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:
import java.util.*;
import java.awt.List;
import java.io.*;
import java.lang.*;
import java.lang.reflect.Array;
public class code8 {

    public static long[] stree = new long[1000000];
    
    public static void main(String[] args) {
        InputReader in = new InputReader(System.in);
        PrintWriter pw = new PrintWriter(System.out);

        // Code starts..

        
        
        
        
        int n = in.nextInt();
        long[] dp = new long[n];
        query[] qr = new query[n];
    
        for(int i=0; i<n; i++)
        {
            int r = in.nextInt();
            int h = in.nextInt();
            qr[i] = new query(r, h, r*(long)r*h, i);
            
            
            
        }
        
        
        
        Arrays.sort(qr);
        long mx = 0;
        for(int i=0; i<n; i++)
        {
            query q = qr[i];
            long x = q.x;
            mx = maxtree(0, n-1, 0, q.idx-1, 0);
            update(0, n-1, q.idx, mx+x, 0, dp);
       
            
        }
        double ans = 0;
        
        for(int i=0; i<n; i++)
            ans = Math.max(((double)dp[i]*2 * Math.asin(1)), ans);

        pw.print(ans);        
        
        // code ends...

        pw.flush();
        pw.close();
    }

    
    
    
    public static void update(int ll, int rl, int idx, long val, int node, long[] dp) {
        
        //System.out.println(ll+" "+rl);
        
        if(idx < ll || idx > rl)
            return;
        
        if(ll==rl)
        {
            dp[idx] = val;
            stree[node] = val;
        }
        else
        {
            
            int mid = (rl+ll)/2;
            if (idx >= ll && idx <= mid) 
                    update(ll, mid, idx, val, 2*node+1, dp); 
            else
                    update(mid+1, rl, idx, val, 2*node + 2, dp); 
             stree[node] = Math.max(stree[2 * node + 1],  
                     stree[2 * node + 2]); 
        }
        return;
    }
    
    
    public static long maxtree(int ll, int rl, int l, int r, int node) {
        if(l <= ll && r >= rl)
            return stree[node];
        
         if (rl < l || ll > r) 
                return 0; 
         
         
        int mid = (ll+rl)/2;
        return Math.max(maxtree(ll, mid, l, r, 2*node+1), 
                        maxtree(mid+1, rl, l, r, 2*node+2));
        
        
    }
    
    
    

    public static long[][] mul(long[][] a, long[][] b){
        
        
        int n = a.length;
        int m = b[0].length;
        long[][] c = new long[n][m];
        
        for(int i=0; i<n; i++)
            for(int j=0; j<m; j++)
            {
                long tmp = 0;
                for(int k=0; k<a[0].length; k++)
                    tmp =( (tmp+mod)%mod+(a[i][k]*b[k][j]+mod)%mod)%mod;
                c[i][j] = (tmp+mod)%mod;
            }
        
        return c;
    }
    
    
    
    public static long[][] pow(long[][] a,int  n)
    {
        
        long[][] res = a;
        while(n>0)
        {
            if(n%2==1)
            {
                res = mul(a, res);
            }
            
            a = mul(a, a);
            
            n/=2;
            
            
        }
        
        return res;
        
        
    }
    
    
    
    
    

    
    
    

    
    public static boolean isSubSequence(char[] str2, String str1) {

        int j = 0;
        int m = str1.length();
        int n = str2.length;

        for (int i = 0; i < n && j < m; i++)

            if (str1.charAt(j) == str2[i])

                j++;

        return (j == m);
    }

    static class InputReader {

        private final InputStream stream;
        private final byte[] buf = new byte[8192];
        private int curChar, snumChars;
        private SpaceCharFilter filter;

        public InputReader(InputStream stream) {
            this.stream = stream;
        }

        public int snext() {
            if (snumChars == -1)
                throw new InputMismatchException();
            if (curChar >= snumChars) {
                curChar = 0;
                try {
                    snumChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (snumChars <= 0)
                    return -1;
            }
            return buf[curChar++];
        }

        public int nextInt() {
            int c = snext();
            while (isSpaceChar(c)) {
                c = snext();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = snext();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = snext();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public long nextLong() {
            int c = snext();
            while (isSpaceChar(c)) {
                c = snext();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = snext();
            }
            long res = 0;
            do {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = snext();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public int[] nextIntArray(int n) {
            int a[] = new int[n];
            for (int i = 0; i < n; i++) {
                a[i] = nextInt();
            }
            return a;
        }

        public String readString() {
            int c = snext();
            while (isSpaceChar(c)) {
                c = snext();
            }
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = snext();
            } while (!isSpaceChar(c));
            return res.toString();
        }

        public String nextLine() {
            int c = snext();
            while (isSpaceChar(c))
                c = snext();
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = snext();
            } while (!isEndOfLine(c));
            return res.toString();
        }

        public boolean isSpaceChar(int c) {
            if (filter != null)
                return filter.isSpaceChar(c);
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

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

        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);
        }
    }

    public static long c = 0;

    public static long mod = (long)Math.pow(10, 6)+3;
    public static int d;
    public static int p;
    public static int q;
    public static boolean flag;
    //public static long INF = Long.MAX_VALUE;

    public static void factSieve(int[] fact, long n) {

        for (int i = 2; i <= n; i += 2)
            fact[i] = 2;

        for (int i = 3; i <= n; i += 2) {
            if (fact[i] == 0) {
                fact[i] = i;

                for (int j = i; (long) j * i <= n; j++) {
                    fact[(int) ((long) i * j)] = i;
                }
            }
        }

        /*
         * int k = 1000; while(k!=1) { System.out.print(a[k]+" "); k /= a[k];
         * 
         * }
         */
    }

    public static long floorsqrt(long n) {
        long ans = 0;
        long l = 0;
        long r = n;
        long mid = 0;
        while (l <= r) {
            mid = (l + r) / 2;
            if (mid * mid == n)
                return mid;

            if (mid * mid > n) {
                r = mid - 1;
            } else {
                ans = mid;
                l = mid + 1;
            }

        }

        return ans;
    }

    public static long fun(int[] a, int[] b, int m, int n) {
        long result = 0;
        for (int i = 0; i < m; i++)
            for (int j = 0; j < m; j++) {
                long[] fib = new long[Math.max(2, n + 2)];
                fib[1] = a[i];
                fib[2] = b[j];
                for (int k = 3; k <= n; k++)
                    fib[k] = (fib[k - 1] % mod + fib[k - 2] % mod) % mod;
                result = (result % mod + fib[n] % mod) % mod;
            }

        return result;

    }

    /*
     * public static double slope(pair p1, pair p2) { double m = INF; if((p1.x -
     * p2.x)!=0) m = p1.y - p2.y/(p1.x - p2.x);
     * 
     * 
     * return Math.abs(m);
     * 
     * }
     */

    public static int count(String[] s, int f) {
        int count = 0;
        int n = s[0].length();

        if (f == 1) {
            for (int i = 0; i < n; i++) {
                for (int j = 0; j < n; j++) {
                    if (i % 2 == 0) {
                        if (j % 2 == 0 && s[i].charAt(j) == '0')
                            count++;
                        if (j % 2 == 1 && s[i].charAt(j) == '1')
                            count++;
                    }
                    if (i % 2 == 1) {
                        if (j % 2 == 1 && s[i].charAt(j) == '0')
                            count++;
                        if (j % 2 == 0 && s[i].charAt(j) == '1')
                            count++;
                    }

                }
            }
        } else {

            count = 0;

            for (int i = 0; i < n; i++) {
                for (int j = 0; j < n; j++) {
                    if (i % 2 == 1) {
                        if (j % 2 == 0 && s[i].charAt(j) == '0')
                            count++;
                        if (j % 2 == 1 && s[i].charAt(j) == '1')
                            count++;
                    }
                    if (i % 2 == 0) {
                        if (j % 2 == 1 && s[i].charAt(j) == '0')
                            count++;
                        if (j % 2 == 0 && s[i].charAt(j) == '1')
                            count++;
                    }

                }
            }

        }

        return count;

    }

    public static int gcd(int p2, int p22) {
        if (p2 == 0)
            return (int) p22;
        return gcd(p22 % p2, p2);
    }

    public static int findGCD(int arr[], int n) {
        int result = arr[0];
        for (int i = 1; i < n; i++)
            result = gcd(arr[i], result);

        return result;
    }

    public static void nextGreater(long[] a, int[] ans) {

        Stack<Integer> stk = new Stack<>();
        stk.push(0);

        for (int i = 1; i < a.length; i++) {

            if (!stk.isEmpty()) {
                int s = stk.pop();
                while (a[s] < a[i]) {
                    ans[s] = i;
                    if (!stk.isEmpty())
                        s = stk.pop();
                    else
                        break;
                }
                if (a[s] >= a[i])
                    stk.push(s);
            }

            stk.push(i);

        }
        return;

    }

    public static void nextGreaterRev(long[] a, int[] ans) {

        int n = a.length;
        int[] pans = new int[n];
        Arrays.fill(pans, -1);
        long[] arev = new long[n];
        for (int i = 0; i < n; i++)
            arev[i] = a[n - 1 - i];

        Stack<Integer> stk = new Stack<>();
        stk.push(0);

        for (int i = 1; i < n; i++) {

            if (!stk.isEmpty()) {
                int s = stk.pop();
                while (arev[s] < arev[i]) {
                    pans[s] = n - i - 1;
                    if (!stk.isEmpty())
                        s = stk.pop();
                    else
                        break;
                }
                if (arev[s] >= arev[i])
                    stk.push(s);
            }

            stk.push(i);

        }

        // for(int i=0; i<n; i++)
        // System.out.print(pans[i]+" ");

        for (int i = 0; i < n; i++)
            ans[i] = pans[n - i - 1];

        return;

    }

    public static void nextSmaller(long[] a, int[] ans) {

        Stack<Integer> stk = new Stack<>();
        stk.push(0);

        for (int i = 1; i < a.length; i++) {

            if (!stk.isEmpty()) {
                int s = stk.pop();
                while (a[s] > a[i]) {
                    ans[s] = i;
                    if (!stk.isEmpty())
                        s = stk.pop();
                    else
                        break;
                }
                if (a[s] <= a[i])
                    stk.push(s);
            }

            stk.push(i);

        }
        return;

    }

    public static long lcm(int[] numbers) {
        long lcm = 1;
        int divisor = 2;
        while (true) {
            int cnt = 0;
            boolean divisible = false;
            for (int i = 0; i < numbers.length; i++) {
                if (numbers[i] == 0) {
                    return 0;
                } else if (numbers[i] < 0) {
                    numbers[i] = numbers[i] * (-1);
                }
                if (numbers[i] == 1) {
                    cnt++;
                }
                if (numbers[i] % divisor == 0) {
                    divisible = true;
                    numbers[i] = numbers[i] / divisor;
                }
            }
            if (divisible) {
                lcm = lcm * divisor;
            } else {
                divisor++;
            }
            if (cnt == numbers.length) {
                return lcm;
            }
        }
    }

    public static long fact(long n) {

        long factorial = 1;
        for (int i = 1; i <= n; i++) {
            factorial *= i;
        }
        return factorial;
    }

    public static int lowerLimit(int[] a, int n) {
        int ans = 0;

        int ll = 0;
        int rl = a.length - 1;
        // System.out.println(a[rl]+" "+n);
        if (a[0] > n)
            return 0;
        if (a[0] == n)
            return 1;
        else if (a[rl] <= n)
            return rl + 1;

        while (ll <= rl) {

            int mid = (ll + rl) / 2;
            if (a[mid] == n) {
                ans = mid + 1;
                break;
            }

            else if (a[mid] > n) {
                rl = mid - 1;

            } else {
                ans = mid + 1;
                ll = mid + 1;
            }
        }

        return ans;
    }

    public static long choose(long total, long choose) {
        if (total < choose)
            return 0;
        if (choose == 0 || choose == total)
            return 1;
        return (choose(total - 1, choose - 1) + choose(total - 1, choose)) % mod;
    }

    public static int[] suffle(int[] a, Random gen) {
        int n = a.length;
        for (int i = 0; i < n; i++) {
            int ind = gen.nextInt(n - i) + i;
            int temp = a[ind];
            a[ind] = a[i];
            a[i] = temp;
        }
        return a;
    }

    public static pair[] suffle(pair[] a, Random gen) {
        int n = a.length;
        for (int i = 0; i < n; i++) {
            int ind = gen.nextInt(n - i) + i;
            pair temp = a[ind];
            a[ind] = a[i];
            a[i] = temp;
        }
        return a;
    }
    public static query[] suffle(query[] a, Random gen) {
        int n = a.length;
        for (int i = 0; i < n; i++) {
            int ind = gen.nextInt(n - i) + i;
            query temp = a[ind];
            a[ind] = a[i];
            a[i] = temp;
        }
        return a;
    }
    
    
    
    
    public static int floorSearch(int arr[], int low, int high, int x) {
        if (low > high)
            return -1;

        if (x > arr[high])
            return high;
        int mid = (low + high) / 2;

        if (mid > 0 && arr[mid - 1] < x && x < arr[mid])
            return mid - 1;

        if (x < arr[mid])
            return floorSearch(arr, low, mid - 1, x);

        return floorSearch(arr, mid + 1, high, x);
    }

    public static void swap(int a, int b) {
        int temp = a;
        a = b;
        b = temp;
    }

    public static ArrayList<Integer> primeFactorization(int n) {
        ArrayList<Integer> a = new ArrayList<Integer>();
        for (int i = 2; i * i <= n; i++) {
            while (n % i == 0) {
                a.add(i);
                n /= i;
            }
        }
        if (n != 1)
            a.add(n);
        return a;
    }
    
    
    

    public static void sieve(boolean[] isPrime, int n) {
        for (int i = 1; i < n; i++)
            isPrime[i] = true;

        isPrime[0] = false;
        isPrime[1] = false;

        for (int i = 2; i * i < n; i++) {
            if (isPrime[i] == true) {
                for (int j = (2 * i); j < n; j += i)
                    isPrime[j] = false;
            }
        }
    }

    public static int lowerbound(ArrayList<Long> net, long c2) {
        int i = Collections.binarySearch(net, c2);
        if (i < 0)
            i = -(i + 2);
        return i;

    }
    
    public static int lowerboundArray(int[] dis, int c2) {
        int i = Arrays.binarySearch(dis, c2);
        if (i < 0)
            i = -(i + 2);
        return i;

    }

    public static int uperbound(ArrayList<Integer> list, int c2) {
        int i = Collections.binarySearch(list, c2);
        if (i < 0)
            i = -(i + 1);
        return i;

    }

    public static int uperboundArray(int[] dis, int c2) {
        int i = Arrays.binarySearch(dis, c2);
        if (i < 0)
            i = -(i + 1);
        return i;

    }

    public static long[] sort(long[] a) {
        Random gen = new Random();
        int n = a.length;
        for (int i = 0; i < n; i++) {
            int ind = gen.nextInt(n - i) + i;
            long temp = a[ind];
            a[ind] = a[i];
            a[i] = temp;
        }

        Arrays.sort(a);
        return a;
    }

    public static int[] sort(int[] a) {
        Random gen = new Random();
        int n = a.length;
        for (int i = 0; i < n; i++) {
            int ind = gen.nextInt(n - i) + i;
            int temp = a[ind];
            a[ind] = a[i];
            a[i] = temp;
        }

        Arrays.sort(a);
        return a;
    }

    public static int GCD(int a, int b) {
        if (b == 0)
            return a;
        else
            return GCD(b, a % b);
    }

    public static long GCD(long a, long b) {
        if (b == 0)
            return a;
        else
            return GCD(b, a % b);
    }

    public static void extendedEuclid(int A, int B) {
        if (B == 0) {
            d = A;
            p = 1;
            q = 0;
        } else {
            extendedEuclid(B, A % B);
            int temp = p;
            p = q;
            q = temp - (A / B) * q;
        }
    }

    public static long LCM(long a, long b) {
        return (a * b) / GCD(a, b);
    }

    public static int LCM(int a, int b) {
        return (a * b) / GCD(a, b);
    }

    public static int binaryExponentiation(int x, int n) {
        int result = 1;
        while (n > 0) {
            if (n % 2 == 1)
                result = result * x;
            x = x * x;
            n = n / 2;
        }
        return result;
    }

    public static int[] countDer(int n) {
        int der[] = new int[n + 1];

        der[0] = 1;
        der[1] = 0;
        der[2] = 1;

        for (int i = 3; i <= n; ++i)
            der[i] = (i - 1) * (der[i - 1] + der[i - 2]);

        // Return result for n
        return der;
    }

    static long binomialCoeff(int n, int k) {
        long C[][] = new long[n + 1][k + 1];
        int i, j;

        // Calculate value of Binomial Coefficient in bottom up manner
        for (i = 0; i <= n; i++) {
            for (j = 0; j <= Math.min(i, k); j++) {
                // Base Cases
                if (j == 0 || j == i)
                    C[i][j] = 1;

                // Calculate value using previosly stored values
                else
                    C[i][j] = C[i - 1][j - 1] + C[i - 1][j];
            }
        }

        return C[n][k];
    }

    public static long binaryExponentiation(long x, long n) {
        long result = 1;
        while (n > 0) {
            if (n % 2 == 1)
                result = result * x;
            x = (x % mod * x % mod) % mod;
            n = n / 2;
        }
        return result;
    }

    public static int modularExponentiation(int x, int n, int M) {
        int result = 1;
        while (n > 0) {
            if (n % 2 == 1)
                result = (result * x) % M;
            x = (x * x) % M;
            n = n / 2;
        }
        return result;
    }

    public static long modularExponentiation(long x, long n, long M) {
        long result = 1;
        while (n > 0) {
            if (n % 2 == 1)
                result = (result * x) % M;
            x = (x * x) % M;
            n = n / 2;
        }
        return result;
    }

    public static int modInverse(int A, int M) {
        return modularExponentiation(A, M - 2, M);
    }

    public static long sie(long A, long M) {
        return modularExponentiation(A, M - 2, M);
    }

    public static boolean checkYear(int year) {
        if (year % 400 == 0)
            return true;

        if (year % 100 == 0)
            return false;

        if (year % 4 == 0)
            return true;
        return false;
    }

    public static boolean isPrime(int n) {

        if (n <= 1)
            return false;
        if (n <= 3)
            return true;

        if (n % 2 == 0 || n % 3 == 0)
            return false;

        for (int i = 5; i * i <= n; i = i + 6) {
            if (n % i == 0 || n % (i + 2) == 0)
                return false;
        }

        return true;
    }

    static class pair implements Comparable<pair>

    {
        Integer x, y;

        pair(int x, int y) {
            this.x = x;
            this.y = y;
        }

        public int compareTo(pair o) {
            int result = x.compareTo(o.x);
            if (result == 0)
                result = y.compareTo(o.y);

            return result;
        }

        public String toString() {
            return x + " " + y;
        }

        public boolean equals(Object o) {
            if (o instanceof pair) {
                pair p = (pair) o;
                return p.x == x && p.y == y;
            }
            return false;
        }

        public int hashCode() {
            return new Long(x).hashCode() * 31 + new Long(y).hashCode();
        }

    }

    static class triplet implements Comparable<triplet> {
        Integer x, y, z;

        triplet(int x, int y, int z) {
            this.x = x;
            this.y = y;
            this.z = z;
        }

        public int compareTo(triplet o) {
            int result = x.compareTo(o.x);
            if (result == 0)
                result = y.compareTo(o.y);
            if (result == 0)
                result = z.compareTo(o.z);

            return result;
        }

        public boolean equlas(Object o) {
            if (o instanceof triplet) {
                triplet p = (triplet) o;
                return x == p.x && y == p.y && z == p.z;
            }
            return false;
        }

        public String toString() {
            return x + " " + y + " " + z;
        }

        public int hashCode() {
            return new Long(x).hashCode() * 31 + new Long(y).hashCode() + new Long(z).hashCode();
        }
    }

    
    static class query implements Comparable<query> {
        Integer l,r, idx;
        Long x;
    
        query(int l, int r, long x, int id)
        {
            this.l = l ;
            this.r = r;
            this.x = x;
            this.idx = id;
        }
        
        public int compareTo(query o) {
            int result = x.compareTo(o.x);
            if(result==0)
                result = - idx.compareTo(o.idx);
                
            return result;
        }

        
    

        
    }
    
    /*
     * static class node implements Comparable<node>
     * 
     * { Integer x, y, z; node(int x,int y, int z) { this.x=x; this.y=y; this.z=z; }
     * 
     * public int compareTo(pair o) { int result = x.compareTo(o.x); if(result==0)
     * result = y.compareTo(o.y); if(result==0) result = z.compareTo(z); return
     * result; }
     * 
     * @Override public int compareTo(node o) { // TODO Auto-generated method stub
     * return 0; } }
     */
}