Vanya smashes potato in a vertical food processor. At each moment of time the height of the potato in the processor doesn't exceed h and the processor smashes k centimeters of potato each second. If there are less than k centimeters remaining, than during this second processor smashes all the remaining potato.

Vanya has n pieces of potato, the height of the i-th piece is equal to ai. He puts them in the food processor one by one starting from the piece number 1 and finishing with piece number n. Formally, each second the following happens:

  1. If there is at least one piece of potato remaining, Vanya puts them in the processor one by one, until there is not enough space for the next piece. 
  2. Processor smashes k centimeters of potato (or just everything that is inside). 



Provided the information about the parameter of the food processor and the size of each potato in a row, compute how long will it take for all the potato to become smashed.

Input

The first line of the input contains integers n, h and k (1 ≤ n ≤ 100 000, 1 ≤ k ≤ h ≤ 109) — the number of pieces of potato, the height of the food processor and the amount of potato being smashed each second, respectively.

The second line contains n integers ai (1 ≤ ai ≤ h) — the heights of the pieces.

Output

Print a single integer — the number of seconds required to smash all the potatoes following the process described in the problem statement.

Examples

Input

5 6 3
5 4 3 2 1


Output

5


Input

5 6 3
5 5 5 5 5


Output

10


Input

5 6 3
1 2 1 1 1


Output

2

Note

Consider the first sample. 

  1. First Vanya puts the piece of potato of height 5 into processor. At the end of the second there is only amount of height 2 remaining inside. 
  2. Now Vanya puts the piece of potato of height 4. At the end of the second there is amount of height 3 remaining. 
  3. Vanya puts the piece of height 3 inside and again there are only 3 centimeters remaining at the end of this second. 
  4. Vanya finally puts the pieces of height 2 and 1 inside. At the end of the second the height of potato in the processor is equal to 3. 
  5. During this second processor finally smashes all the remaining potato and the process finishes. 



In the second sample, Vanya puts the piece of height 5 inside and waits for 2 seconds while it is completely smashed. Then he repeats the same process for 4 other pieces. The total time is equal to 2·5 = 10 seconds.

In the third sample, Vanya simply puts all the potato inside the processor and waits 2 seconds.
//package R355;

import java.io.*;
import java.util.*;

import java.awt.Point;
import java.awt.geom.Line2D;
import java.io.BufferedReader;
import java.io.File;
import java.io.FileInputStream;
import java.io.FileReader;
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.security.GuardedObject;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.Comparator;
import java.util.HashMap;
import java.util.HashSet;
import java.util.Hashtable;
import java.util.InputMismatchException;
import java.util.LinkedList;
import java.util.List;
import java.util.Map;
import java.util.PriorityQueue;
import java.util.Queue;
import java.util.Random;
import java.util.Scanner;
import java.util.Stack;
import java.util.StringTokenizer;
import java.util.TreeMap;
import java.util.TreeSet;
import java.io.InputStream;
import java.math.BigInteger;






/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */

public class B {
    public static void main(String[] args) throws IOException {
        InputStream inputStream = System.in;


        OutputStream outputStream = System.out;
        FastScanner in;
        PrintWriter out;

        in=new FastScanner(System.in);
        out=new PrintWriter(System.out);
        //in=new FastScanner(new FileInputStream(new File("C://Users//KANDARP//Desktop//coding_contest_creation (1).txt")));

        TaskC solver = new TaskC();
        long var=System.currentTimeMillis();
        solver.solve(1, in, out);
        /*if(System.getProperty("ONLINE_JUDGE")==null){
            out.println("["+(double)(System.currentTimeMillis()-var)/1000+"]");
        }*/
        out.close();
    }
}
class Pair {

    long x,y,index;
    long  r1,r2;

    Pair(long x,long y,int index){
        this.x=x;
        this.y=y;
        this.index=index;
    }
    public String toString(){
        return this.x+" "+this.y+" ";
    }

}
class Edge implements  Comparable<Edge>{
    int u;
    int v;
    int time;
    long cost;
    long wcost;
    public Edge(int u,int v,long cost,long wcost){
        this.u=u;
        this.v=v;
        this.cost=cost;
        this.wcost=wcost;
        time=Integer.MAX_VALUE;
    }
    public int other(int x){
        if(u==x)return v;
        return u;
    }
    @Override
    public int compareTo(Edge o) {
        // TODO Auto-generated method stub
        return Long.compare(cost, o.cost);
    }
}
class queary{
    int type;
    int l;
    int r;
    int index;
    queary(int type,int l,int r,int index){
        this.type=type;
        this.l=l;
        this.r=r;
        this.index=index;
    }
}
class TaskC {
    static long mod=1000000007;
    static int prime_len=1000010;
    static int prime[]=new int[prime_len];
    static long n_prime[]=new long[prime_len];
    static ArrayList<Integer> primes=new ArrayList<>();
    static{
        for(int i=2;i<=Math.sqrt(prime.length);i++){
            for(int j=i*i;j<prime.length;j+=i){

                prime[j]=i;

            }
        }
        for(int i=2;i<prime.length;i++){
            n_prime[i]=n_prime[i-1];
            if(prime[i]==0){
                n_prime[i]++;
            }

        }
        //  System.out.println("end");

        //  prime[0]=true;
        //  prime[1]=1;
    }
    /*
     *  long pp[]=new long[10000001];
            pp[0]=0;
            pp[1]=1;
            for(int i=2;i<pp.length;i++){
                if(prime[i]!=0){
                    int gcd=(int)greatestCommonDivisor(i/prime[i], prime[i]);
                    pp[i]=(pp[i/prime[i]]*pp[prime[i]]*gcd)/pp[(int)gcd];
                }
                else
                    pp[i]=i-1;
            }


}
     * */

    class TrieNode{
        int value;
        TrieNode children[];
        public TrieNode(int value,TrieNode children[] ){
            this.value=value;
            this.children=children;
        }
    }
    class Trie{
        TrieNode root;
        int count;
        public Trie(TrieNode root,int count){
            this.root=root;
            this.count=count;
        }
    }
    public void insert(Trie t,char key[]){
        t.count++;
        int length=key.length;
        int level=0;
        TrieNode current=t.root;
        if(current==null){
            t.root=new TrieNode(0, new TrieNode[26]);
            current=t.root;
        }
        for(level=0;level<length;level++){
            int index=key[level]-'a';
            if(current.children[index]==null){
                current.children[index]=new TrieNode(0,new TrieNode[26]);
            }
            current=current.children[index];
        }
        current.value=t.count;
    }
    public int search(Trie t,char key[]){
        TrieNode current=t.root;
        if(current==null){
            return 0;
        }
        int length=key.length;
        int level=0;
        for(level=0;level<length;level++){
            int index=key[level]-'a';
            if(current.children[index]==null){
                return 0;
            }
            current=current.children[index];
        }
        return current.value;
    }
    class point implements Comparable<point>{
        long x;
        long y;
        public point(long x,long y){
            this.x=x;
            this.y=y;
        }
        @Override
        public int compareTo(point o) {
            // TODO Auto-generated method stub
            if(o.x==x && o.y==y)
                return 0;
            else return (int)Math.max(x-o.x, y-o.y);
        }
        public int hashCode(){
            return (int)(x+y);

        }
        public boolean equals(Object z){
            if(z!=null){
                point o=(point)z;
                if(o.x==x && o.y==y)
                    return true;
            }
            return false;
        }

    }
    class Edge {
        int t, rev, cap, f;

        public Edge(int t, int rev, int cap) {
            this.t = t;
            this.rev = rev;
            this.cap = cap;
        }
    }

    class MaxFlowDinic {


        public  List<Edge>[] createGraph(int nodes) {
            List<Edge>[] graph = new List[nodes];
            for (int i = 0; i < nodes; i++)
                graph[i] = new ArrayList<>();
            return graph;
        }

        public  void addEdge(List<Edge>[] graph, int s, int t, int cap) {
            graph[s].add(new Edge(t, graph[t].size(), cap));
            graph[t].add(new Edge(s, graph[s].size() - 1, 0));
        }

        boolean dinicBfs(List<Edge>[] graph, int src, int dest, int[] dist) {
            Arrays.fill(dist, -1);
            dist[src] = 0;
            int[] Q = new int[graph.length];
            int sizeQ = 0;
            Q[sizeQ++] = src;
            for (int i = 0; i < sizeQ; i++) {
                int u = Q[i];
                for (Edge e : graph[u]) {
                    if (dist[e.t] < 0 && e.f < e.cap) {
                        dist[e.t] = dist[u] + 1;
                        Q[sizeQ++] = e.t;
                    }
                }
            }
            return dist[dest] >= 0;
        }

        int dinicDfs(List<Edge>[] graph, int[] ptr, int[] dist, int dest, int u, int f) {
            if (u == dest)
                return f;
            for (; ptr[u] < graph[u].size(); ++ptr[u]) {
                Edge e = graph[u].get(ptr[u]);
                if (dist[e.t] == dist[u] + 1 && e.f < e.cap) {
                    int df = dinicDfs(graph, ptr, dist, dest, e.t, Math.min(f, e.cap - e.f));
                    if (df > 0) {
                        e.f += df;
                        graph[e.t].get(e.rev).f -= df;
                        return df;
                    }
                }
            }
            return 0;
        }

        public  int maxFlow(List<Edge>[] graph, int src, int dest) {
            int flow = 0;
            int[] dist = new int[graph.length];
            while (dinicBfs(graph, src, dest, dist)) {
                int[] ptr = new int[graph.length];
                while (true) {
                    int df = dinicDfs(graph, ptr, dist, dest, src, Integer.MAX_VALUE);
                    if (df == 0)
                        break;
                    flow += df;
                }
            }
            return flow;
        }
    }
    //int arr[]=new int[1000000000];

    public void solve(int testNumber, FastScanner in, PrintWriter out) throws IOException {
        int n = in.nextInt();
        long h = in.nextLong();
        long k = in.nextLong();

        int a[]= new int[n];
        for(int i=0;i<n;i++){
            a[i] = in.nextInt();
        }
        long  p =0;
        int index = n;
        long ans =0;

        for(int i =0;i<n;i++){
            if(p + a[i] > h) {
                index = i;
                break;
            }
            p += a[i];
        }
        for(int i =index;i<n;i++){
            long x = Math.max(0,(long)Math.ceil((a[i] - h + p) * 1.0 /k));
            p -= x*k;
            p = Math.max(p,0);
            p += a[i];
            ans += x;
        }
        if(p >= 0 ){
            ans += (long)Math.ceil(p *1.0/k);
        }
        out.println(ans);
    }

    public int binarySearchIndex(long val , int start , int end , long[] arr){
        if(end - start <=1) {
            if(arr[end] <= val){
                return end;
            }
            else if(arr[start] <= val){
                return start;
            }
            else{
                return -1;
            }
        }
        int mid = (start + end + 1)/2;

        if(arr[mid] <= val){
            return binarySearchIndex(val,mid,end,arr);
        }
        else{
            return binarySearchIndex(val,start,mid,arr);
        }
    }


    public long[] fun(long n,int k,int a){
        long arr[]=new long[k];
        for(int i=0;i<k;i++){

            arr[(int)(pow(i, a, k)%k)]+=((n/k)%mod+ ((i!=0  &&  i<=n%k)? 1: 0))%mod;
        }
        return arr;
    }


    public long getAns(int d[],int n){
        if(d[0]<0 && d[n-1]>0){

            return Math.min(-2*d[0]+d[n-1], 2*d[n-1]-d[0]);


        }
        else{
            if(d[0]<0){
                return d[0]*-1;
            }
            else{
                return(d[n-1]*1);
            }
        }

        // return 0;
    }
    public boolean isTriangle(int x,int y,int z){
        if(x+y>z && x+z>y && y+z>x){
            return true;
        }
        return false;
    }
    public long optimize(long x){
        long y=x;
        if(x%10<5){
            x=x-x%10;

        }
        else{
            x=x+(10-x%10);
        }
        return y-x;
    }
    public static long[][] matrixexpo(long m[][],String n,long mod){
        if(n.equals("1")){
            return m.clone();
        }
        if(n.equals("10")){
            return mulmatrix(m, m , mod);
        }
        else{
            long temp [][]=matrixexpo(m,n.substring(0,n.length()-1),mod);
            temp=mulmatrix(temp, temp, mod);
            if(n.charAt(n.length()-1)=='0')return temp;
            else return mulmatrix(temp, m,mod);
        }
    }

    public static long[] mul(long[] a, long[] b)
    {
        int n = Math.max(a.length, b.length);
        int h = Integer.highestOneBit(n);
        if(n > h)h *= 2;
        if(a.length < h)a = Arrays.copyOf(a, h);
        if(b.length < h)b = Arrays.copyOf(b, h);
        return mul2(a, b, 0, h, 0, h);
    }

    public static long[] mul2(long[] a, long[] b, int al, int ar, int bl, int br)
    {
        int n = ar-al;
        if((n&n-1) != 0)throw new RuntimeException();
        if(n <= 1<<6){
            long[] res = muln(a, b, al, ar, bl, br);
            return res;
        }

        long[] c0 = mul2(a, b, al+0, al+n/2, bl+0, bl+n/2);
        long[] c2 = mul2(a, b, al+n/2, al+n, bl+n/2, bl+n);

        long[] ab0 = new long[n/2];
        long[] ab1 = new long[n/2];
        for(int i = 0;i < n/2;i++){
            ab0[i] = a[al+i] + a[al+i+n/2];
            ab1[i] = b[bl+i] + b[bl+i+n/2];
            if(ab0[i] >= mod)ab0[i] -= mod;
            if(ab1[i] >= mod)ab1[i] -= mod;
        }

        int e = n+c2.length;
        long[] ret = new long[e];
        for(int i = 0;i < c0.length;i++){
            ret[i] += c0[i];
            if(ret[i] >= mod)ret[i] -= mod;
        }
        for(int i = 0;i < c2.length;i++){
            ret[i+n] += c2[i];
            if(ret[i+n] >= mod)ret[i+n] -= mod;
        }

        long[] c1 = mul2(ab0, ab1, 0, n/2, 0, n/2);
        for(int i = 0;i < c1.length;i++){
            c1[i] -= c0[i] + c2[i];
            if(c1[i] < 0)c1[i] += mod;
            if(c1[i] < 0)c1[i] += mod;
        }
        for(int i = 0;i < c1.length;i++){
            ret[i+n/2] += c1[i];
            if(ret[i+n/2] >= mod)ret[i+n/2] -= mod;
        }
        return ret;
    }

    public static long[] muln(long[] a, long[] b, int al, int ar, int bl, int br)
    {
        int n = ar - al;
        long[] ret = new long[2*n];
        for(int i = 0;i < 2*n;i++){
            long tot = 0;
            for(int j = Math.max(i-n+1, 0);j <= i && j < n;j++){
                tot += a[al+j] * b[bl+i-j];
            }
            ret[i] = tot % mod;
        }
        return ret;
    }

    public static long[][] mulmatrix(long m1[][],long m2[][],long mod){
        long ans[][]=new long[m1.length][m2[0].length];
        for(int i=0;i<m1.length;i++){
            for(int j=0;j<m2[0].length;j++){
                for(int k=0;k<m1.length;k++){
                    ans[i][j]+=(m1[i][k]*m2[k][j]);
                    ans[i][j]%=mod;
                }
            }
        }
        return ans;
    }
    long pow(long x,long y,long mod){
        if(y<=0){
            return 1;
        }
        if(y==1){
            return x%mod;
        }
        long temp=pow(x,y/2,mod);
        if(y%2==0){
            return (temp*temp)%mod;
        }
        else{
            return (((temp*temp)%mod)*x)%mod;
        }
    }




    static long greatestCommonDivisor (long m, long n){
        long x;
        long y;
        while(m%n != 0){
            x = n;
            y = m%n;
            m = x;
            n = y;
        }
        return n;
    }
    static void dfs(List<Integer>[] graph, boolean[] used, List<Integer> res, int u,int parent,List<Integer> collection) {

        used[u] = true;
        Integer uu=new Integer(u);
        collection.add(uu);
        for (int v : graph[u]){
            if (!used[v]){
                dfs(graph, used, res, v,u,collection);

            }
            else if(collection.contains(v)){
                System.out.println("Impossible");
                System.exit(0);
            }
        }
        collection.remove(uu);
        res.add(u);
    }


    public static List<Integer> topologicalSort(List<Integer>[] graph) {
        int n = graph.length;
        boolean[] used = new boolean[n];
        List<Integer> res = new ArrayList<>();
        for (int i = 0; i < n; i++)
            if (!used[i])
                dfs(graph, used, res, i,-1,new ArrayList<Integer>());
        Collections.reverse(res);
        return res;
    }

}








class LcaSparseTable {

    int len;
    int[][] up;
    int[][] max;
    int[] tin;
    int[] tout;
    int time;
    int []lvel;

    void dfs(List<Integer>[] tree, int u, int p) {
        tin[u] = time++;
        lvel[u]=lvel[p]+1;
        up[0][u] = p;
        if(u!=p)
            //max[0][u]=weight(u,p);
            for (int i = 1; i < len; i++)
            {
                up[i][u] = up[i - 1][up[i - 1][u]];
                max[i][u]=Math.max(max[i-1][u],max[i-1][up[i-1][u]]);
            }
        for (int v : tree[u])
            if (v != p)
                dfs(tree, v, u);
        tout[u] = time++;
    }

    public LcaSparseTable(List<Integer>[] tree, int root) {
        int n = tree.length;
        len = 1;
        while ((1 << len) <= n) ++len;
        up = new int[len][n];
        max=new int[len][n];
        tin = new int[n];
        tout = new int[n];
        lvel=new int[n];
        lvel[root]=0;
        dfs(tree, root, root);
    }

    boolean isParent(int parent, int child) {
        return tin[parent] <= tin[child] && tout[child] <= tout[parent];
    }

    public int lca(int a, int b) {
        if (isParent(a, b))
            return a;
        if (isParent(b, a))
            return b;
        for (int i = len - 1; i >= 0; i--)
            if (!isParent(up[i][a], b))
                a = up[i][a];
        return up[0][a];
    }
    public long max(int a,int b){
        int lca=lca(a,b);
        //    System.out.println("LCA "+lca);
        long ans=0;
        int h=lvel[a]-lvel[lca];
        //  System.out.println("Height "+h);
        int index=0;
        while(h!=0){
            if(h%2==1){
                ans=Math.max(ans,max[index][a]);
                a=up[index][a];
            }
            h/=2;
            index++;
        }
        h=lvel[b]-lvel[lca];
        // System.out.println("Height "+h);

        index=0;
        while(h!=0){
            if(h%2==1){
                ans=Math.max(ans,max[index][b]);
                b=up[index][b];
            }
            h/=2;
            index++;
        }
        return ans;
    }



    static void dfs1(List<Integer>[] graph, boolean[] used, List<Integer> res, int u) {
        used[u] = true;
        for (int v : graph[u])
            if (!used[v])
                dfs1(graph, used, res, v);
        res.add(u);
    }


    int phi(int n) {
        int res = n;
        for (int i = 2; i * i <= n; ++i) {
            if (n % i == 0) {
                while (n % i == 0) {
                    n /= i;
                }
                res -= res / i;
            }
        }
        if (n != 1) {
            res -= res / n;
        }
        return res;
    }



    public static long[][] mulmatrix(long m1[][],long m2[][],long mod){
        long ans[][]=new long[m1.length][m2[0].length];
        for(int i=0;i<m1.length;i++){
            for(int j=0;j<m2[0].length;j++){
                for(int k=0;k<m1.length;k++){
                    ans[i][j]+=(m1[i][k]*m2[k][j]);
                    ans[i][j]%=mod;
                }
            }
        }
        return ans;
    }
    public static long[][] matrixexpo(long m[][],String n,long mod){
        if(n.equals("1")){
            return m.clone();
        }
        if(n.equals("10")){
            return mulmatrix(m, m , mod);
        }
        else{
            long temp [][]=matrixexpo(m,n.substring(0,n.length()-1),mod);
            temp=mulmatrix(temp, temp, mod);
            if(n.charAt(n.length()-1)=='0')return temp;
            else return mulmatrix(temp, m,mod);
        }
    }
    public static boolean isCompatible(long x[],long y[]){

        for(int i=0;i<x.length-1;i++){
            if(x[i]==y[i] && x[i+1]==y[i+1] && x[i]==x[i+1] && y[i]==y[i+1]){
                return false;
            }
        }
        return true;
    }


    long pow(long x,long y,long mod){
        if(y<=0){
            return 1;
        }
        if(y==1){
            return x%mod;
        }
        long temp=pow(x,y/2,mod);
        if(y%2==0){
            return (temp*temp)%mod;
        }
        else{
            return (((temp*temp)%mod)*x)%mod;
        }
    }


    long no_of_primes(long m,long n,long k){
        long count=0,i,j;
        int primes []=new int[(int)(n-m+2)];
        if(m==1)    primes[0] = 1;
        for(i=2; i<=Math.sqrt(n); i++)
        {
            j = (m/i);    j *= i;
            if(j<m)
                j+=i;
            for(; j<=n; j+=i)
            {
                if(j!=i)
                    primes[(int)(j-m)] = 1;
            }
        }

        for(i=0; i<=n-m; i++)
            if(primes[(int)i]==0 && (i-1)%k==0)
                count++;
        return count;
    }

}

class SegTree {
    int n;
    static long constt=Long.parseLong("111111111111111111111111111111",2);
    long  t[];
    long mod=(long)(1000000007);
    SegTree(int n,long  t[]){
        this.n=n;
        this.t=t;
        build();
    }

    void build() {  // build the tree

        for (int i = n - 1; i >= 0; --i){
            t[i]=(t[i<<1]&t[i<<1|1]);
        }
    }

    void modify(int p, long value) {  // set value at position p
        for (t[p += n]=value; p > 1; p >>= 1) t[p>>1] = (t[p]&t[p^1]);
        //  System.out.println(Arrays.toString(t));
    }

    long query(int l, int r) {  // sum on interval [l, r)
        long res=constt;

        for (l += n, r += n; l < r; l >>= 1, r >>= 1) {
            if ((l&1)!=0) res=res&t[l++];
            if ((r&1)!=0) res=res&t[--r];
        }
        return res;


    }


    //
//
//
}
class FastScanner
{

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

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

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

    private int[] parent;  // parent[i] = parent of i
    private byte[] rank;   // rank[i] = rank of subtree rooted at i (never more than 31)
    private int count;     // number of components
    public UF(int N) {
        if (N < 0) throw new IllegalArgumentException();
        count = N;
        parent = new int[N];
        rank = new byte[N];
        for (int i = 0; i < N; i++) {
            parent[i] = i;
            rank[i] = 0;
        }
    }

    public int find(int p) {
        if (p < 0 || p >= parent.length) throw new IndexOutOfBoundsException();
        while (p != parent[p]) {
            parent[p] = parent[parent[p]];    // path compression by halving
            p = parent[p];
        }
        return p;
    }
    public int count() {
        return count;
    }

    public boolean connected(int p, int q) {
        return find(p) == find(q);
    }

    public boolean union(int p, int q) {
        int rootP = find(p);
        int rootQ = find(q);
        if (rootP == rootQ) return false;

        // make root of smaller rank point to root of larger rank
        if      (rank[rootP] < rank[rootQ]) parent[rootP] = rootQ;
        else if (rank[rootP] > rank[rootQ]) parent[rootQ] = rootP;
        else {
            parent[rootQ] = rootP;
            rank[rootP]++;
        }
        count--;
        return true;
    }




}
class MyScanner {
    BufferedReader br;
    StringTokenizer st;

    public MyScanner() {
        br = new BufferedReader(new InputStreamReader(System.in));
    }

    String next() {
        while (st == null || !st.hasMoreElements()) {
            try {
                st = new StringTokenizer(br.readLine());
            } catch (IOException e) {
                e.printStackTrace();
            }
        }
        return st.nextToken();
    }

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

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

    double nextDouble() {
        return Double.parseDouble(next());
    }

    String nextLine() {
        String str = "";
        try {
            str = br.readLine();
        } catch (IOException e) {
            e.printStackTrace();
        }
        return str;
    }
}

