Problem: Masha is fond of cacti. When she was a little girl, she decided to plant a tree. Now Masha wants to make a nice cactus out of her tree.

Recall that tree is a connected undirected graph that has no cycles. Cactus is a connected undirected graph such that each vertex belongs to at most one cycle.

Masha has some additional edges that she can add to a tree. For each edge she knows which vertices it would connect and the beauty of this edge. Masha can add some of these edges to the graph if the resulting graph is a cactus. Beauty of the resulting cactus is sum of beauties of all added edges. 

Help Masha find out what maximum beauty of the resulting cactus she can achieve.

Input

The first line of the input data contains two integers n and m — the number of vertices in a tree, and the number of additional edges available (3 ≤ n ≤ 2·105; 0 ≤ m ≤ 2·105).

Let us describe Masha's tree. It has a root at vertex 1. The second line contains n - 1 integers: p2, p3, ..., pn, here pi — is the parent of a vertex i — the first vertex on a path from the vertex i to the root of the tree (1 ≤ pi < i).

The following m lines contain three integers ui, vi and ci — pairs of vertices to be connected by the additional edges that Masha can add to the tree and beauty of edge (1 ≤ ui, vi ≤ n; ui ≠ vi; 1 ≤ ci ≤ 104).

It is guaranteed that no additional edge coincides with the edge of the tree.

Output

Output one integer — the maximum beauty of a cactus Masha can achieve.

Example

Input

7 3
1 1 2 2 3 3
4 5 1
6 7 1
2 3 1


Output

2

Solution (in JAVA):

Solution:

import java.io.*;
import java.util.ArrayList;
import java.util.List;

/**
 * Created by dalt on 2018/4/1.
 */
public class CF856D {
    public static BlockReader input;
    public static PrintStream output;

    public static void main(String[] args) throws FileNotFoundException {
        if (System.getProperty("ONLINE_JUDGE") == null) {
            input = new BlockReader(new FileInputStream("D:\\DataBase\\TESTCASE\\codeforces\\CF856D.in"));
            output = System.out;
        } else {
            input = new BlockReader(System.in);
            output = new PrintStream(new BufferedOutputStream(System.out), false);
        }

        solve();

        output.flush();
    }

    public static void solve() {
        int n = input.nextInteger();
        int m = input.nextInteger();

        Node[] nodes = new Node[n + 1];
        for (int i = 1; i <= n; i++) {
            nodes[i] = new Node();
            nodes[i].id = i;
        }

        for (int i = 2; i <= n; i++) {
            int id = input.nextInteger();
            Node father = nodes[id];
            father.children.add(nodes[i]);
            Node.join(father, nodes[i]);
        }

        for (int i = 1; i <= m; i++) {
            PseudoEdge edge = new PseudoEdge();
            edge.a = nodes[input.nextInteger()];
            edge.b = nodes[input.nextInteger()];
            edge.beauty = input.nextInteger();

            Node lca = Node.lca(edge.a, edge.b);
            lca.pseudoEdgeList.add(edge);
        }

        dpOnTree(nodes[1]);

        output.println(nodes[1].include);
    }


    public static void dpOnTree(Node node) {
        int notInclude = 0;
        for (Node child : node.children) {
            dpOnTree(child);
            notInclude += child.include;
        }

        long max = notInclude;
        for (PseudoEdge edge : node.pseudoEdgeList) {
            Node.getPath(edge.a, edge.b);
            Node.splay(edge.a);

            max = Math.max(max, edge.beauty + (notInclude - edge.a.sum));
        }
        node.include = max;
        node.notInclude = notInclude;
        node.pushUp();
    }


    public static class Node {
        static final Node NIL = new Node();

        static {
            NIL.highest = NIL;
            NIL.depth = Integer.MAX_VALUE;
            NIL.father = NIL;
            NIL.sum = 0;
        }

        int id;
        List<Node> children = new ArrayList<>();
        long include;
        long notInclude;
        List<PseudoEdge> pseudoEdgeList = new ArrayList<>();
        int depth;
        Node highest;
        Node left = NIL;
        Node right = NIL;
        Node father = NIL;
        long sum;
        boolean rev;
        Node pathFather = NIL;

        public static void join(Node father, Node child) {
            makeRoot(child);
            child.pathFather = father;
            child.depth = father.depth + 1;
        }

        public static void zig(Node x) {
            Node y = x.father;
            Node z = y.father;
            Node t = x.right;

            z.replaceChild(y, x);
            x.asRight(y);
            y.asLeft(t);

            y.pushUp();
        }

        public static void zag(Node x) {
            Node y = x.father;
            Node z = y.father;
            Node t = x.left;

            z.replaceChild(y, x);
            x.asLeft(y);
            y.asRight(t);

            y.pushUp();
        }

        public static void splay(Node x) {
            if (x == NIL) {
                return;
            }

            Node y, z;
            while ((y = x.father) != NIL) {
                if ((z = y.father) == NIL) {
                    y.pushDown();
                    x.pushDown();

                    if (x == y.left) {
                        zig(x);
                    } else {
                        zag(x);
                    }
                } else {
                    z.pushDown();
                    y.pushDown();
                    x.pushDown();

                    if (y == z.left) {
                        if (x == y.left) {
                            zig(y);
                            zig(x);
                        } else {
                            zag(x);
                            zig(x);
                        }
                    } else {
                        if (x == y.left) {
                            zig(x);
                            zag(x);
                        } else {
                            zag(y);
                            zag(x);
                        }
                    }
                }
            }

            x.pushDown();
            x.pushUp();
        }

        public static void access(Node x) {
            Node last = NIL;
            while (x != NIL) {
                splay(x);
                x.right.father = NIL;
                x.right.pathFather = x;
                x.asRight(last);
                x.pushUp();

                last = x;
                x = x.pathFather;
            }
        }

        public static void makeRoot(Node x) {
            access(x);
            Node.splay(x);
            x.reverse();
        }

        public static Node lca(Node a, Node b) {
            getPath(a, b);
            Node.splay(a);
            return a.highest;
        }

        public static void getPath(Node a, Node b) {
            makeRoot(a);
            access(b);
        }

        @Override
        public String toString() {
            return "" + id;
        }

        public void replaceChild(Node oldNode, Node newNode) {
            if (left == oldNode) {
                asLeft(newNode);
            } else {
                asRight(newNode);
            }
        }

        public void asRight(Node x) {
            right = x;
            x.father = this;
        }

        public void asLeft(Node x) {
            left = x;
            x.father = this;
        }

        public void pushUp() {
            sum = left.sum + right.sum + (include - notInclude);
            highest = this;
            if (highest.depth > left.highest.depth) {
                highest = left.highest;
            }
            if (highest.depth > right.highest.depth) {
                highest = right.highest;
            }
        }

        public void pushDown() {
            if (rev) {
                Node tmp = left;
                left = right;
                right = tmp;

                left.reverse();
                right.reverse();

                rev = false;
            }

            left.pathFather = pathFather;
            right.pathFather = pathFather;
        }

        public void reverse() {
            rev = !rev;
        }
    }

    public static class PseudoEdge {
        Node a;
        Node b;
        int beauty;

        @Override
        public String toString() {
            return a.toString() + ":" + b.toString() + ":" + beauty;
        }
    }

    public static class BlockReader {
        static final int EOF = -1;
        InputStream is;
        byte[] dBuf;
        int dPos, dSize, next;
        StringBuilder builder = new StringBuilder();

        public BlockReader(InputStream is) {
            this(is, 4096);
        }

        public BlockReader(InputStream is, int bufSize) {
            this.is = is;
            dBuf = new byte[bufSize];
            next = nextByte();
        }

        public int nextByte() {
            while (dPos >= dSize) {
                if (dSize == -1) {
                    return EOF;
                }
                dPos = 0;
                try {
                    dSize = is.read(dBuf);
                } catch (Exception e) {
                }
            }
            return dBuf[dPos++];
        }

        public String nextBlock() {
            builder.setLength(0);
            skipBlank();
            while (next != EOF && !Character.isWhitespace(next)) {
                builder.append((char) next);
                next = nextByte();
            }
            return builder.toString();
        }

        public void skipBlank() {
            while (Character.isWhitespace(next)) {
                next = nextByte();
            }
        }

        public int nextInteger() {
            skipBlank();
            int ret = 0;
            boolean rev = false;
            if (next == '+' || next == '-') {
                rev = next == '-';
                next = nextByte();
            }
            while (next >= '0' && next <= '9') {
                ret = (ret << 3) + (ret << 1) + next - '0';
                next = nextByte();
            }
            return rev ? -ret : ret;
        }

        public int nextBlock(char[] data, int offset) {
            skipBlank();
            int index = offset;
            int bound = data.length;
            while (next != EOF && index < bound && !Character.isWhitespace(next)) {
                data[index++] = (char) next;
                next = nextByte();
            }
            return index - offset;
        }

        public boolean hasMore() {
            skipBlank();
            return next != EOF;
        }
    }
}