInt();
			}
			return array;
		}
	}

}