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:
//package croc2013.r2;
import java.io.ByteArrayInputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.Comparator;
import java.util.InputMismatchException;

public class E {
	InputStream is;
	PrintWriter out;
	String INPUT = "";
	
	int L, W;
	
	void solve()
	{
		int n = ni();
		L = ni(); W = ni();
		int[] from = new int[n-1];
		int[] to = new int[n-1];
		int[] w = new int[n-1];
		for(int i = 0;i < n-1;i++){
			from[i] = i+1;
			to[i] = ni()-1;
			w[i] = ni();
		}
		int[][][] g = packWU(n, from, to, w);
		
		long ct = separate(g, 0, new boolean[n], new int[n], new int[n], new int[n]);
		out.println(ct);
	}
	
	long separate(int[][][] g, int root, boolean[] sed, int[] par, int[] ord, int[] des)
	{
		// 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[0] && !sed[nex[0]]){
					ord[r++] = nex[0];
					par[nex[0]] = 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[0] && !sed[e[0]])des[cur] += des[e[0]];
			}
			if(r-des[cur] <= r/2){
				for(int[] e : g[cur]){
					if(par[cur] != e[0] && !sed[e[0]] && des[e[0]] >= r/2+1)continue outer;
				}
				sep = cur;
				break;
			}
		}
		
		sed[sep] = true;
		
		int[] curs = new int[r];
		int[] pres = new int[r];
		int[] inds = new int[r];
		int[] ds = new int[r];
		long[] fs = new long[r];
		int[] dlist = new int[r];
		long[] flist = new long[r];
		int lp = 0;
		long ret = 0;
//		tr("sep", sep);
		for(int[] e : g[sep]){
			if(!sed[e[0]]){
				int sp = 0;
				curs[sp] = e[0]; pres[sp] = sep; inds[sp] = 0; ds[sp] = 1; fs[sp] = e[1]; sp++;
				int slp = lp;
				while(sp > 0){
					int cur = curs[sp-1], pre = pres[sp-1], ind = inds[sp-1], d = ds[sp-1];
					long f = fs[sp-1];
					if(ind == 0){
						dlist[lp] = d;
						flist[lp] = f;
						if(d <= L && f <= W){
							ret++;
						}
						lp++;
					}
					if(ind < g[cur].length){
						int[] le = g[cur][ind];
						inds[sp-1]++;
						if(le[0] != pre & !sed[le[0]]){
							curs[sp] = le[0]; pres[sp] = cur; inds[sp] = 0; ds[sp] = d + 1; fs[sp] = f + le[1]; sp++;
						}
						continue;
					}else{
						sp--;
					}
				}
				ret -= total(dlist, flist, slp, lp);
			}
		}
		ret += total(dlist, flist, 0, lp);
//		tr(ret, dlist, flist, sep);
		
		for(int[] e : g[sep]){
			if(!sed[e[0]])ret += separate(g, e[0], sed, par, ord, des);
		}
		return ret;
	}
	
	long total(int[] dlist, long[] flist, int l, int r)
	{
		int n = r-l;
		int[][] co = new int[2*n][];
		long count = 0;
		for(int i = 0;i < n;i++){
			co[2*i] = new int[]{(int)Math.min(flist[l+i], W+1), dlist[l+i], 0};
			co[2*i+1] = new int[]{W-(int)Math.min(flist[l+i], W+1), L-dlist[l+i], 1};
			if(co[2*i][0] <= co[2*i+1][0] && co[2*i][1] <= co[2*i+1][1]){
				count--;
			}
		}
		// 0:put, 1:get
		Arrays.sort(co, new Comparator<int[]>() {
			public int compare(int[] a, int[] b) {
				if(a[0] != b[0])return a[0] - b[0];
				return a[2] - b[2];
			}
		});
		int[] ft = new int[n+2];
		for(int i = 0;i < 2*n;i++){
			if(co[i][2] == 0){
				addFenwick(ft, co[i][1], 1);
			}else{
				if(co[i][1] >= 0){
					count += sumFenwick(ft, Math.min(n, co[i][1]));
				}
			}
		}
//		tr(co);
//		tr("count", count);
		return count/2;
	}
	
	public static int sumFenwick(int[] ft, int i)
	{
		int sum = 0;
		for(i++;i > 0;i -= i&-i)sum += ft[i];
		return sum;
	}
	
	public static void addFenwick(int[] ft, int i, int v)
	{
		if(v == 0)return;
		int n = ft.length;
		for(i++;i < n;i += i&-i)ft[i] += v;
	}
	
	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;
	}
	
	void run() throws Exception
	{
		is = oj ? System.in : new ByteArrayInputStream(INPUT.getBytes());
		out = new PrintWriter(System.out);
		
		long s = System.currentTimeMillis();
		solve();
		out.flush();
		tr(System.currentTimeMillis()-s+"ms");
	}
	
	public static void main(String[] args) throws Exception { new E().run(); }
	
	private byte[] inbuf = new byte[1024];
	private int lenbuf = 0, ptrbuf = 0;
	
	private int readByte()
	{
		if(lenbuf == -1)throw new InputMismatchException();
		if(ptrbuf >= lenbuf){
			ptrbuf = 0;
			try { lenbuf = is.read(inbuf); } catch (IOException e) { throw new InputMismatchException(); }
			if(lenbuf <= 0)return -1;
		}
		return inbuf[ptrbuf++];
	}
	
	private int ni()
	{
		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();
		}
	}
	
	private boolean oj = System.getProperty("ONLINE_JUDGE") != null;
	private void tr(Object... o) { if(!oj)System.out.println(Arrays.deepToString(o)); }
}