Problem: You've got a weighted tree, consisting of n vertices. Each edge has a non-negative weight. The length of the path between any two vertices of the tree is the number of edges in the path. The weight of the path is the total weight of all edges it contains. 

Two vertices are close if there exists a path of length at most l between them and a path of weight at most w between them. Count the number of pairs of vertices v, u (v < u), such that vertices v and u are close.

Input

The first line contains three integers n, l and w (1 ≤ n ≤ 105, 1 ≤ l ≤ n, 0 ≤ w ≤ 109). The next n - 1 lines contain the descriptions of the tree edges. The i-th line contains two integers pi, wi (1 ≤ pi < (i + 1), 0 ≤ wi ≤ 104), that mean that the i-th edge connects vertex (i + 1) and pi and has weight wi.

Consider the tree vertices indexed from 1 to n in some way.

Output

Print a single integer — the number of close pairs.

Please, do not use the %lld specifier to read or write 64-bit integers in С++. It is preferred to use the cin, cout streams or the %I64d specifier.

Examples

Input

4 4 6
1 3
1 4
1 3


Output

4


Input

6 2 17
1 3
2 5
2 13
1 6
5 9


Output

9

Solution (in JAVA):

Solution:
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.io.PrintStream;
import java.io.BufferedInputStream;
import java.util.InputMismatchException;
import java.io.IOException;
import java.util.Collections;
import java.io.InputStream;
import java.util.ArrayList;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
	public static void main(String[] args) {
		InputStream inputStream = System.in;
		OutputStream outputStream = System.out;
		BufferedInputStream in = new BufferedInputStream(inputStream);
		PrintWriter out = new PrintWriter(outputStream);
		TaskE solver = new TaskE();
		solver.solve(1, in, out);
		out.close();
	}

	static class TaskE {
		int n;
		int w;
		int l;
		int[][][] gw;
		int[][] g;
		int[] distFromRoot;
		boolean[] visited;
		int[] qu;
		int[] p;
		int[] save;
		int[] depth;
		long ans = 0;
		long ans2 = 0;
		BinaryIndexTree bin;

		long count(ArrayList<Pa> lp, int fi, int se) {
			int tot = 0;
			long re = 0;
			Collections.sort(lp);

			for (int i = lp.size() - 1, j = 0; i >= 0; --i) {
				while (j < lp.size() && lp.get(j).first + lp.get(i).first <= fi) {
					bin.add(lp.get(j).second, 1);
					save[tot++] = lp.get(j).second;
					j++;
				}

				re += bin.sum(se - lp.get(i).second + 1);

				if (lp.get(i).first * 2 <= fi && lp.get(i).second * 2 <= se) re--;
			}

			for (int i = 0; i < tot; ++i) {
				bin.add(save[i], -1);
			}
			return re;
		}

		void calc(int x) {

			//bfs
			int fq = 0, lq = 0;
			qu[lq++] = x;
			distFromRoot[x] = 0;
			p[x] = -1;
			depth[x] = 0;

			ArrayList<Pa> all = new ArrayList<>();
			while (fq < lq) {
				int front = qu[fq++];
				for (int[] ed : gw[front]) {
					int u = ed[0];
					if (u != p[front] && !visited[u]) {
						qu[lq++] = u;
						distFromRoot[u] = distFromRoot[front] + ed[1];
						depth[u] = depth[front] + 1;
						p[u] = front;
						all.add(new Pa(distFromRoot[u], depth[u]));

						if (distFromRoot[u] <= w && depth[u] <= l) ans2++;
					}
				}
			}

			ans += count(all, w, l);

			for (int child : g[x])
				if (!visited[child]) {
					fq = lq = 0;
					qu[lq++] = child;
					while (fq < lq) {
						int front = qu[fq++];
						for (int u : g[front])
							if (u != p[front] && !visited[u]) {
								qu[lq++] = u;
							}
					}

					all.clear();
					for (int i = 0; i < lq; ++i) {
						int u = qu[i];
						all.add(new Pa(distFromRoot[u], depth[u]));
					}
					ans -= count(all, w, l);

				}

		}

		public void solve(int testNumber, BufferedInputStream _in, PrintWriter out) {
			InputReader in = new InputReader(_in);
			long startTime = System.currentTimeMillis();

			n = in.nextInt();
			l = in.nextInt();
			w = in.nextInt();
			int[] from = new int[n - 1];
			int[] to = new int[n - 1];
			int[] w = new int[n - 1];
			int P;
			for (int i = 0; i < n - 1; ++i) {
				P = in.nextInt() - 1;
				w[i] = in.nextInt();
				from[i] = P;
				to[i] = i + 1;
			}
			gw = Graphs.packWU(n, from, to, w);
			g = Graphs.packU(n, from, to);
			distFromRoot = new int[n];
			visited = new boolean[n];
			qu = new int[n];
			p = new int[n];
			bin = new BinaryIndexTree(l + 10);
			save = new int[n];
			depth = new int[n];

			Graphs._Centroid cent = new Graphs._Centroid(n);
			cent.g = g;
			cent.ctpar = new int[n];
			cent.buildCentroidTree(0);

			for (int x : cent.cent) {
				calc(x);
				visited[x] = true;
			}
			out.println(ans / 2 + ans2);
			in.close();
			System.err.println("Time: " + (System.currentTimeMillis() - startTime) + " miliseconds");
		}

	}

	static class Graphs {
		public static int[][] packU(int n, int[] from, int[] to) {
			int[][] g = new int[n][];
			int[] p = new int[n];
			for (int f : from)
				p[f]++;
			for (int t : to)
				p[t]++;
			for (int i = 0; i < n; i++)
				g[i] = new int[p[i]];
			for (int i = 0; i < from.length; i++) {
				g[from[i]][--p[from[i]]] = to[i];
				g[to[i]][--p[to[i]]] = from[i];
			}
			return g;
		}

		public static int[][][] packWU(int n, int[] from, int[] to, int[] w) {
			int[][][] g = new int[n][][];
			int[] p = new int[n];
			for (int f : from)
				p[f]++;
			for (int t : to)
				p[t]++;
			for (int i = 0; i < n; i++)
				g[i] = new int[p[i]][2];
			for (int i = 0; i < from.length; i++) {
				--p[from[i]];
				g[from[i]][p[from[i]]][0] = to[i];
				g[from[i]][p[from[i]]][1] = w[i];
				--p[to[i]];
				g[to[i]][p[to[i]]][0] = from[i];
				g[to[i]][p[to[i]]][1] = w[i];
			}
			return g;
		}

		static class _Centroid {
			int[][] g;
			boolean[] sed;
			int[] par;
			int[] ord;
			int[] des;
			int[] ctpar;
			int[] cent;
			int ncent = 0;

			_Centroid(int n) {
				des = new int[n];
				ord = new int[n];
				sed = new boolean[n];
				par = new int[n];
				cent = new int[n];
			}

			int buildCentroidTree(int root) {
				// parent and level-order
				ord[0] = root;
				par[root] = -1;
				int r = 1;
				for (int p = 0; p < r; p++) {
					int cur = ord[p];
					for (int nex : g[cur]) {
						if (par[cur] != nex && !sed[nex]) {
							ord[r++] = nex;
							par[nex] = cur;
						}
					}
				}
				// if(r == 1)return;

				// DP and find a separator
				int sep = -1; // always exists
				outer:
				for (int i = r - 1; i >= 0; i--) {
					int cur = ord[i];
					des[cur] = 1;
					for (int e : g[cur]) {
						if (par[cur] != e && !sed[e]) des[cur] += des[e];
					}
					if (r - des[cur] <= r / 2) {
						for (int e : g[cur]) {
							if (par[cur] != e && !sed[e] && des[e] >= r / 2 + 1) continue outer;
						}
						sep = cur;
						break;
					}
				}
				cent[ncent++] = sep;
				sed[sep] = true;
				for (int e : g[sep]) {
					if (!sed[e]) ctpar[buildCentroidTree(e)] = sep;
				}
				return sep;
			}

		}

	}

	static class BinaryIndexTree {
		long[] a;

		public BinaryIndexTree(int n) {
			a = new long[n];
		}

		public long sum(int i) {
			long sum = 0;
			while (i > 0) {
				sum += a[i - 1];
				i -= Integer.lowestOneBit(i);
			}
			return sum;
		}

		void add(int i, long delta) {
			while (i < a.length) {
				a[i] += delta;
				i += Integer.lowestOneBit(i + 1);
			}
		}

	}

	static class InputReader {
		private InputStream stream;
		private byte[] buf = new byte[1024];
		private int curChar;
		private int numChars;

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

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

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

		public static boolean isSpaceChar(int c) {
			return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
		}

		public void close() {

		}

	}

	static class Pa implements Comparable<Pa> {
		int first;
		int second;

		public Pa(int first, int second) {
			this.first = first;
			this.second = second;
		}


		public int compareTo(Pa o) {
			return Integer.compare(first, o.first);
		}

	}
}