Problem: As you know, every birthday party has a cake! This time, Babaei is going to prepare the very special birthday party's cake.

Simple cake is a cylinder of some radius and height. The volume of the simple cake is equal to the volume of corresponding cylinder. Babaei has n simple cakes and he is going to make a special cake placing some cylinders on each other.

However, there are some additional culinary restrictions. The cakes are numbered in such a way that the cake number i can be placed only on the table or on some cake number j where j < i. Moreover, in order to impress friends Babaei will put the cake i on top of the cake j only if the volume of the cake i is strictly greater than the volume of the cake j.

Babaei wants to prepare a birthday cake that has a maximum possible total volume. Help him find this value.

Input

The first line of the input contains a single integer n (1 ≤ n ≤ 100 000) — the number of simple cakes Babaei has.

Each of the following n lines contains two integers ri and hi (1 ≤ ri, hi ≤ 10 000), giving the radius and height of the i-th cake.

Output

Print the maximum volume of the cake that Babaei can make. Your answer will be considered correct if its absolute or relative error does not exceed 10 - 6.

Namely: let's assume that your answer is a, and the answer of the jury is b. The checker program will consider your answer correct, if <image>.

Examples

Input

2
100 30
40 10


Output

942477.796077000


Input

4
1 1
9 7
1 4
10 7


Output

3983.539484752

Note

In first sample, the optimal way is to choose the cake number 1.

In second sample, the way to get the maximum volume is to use cakes with indices 1, 2 and 4.

Solution (in JAVA):

Solution:
/**
 * Created by ankurverma1994
 */

import java.io.*;
import java.util.*;
import java.math.*;

public class BCAKE {
    final int mod = (int) 1e9 + 7;
    final double eps = 1e-6;
    final double pi = Math.PI;

    //------------> Solution starts here!!
    @SuppressWarnings("Main Logic")
    void solve() {
        int n = ii();
        long v[][] = new long[n][2];
        for (int i = 0; i < n; i++) {
            int r = ii(), h = ii();
            v[i][0] = 1L * r * r * h;
            v[i][1] = i;
        }
        Arrays.sort(v, new Comparator<long[]>() {
            public int compare(long[] a, long[] b) {
                if (a[0] != b[0])
                    return Long.compare(a[0], b[0]);
                return Long.compare(b[1], a[1]);
            }
        });
        SegmentTree tree = new SegmentTree(n);
        long ans = 0;
        for (int i = 0; i < n; i++) {
            long max = tree.query(0, (int) v[i][1]);
            tree.update((int) v[i][1], max + v[i][0]);
            ans = Math.max(ans, max + v[i][0]);
        }
        out.println(pi * ans);
    }

    class SegmentTree {
        long tree[];
        long a[];
        int n;

        long operation(long a, long b) {
            return Math.max(a, b);
        }

        SegmentTree(int n) {
            tree = new long[4 * n];
            this.a = new long[n];
            this.n = n;
        }

        void update(int x, long v) {
            put(0, n - 1, 0, x, v);
        }

        void put(int s, int e, int c, int x, long v) {
            if (s == e) {
                tree[c] = a[s] = v;
                return;
            }
            int m = (s + e) >> 1;
            if (x <= m) put(s, m, 2 * c + 1, x, v);
            else put(m + 1, e, 2 * c + 2, x, v);
            tree[c] = operation(tree[2 * c + 1], tree[2 * c + 2]);
        }

        long query(int l, int r) {
            return get(0, n - 1, 0, l, r);
        }

        long get(int s, int e, int c, int l, int r) {
            if (s == l && e == r) return tree[c];
            int m = (s + e) >> 1;
            if (r <= m) return get(s, m, 2 * c + 1, l, r);
            if (l > m) return get(m + 1, e, 2 * c + 2, l, r);
            return operation(get(s, m, 2 * c + 1, l, m), get(m + 1, e, 2 * c + 2, m + 1, r));
        }
    }

    //------------> Solution ends here!!
    InputStream obj;
    PrintWriter out;
    String check = "";

    public static void main(String[] args) throws IOException {
        new Thread(null, new Runnable() {
            public void run() {
                try {
                    new BCAKE().main1();
                } catch (IOException e) {
                    e.printStackTrace();
                } catch (StackOverflowError e) {
                    System.out.println("RTE");
                }
            }
        }, "1", 1 << 26).start();
    }

    void main1() throws IOException {
        out = new PrintWriter(System.out);
        obj = check.isEmpty() ? System.in : new ByteArrayInputStream(check.getBytes());
        // obj=check.isEmpty() ? new FileInputStream("/home/ankurverma1994/input.txt") : new ByteArrayInputStream(check.getBytes());
        solve();
        out.flush();
        out.close();
    }

    byte inbuffer[] = new byte[1024];
    int lenbuffer = 0, ptrbuffer = 0;

    int readByte() {
        if (lenbuffer == -1) throw new InputMismatchException();
        if (ptrbuffer >= lenbuffer) {
            ptrbuffer = 0;
            try {
                lenbuffer = obj.read(inbuffer);
            } catch (IOException e) {
                throw new InputMismatchException();
            }
        }
        if (lenbuffer <= 0) return -1;
        return inbuffer[ptrbuffer++];
    }

    String is() {
        int b = skip();
        StringBuilder sb = new StringBuilder();
        while (!(isSpaceChar(b))) // when nextLine, (isSpaceChar(b) && b!=' ')
        {
            sb.appendCodePoint(b);
            b = readByte();
        }
        return sb.toString();
    }

    int ii() {
        int num = 0, b;
        boolean minus = false;
        while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-')) ;
        if (b == '-') {
            minus = true;
            b = readByte();
        }
        while (true) {
            if (b >= '0' && b <= '9') {
                num = num * 10 + (b - '0');
            } else {
                return minus ? -num : num;
            }
            b = readByte();
        }
    }

    long il() {
        long num = 0;
        int b;
        boolean minus = false;
        while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-')) ;
        if (b == '-') {
            minus = true;
            b = readByte();
        }
        while (true) {
            if (b >= '0' && b <= '9') {
                num = num * 10 + (b - '0');
            } else {
                return minus ? -num : num;
            }
            b = readByte();
        }
    }

    boolean isSpaceChar(int c) {
        return (!(c >= 33 && c <= 126));
    }

    int skip() {
        int b;
        while ((b = readByte()) != -1 && isSpaceChar(b)) ;
        return b;
    }

    float nf() {
        return Float.parseFloat(is());
    }

    double id() {
        return Double.parseDouble(is());
    }

    char ic() {
        return (char) skip();
    }

    int[] iia(int n) {
        int a[] = new int[n];
        for (int i = 0; i < n; i++) a[i] = ii();
        return a;
    }

    long[] ila(int n) {
        long a[] = new long[n];
        for (int i = 0; i < n; i++) a[i] = il();
        return a;
    }

    String[] isa(int n) {
        String a[] = new String[n];
        for (int i = 0; i < n; i++) a[i] = is();
        return a;
    }

    double[][] idm(int n, int m) {
        double a[][] = new double[n][m];
        for (int i = 0; i < n; i++) for (int j = 0; j < m; j++) a[i][j] = id();
        return a;
    }

    int[][] iim(int n, int m) {
        int a[][] = new int[n][m];
        for (int i = 0; i < n; i++) for (int j = 0; j < m; j++) a[i][j] = ii();
        return a;
    }
}