Problem: The crowdedness of the discotheque would never stop our friends from having fun, but a bit more spaciousness won't hurt, will it?

The discotheque can be seen as an infinite xy-plane, in which there are a total of n dancers. Once someone starts moving around, they will move only inside their own movement range, which is a circular area Ci described by a center (xi, yi) and a radius ri. No two ranges' borders have more than one common point, that is for every pair (i, j) (1 ≤ i < j ≤ n) either ranges Ci and Cj are disjoint, or one of them is a subset of the other. Note that it's possible that two ranges' borders share a single common point, but no two dancers have exactly the same ranges.

Tsukihi, being one of them, defines the spaciousness to be the area covered by an odd number of movement ranges of dancers who are moving. An example is shown below, with shaded regions representing the spaciousness if everyone moves at the same time.

<image>

But no one keeps moving for the whole night after all, so the whole night's time is divided into two halves — before midnight and after midnight. Every dancer moves around in one half, while sitting down with friends in the other. The spaciousness of two halves are calculated separately and their sum should, of course, be as large as possible. The following figure shows an optimal solution to the example above.

<image>

By different plans of who dances in the first half and who does in the other, different sums of spaciousness over two halves are achieved. You are to find the largest achievable value of this sum.

Input

The first line of input contains a positive integer n (1 ≤ n ≤ 1 000) — the number of dancers.

The following n lines each describes a dancer: the i-th line among them contains three space-separated integers xi, yi and ri ( - 106 ≤ xi, yi ≤ 106, 1 ≤ ri ≤ 106), describing a circular movement range centered at (xi, yi) with radius ri.

Output

Output one decimal number — the largest achievable sum of spaciousness over two halves of the night.

The output is considered correct if it has a relative or absolute error of at most 10 - 9. Formally, let your answer be a, and the jury's answer be b. Your answer is considered correct if <image>.

Examples

Input

5
2 1 6
0 4 1
2 -1 3
1 -2 1
4 -1 1


Output

138.23007676


Input

8
0 0 1
0 0 2
0 0 3
0 0 4
0 0 5
0 0 6
0 0 7
0 0 8


Output

289.02652413

Note

The first sample corresponds to the illustrations in the legend.

Solution (in JAVA):

Solution:
import java.io.*;
import java.util.*;


public class CF418D {

    private static final boolean TEST_CASES = false;
    private int[][] cont;

    void solve(int testCaseNo, InputReader in, PrintWriter out) {
        final int n = in.nextInt();
        Node[] nodes = new Node[n];
        for (int i = 0; i < n; i++) {
            int x = in.nextInt(), y = in.nextInt(), r = in.nextInt();
            nodes[i] = new Node(x, y, r);
        }
        Arrays.sort(nodes, (o1, o2) -> Integer.compare(o2.r, o1.r));
        for (int i = 0; i < n; ++i) {
            Node node = nodes[i];
            node.sign = 1;
            node.parent = -1;
            node.gp = 0;
            node.id = i;
        }
        cont = new int[n][n];

        makeTreeLinks(nodes);

        long res = calc(nodes);
        for (int i = 0; i < n; i++) {
            changeGroup(i, nodes);
            long newSum = calc(nodes);
            if (newSum < res)
                changeGroup(i, nodes);
            else res = newSum;
        }
        double r = Math.PI*res;
        out.println(r);
    }

    private void changeGroup(int c, Node[] nodes) {
        deleteNode(c, nodes);
        nodes[c].gp = 1 - nodes[c].gp;
        addNode(c, nodes);
    }


    private void addNode(int c, Node[] nodes) {
        int curGP = nodes[c].gp;

        int par = -1;
        for (int i = 0; i < nodes.length; i++) {
            if (nodes[i].gp != curGP) continue;
            if (contains(i, c, nodes)) par = i;
        }

        // children can be decendants also!

        addLink(par, c, nodes);
        for (int i = 0; i < nodes.length; i++) {
            Node node = nodes[i];
            if (node.gp != curGP) continue;
            if (node.parent != par) continue;
            if (i == c) continue;
            if (!contains(c, i, nodes)) continue;
            removeLink(par, i, nodes);
            addLink(c, i, nodes);
        }

//        for (Node node : nodes) {
//            if (node.gp != curGP) continue;
//            if (contains(c, node.id, nodes) && contains(node.parent, c, nodes)) {
//                addLink(node.parent, c, nodes);
//                removeLink(node.parent, node.id, nodes);
//                addLink(c, node.id, nodes);
//            } else if (contains(node.id, c, nodes)) {
//                boolean excep = true;
//                for (Integer nn : node.children) {
//                    if (contains(c, nn, nodes)) {
//                        excep = false;
//                        break;
//                    }
//                }
//                if (excep) {
//                    addLink(node.id, c, nodes);
//                }
//            }
//        }
    }

    private void deleteNode(int c, Node[] nodes) {
        for (Integer ch : nodes[c].children)
            addLink(nodes[c].parent, ch, nodes);
        nodes[c].children.clear();
        removeLink(nodes[c].parent, c, nodes);
    }

    private void addLink(int par, Integer ch, Node[] nodes) {
        nodes[ch].parent = par;
        if (par > -1) nodes[par].children.add(ch);
    }

    private void removeLink(int parent, int child, Node[] nodes) {
        if (parent > -1) nodes[parent].children.remove(child);
        nodes[child].parent = -1;
    }

    private long calc(Node[] nodes) {
        long res = 0;
        for (Node n : nodes) {
            n.sign = 1;
            if (n.parent > -1) n.sign = (-1) * nodes[n.parent].sign;
            res += n.val * n.sign;
        }
        return res;
    }

    private void makeTreeLinks(Node[] nodes) {
        final int n = nodes.length;
        for (int i = 0; i <n; i++) {
            int par = findParent(nodes, i);
            addLink(par, i, nodes);
        }
    }

    private int findParent(Node[] nodes, int c) {
        final int n = nodes.length;
        for (int i = c-1; i >= 0; --i) {
            if (contains(i, c, nodes)) {
                return i;
            }
        }
        return -1;
    }


    private boolean contains(int p, int c, Node[] nodes) {
        if (p == c) return false;
        if (p == -1) return true;
        Node par = nodes[p];
        Node child = nodes[c];
        if (par.gp != child.gp) return false;

        if (cont[p][c] != 0) {
            if (cont[p][c] > 0) return true;
            return false;
        }

        if (par.r <= child.r) {
            cont[p][c] = -1;
            return false;
        }
        double thres = par.r + child.r;
        double dist = findDist(par.x, par.y, child.x, child.y);

        if (dist < thres) {
            cont[p][c] = 1;
            return true;
        } else {
            cont[p][c] = -1;
            return false;
        }
    }

    private double findDist(long x, long y, long x1, long y1) {
        return Math.sqrt((x - x1) * (x - x1) + (y - y1) * (y - y1));
    }

    static class Node {
        int x, y, r;
        int gp;
        int parent;
        int id;
        int sign;
        long val;
        Set<Integer> children = new HashSet<>();
        Node(int xx, int yy, int rr) {
            x = xx; y = yy; r = rr;
            val = (long)rr * rr;
        }
    }


    private static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

        /**
         * @return null if end of stream
         */
        public String readLine() {
            try {
                return reader.readLine();
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

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

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

    }

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

        int testCases = TEST_CASES ? in.nextInt() : 1;

        CF418D solver = new CF418D();
        for (int testCase = 0; testCase < testCases; testCase++) {
            solver.solve(testCase, in, out);
        }
        out.flush();
        out.close();
    }
}