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 c355;

import java.io.IOException;
import java.util.InputMismatchException;

public class q1 
{


	
	
	   public static void main(String args[])
	   {
		   FasterScanner s=new FasterScanner();  
		   int n=s.nextInt();
		   int h=s.nextInt();
		   int k=s.nextInt();long rem=0;
		   long ans=0;
		   for(int i=0;i<n;i++)
		   {
			   int tmp=s.nextInt();
			   if((tmp+rem)>=k)
				   {

				   if((tmp+rem)>h)
					   {
					   ans++;
					   rem=0;
					   }
				   ans+=(tmp+rem)/k;
				   rem=(tmp+rem)%k;
				//   System.out.println(rem+" "+tmp+" "+ans);
				   }
			   else
			   {
				   rem+=tmp;
			   }
			   
		   }
		   if(rem>0)
			   ans++;
		   
		   System.out.println(ans);
	   }
	   
		public static long gcd(long a, long b) 
		{

			if(a==b)
				return a;
			if(a==0)
				return b;
			if(b==0)
				return a;

			if(a>b)
				return gcd(b,a%b);
			else
				return gcd(a,b%a);
		}

		public static long modPow( long a, long b, long mod )
	    {
	    	long res=1,pow=a;
	    	while( b>0 )
	    	{
	    		if( (b&1)==1 )
	    		{
	    			res = (pow*res)%mod;
	    		}
	    		pow = (pow*pow)%mod;
	    		b=b/2;
	    	}
	    	return res;
	    }
		
		static class nck
		{
			public static long ncr[][];
			
			public nck(long z,long p)//z==maxvalue  p==mod
			{
				generateNCR(z, p);
			}
			
		    private static void generateNCR( long z, long p )
		    {
		    	ncr = new long[(int)z+1][(int)z+1];
		    	ncr[0][0] = 1;
		    	for(int i=1; i<=z; i++)
		    	{
		    		ncr[i][0] = 1;
		    		ncr[0][i] = 0;
		    	}
		        for(int i=1; i<=z; i++)
		        {
		            for(int j=1; j<=z; j++)
		            {
		                ncr[i][j] = (ncr[i-1][j] + ncr[i-1][j-1]) % p;
		            }
		        }
		    }

		    private static long lucas(long n, long k, long p) 
		    {
		    
		        long ans = 1;
		        
		        while(n>0)
		        {
		            int N = (int)(n%p);
		            int K = (int)(k%p);
		            if(K>N)
		                return 0;
		            ans *= (ncr[N][K] );
		            n /= p;
		            k /= p;
		        }
		        return ans % p;
			
	    }
		}
		
		
		

		
		

		
		
		
		
		static class SegTree
		{
			static int seg[];
			static int dp[];
			int n;
			int d;
			public SegTree(int[] arr,int defaul)
			{
				this.dp=arr;
				n=dp.length;
				seg=new int[4*arr.length];
				build(1,0,n);
				this.d=defaul;
			}

			public void build(int id,int l,int r){
				if(r-l<2){
					seg[id]=dp[l];
					return;
				}
				int mid=(l+r)/2;
				build(2*id,l,mid);
				build(2*id+1,mid,r);
				seg[id]=merge(seg[2*id],seg[2*id+1]);
			}

			public int query(int l,int r)
			{
				return givemin(1,l,r,0,n);
			}

			public  int givemin(int id,int x,int y,int l,int r){
				if(x<=l && y>=r){
					return seg[id];
				}
				if(y<=l || r<=x){
					return d;
				}
				int mid=(l+r)/2;
				return merge(givemin(2*id, x, y, l, mid),givemin(2*id+1, x, y, mid, r));
			}

			public int upd(int id,int value)
			{
				return update(1,id,value,0,n);
			}
			public  int update(int id,int p,int value,int l,int r){
				if(r-l<2){
					dp[p]=value;
					seg[id]=value;
					return value;
				}
				int mid=(l+r)/2;
				if(p<mid){
					update(2*id, p, value, l, mid);
					seg[id]=merge(seg[2*id], seg[2*id+1]);
					return seg[id];
				}
				else{
					update(2*id+1, p, value, mid,r);
					seg[id]=merge(seg[2*id+1], seg[2*id]);
					return seg[id];

				}
			}

			public int merge(int l,int r)
			{

				//set initial value
				return l+r;
			}
		}


		static 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;   
			int[] seg;
			int max;
			// number of components
			public UF(int N) {
				if (N < 0) throw new IllegalArgumentException();
				count = N;
				parent = new int[N];
				rank = new byte[N];
				seg=new int[N];
				for (int i = 0; i < N; i++) {
					parent[i] = i;
					rank[i] = 0;
					seg[i]=1;
				}
				max=1;
			}

			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) {
				//    System.out.println("uf "+p+" "+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;
					seg[rootQ]+=seg[rootP];
					max=Math.max(seg[rootQ],max);
				}
				else if (rank[rootP] > rank[rootQ])
				{
					parent[rootQ] = rootP;
					seg[rootP]+=seg[rootQ];
					max=Math.max(seg[rootP],max);
				}
				else {
					parent[rootQ] = rootP;
					rank[rootP]++;
					seg[rootP]+=seg[rootQ];
					max=Math.max(seg[rootP],max);
				}
				count--;
				return true;
			}

		}



		static class SparseTable
		{
			int[][] st;
			public SparseTable(int[] h){
				int n=h.length;
				int MAX_LOG=(int)Math.ceil(Math.log(n)/Math.log(2))+1;
				st=new int[n][MAX_LOG];
				for (int i = 0; i < n; i++)
					st[i][0] = h[i];
				for (int j = 1; (1 << j) <= n; j++)
				{
					for (int i = 0;( i + (1 << j) - 1 )< n; i++)
					{
						st[i][j]=Math.max(st[i][j-1],st[i+(1<<(j-1))][j-1]);
					}
				}
			}
			public int query(int l,int r)
			{
				int x=(int )Math.floor((Math.log(r-l+1)/Math.log(2)));
				int ans=Math.max(st[l][x],st[r-(1<<x)+1][x]);
				return ans;
			}

		}

		public static class FasterScanner {
			private byte[] buf = new byte[1024];
			private int curChar;
			private int numChars;

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

			public String nextLine() {
				int c = read();
				while (isSpaceChar(c))
					c = read();
				StringBuilder res = new StringBuilder();
				do {
					res.appendCodePoint(c);
					c = read();
				} while (!isEndOfLine(c));
				return res.toString();
			}

			public String nextString() {
				int c = read();
				while (isSpaceChar(c))
					c = read();
				StringBuilder res = new StringBuilder();
				do {
					res.appendCodePoint(c);
					c = read();
				} while (!isSpaceChar(c));
				return res.toString();
			}

			public long nextLong() {
				int c = read();
				while (isSpaceChar(c))
					c = read();
				int sgn = 1;
				if (c == '-') {
					sgn = -1;
					c = read();
				}
				long 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 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 int[] nextIntArray(int n) {
				int[] arr = new int[n];
				for (int i = 0; i < n; i++) {
					arr[i] = nextInt();
				}
				return arr;
			}

			public long[] nextLongArray(int n) {
				long[] arr = new long[n];
				for (int i = 0; i < n; i++) {
					arr[i] = nextLong();
				}
				return arr;
			}

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

			private boolean isEndOfLine(int c) {
				return c == '\n' || c == '\r' || c == -1;
			}
		}

}
