N people are waiting in a single line in front of the Takahashi Store. The cash on hand of the i-th person from the front of the line is a positive integer A_i.

Mr. Takahashi, the shop owner, has decided on the following scheme: He picks a product, sets a positive integer P indicating its price, and shows this product to customers in order, starting from the front of the line. This step is repeated as described below.

At each step, when a product is shown to a customer, if price P is equal to or less than the cash held by that customer at the time, the customer buys the product and Mr. Takahashi ends the current step. That is, the cash held by the first customer in line with cash equal to or greater than P decreases by P, and the next step begins.

Mr. Takahashi can set the value of positive integer P independently at each step.

He would like to sell as many products as possible. However, if a customer were to end up with 0 cash on hand after a purchase, that person would not have the fare to go home. Customers not being able to go home would be a problem for Mr. Takahashi, so he does not want anyone to end up with 0 cash.

Help out Mr. Takahashi by writing a program that determines the maximum number of products he can sell, when the initial cash in possession of each customer is given.

Constraints

* 1 ≦ | N | ≦ 100000
* 1 ≦ A_i ≦ 10^9(1 ≦ i ≦ N)
* All inputs are integers.

Input

Inputs are provided from Standard Inputs in the following form.


N
A_1
:
A_N


Output

Output an integer representing the maximum number of products Mr. Takahashi can sell.

Examples

Input

3
3
2
5


Output

3


Input

15
3
1
4
1
5
9
2
6
5
3
5
8
9
7
9


Output

18
import java.io.*;
import java.util.*;

public class Main {
	static InputStream is;
	static PrintWriter out;
	static String INPUT = "";

	static final long mod = (long) 1e9 + 7;
	static final int dx[] = { -1, 0, 1, 0 }, dy[] = { 0, -1, 0, 1 };
	static final int[] dx8 = { -1, -1, -1, 0, 0, 1, 1, 1 }, dy8 = { -1, 0, 1, -1, 1, -1, 0, 1 };
	static final int inf = Integer.MAX_VALUE / 3;
	static final long linf = Long.MAX_VALUE / 3;
	static final double dinf = Double.MAX_VALUE / 3;
	static final double eps = 1e-10;
	static final double pi = Math.PI;
	static StringBuilder sb = new StringBuilder();

	static void solve() {
		int n = ni();
		int a[] = na(n);
		int max = 0;
		long ans = 0;
		for(int i=0;i<n;i++) {
			if(i==0) {
				ans += a[i]-1;
				a[i] = 1;
				max = 1;
				continue;
			}
			if(a[i]>=max+2) {
				ans += a[i]/(max+1);
				a[i] %= (max+1);
				if(a[i]==0) {
					ans--;
				}
				a[i]=1;
			}
			max = max(max, a[i]);			
		}
		out.println(ans);
	}

	//libraries		
	static void reverse(int ar[]) {
		int len = ar.length;
		for (int i = 0; i < len / 2; i++) {
			int t = ar[i];
			ar[i] = ar[len - 1 - i];
			ar[len - 1 - i] = t;
		}
	}

	static void reverse(long ar[]) {
		int len = ar.length;
		for (int i = 0; i < len / 2; i++) {
			long t = ar[i];
			ar[i] = ar[len - 1 - i];
			ar[len - 1 - i] = t;
		}
	}

	static void reverse(double ar[]) {
		int len = ar.length;
		for (int i = 0; i < len / 2; i++) {
			double t = ar[i];
			ar[i] = ar[len - 1 - i];
			ar[len - 1 - i] = t;
		}
	}

	static <T> void reverse(List<T> ls) {
		int sz = ls.size();
		for (int i = 0; i < sz / 2; i++) {
			T t = ls.get(i);
			ls.set(i, ls.get(sz - 1 - i));
			ls.set(sz - 1 - i, t);
		}
	}

	static void sbnl() {//StringBuilderに改行文字をappendする
		sb.append("\n");
	}

	static int lowerBound(int[] a, int x) {
		int l = -1, r = a.length;
		while (r - l > 1) {
			int c = (l + r) / 2;
			if (a[c] < x) {
				l = c;
			} else {
				r = c;
			}
		}
		return r;
	}

	static int upperBound(int[] a, int x) {
		int l = -1, r = a.length;
		while (r - l > 1) {
			int c = (l + r) / 2;
			if (a[c] <= x) {
				l = c;
			} else {
				r = c;
			}
		}
		return r;
	}

	static int rlowerBound(int[] a, int x) {
		int l = -1, r = a.length;
		while (r - l > 1) {
			int c = (l + r) / 2;
			if (a[c] > x) {
				l = c;
			} else {
				r = c;
			}
		}
		return r;
	}

	static int rupperBound(int[] a, int x) {
		int l = -1, r = a.length;
		while (r - l > 1) {
			int c = (l + r) / 2;
			if (a[c] >= x) {
				l = c;
			} else {
				r = c;
			}
		}
		return r;
	}

	static int lowerBound(long[] a, long x) {
		int l = -1, r = a.length;
		while (r - l > 1) {
			int c = (l + r) / 2;
			if (a[c] < x) {
				l = c;
			} else {
				r = c;
			}
		}
		return r;
	}

	static int upperBound(long[] a, long x) {
		int l = -1, r = a.length;
		while (r - l > 1) {
			int c = (l + r) / 2;
			if (a[c] <= x) {
				l = c;
			} else {
				r = c;
			}
		}
		return r;
	}

	static int rlowerBound(long[] a, long x) {
		int l = -1, r = a.length;
		while (r - l > 1) {
			int c = (l + r) / 2;
			if (a[c] > x) {
				l = c;
			} else {
				r = c;
			}
		}
		return r;
	}

	static int rupperBound(long[] a, long x) {
		int l = -1, r = a.length;
		while (r - l > 1) {
			int c = (l + r) / 2;
			if (a[c] >= x) {
				l = c;
			} else {
				r = c;
			}
		}
		return r;
	}

	static int lowerBound(double[] a, double x) {
		int l = -1, r = a.length;
		while (r - l > 1) {
			int c = (l + r) / 2;
			if (a[c] < x) {
				l = c;
			} else {
				r = c;
			}
		}
		return r;
	}

	static int upperBound(double[] a, double x) {
		int l = -1, r = a.length;
		while (r - l > 1) {
			int c = (l + r) / 2;
			if (a[c] <= x) {
				l = c;
			} else {
				r = c;
			}
		}
		return r;
	}

	static int rlowerBound(double[] a, double x) {
		int l = -1, r = a.length;
		while (r - l > 1) {
			int c = (l + r) / 2;
			if (a[c] > x) {
				l = c;
			} else {
				r = c;
			}
		}
		return r;
	}

	static int rupperBound(double[] a, double x) {
		int l = -1, r = a.length;
		while (r - l > 1) {
			int c = (l + r) / 2;
			if (a[c] >= x) {
				l = c;
			} else {
				r = c;
			}
		}
		return r;
	}

	static <T> int lowerBound(List<T> ls, T x) throws RuntimeException {
		if (ls.size() == 0)
			return -1;
		if (ls.get(0) instanceof Integer) {
			return ~Collections.binarySearch(ls, x, (t1, t2) -> ((Integer) t1).compareTo((Integer) t2) >= 0 ? 1 : -1);
		} else if (ls.get(0) instanceof Long) {
			return ~Collections.binarySearch(ls, x, (t1, t2) -> ((Long) t1).compareTo((Long) t2) >= 0 ? 1 : -1);
		} else if (ls.get(0) instanceof Double) {
			return ~Collections.binarySearch(ls, x, (t1, t2) -> ((Double) t1).compareTo((Double) t2) >= 0 ? 1 : -1);
		} else {
			System.err.println(
					String.format("%s:数値でないリストを二分探索しています。", Thread.currentThread().getStackTrace()[1].getMethodName()));
			throw new RuntimeException();
		}
	}

	static <T> int upperBound(List<T> ls, T x) throws RuntimeException {
		if (ls.size() == 0)
			return -1;
		if (ls.get(0) instanceof Integer) {
			return ~Collections.binarySearch(ls, x, (t1, t2) -> ((Integer) t1).compareTo((Integer) t2) > 0 ? 1 : -1);
		} else if (ls.get(0) instanceof Long) {
			return ~Collections.binarySearch(ls, x, (t1, t2) -> ((Long) t1).compareTo((Long) t2) > 0 ? 1 : -1);
		} else if (ls.get(0) instanceof Double) {
			return ~Collections.binarySearch(ls, x, (t1, t2) -> ((Double) t1).compareTo((Double) t2) > 0 ? 1 : -1);
		} else {
			System.err.println(
					String.format("%s:数値でないリストを二分探索しています。", Thread.currentThread().getStackTrace()[1].getMethodName()));
			throw new RuntimeException();
		}
	}

	static <T> int rupperBound(List<T> ls, T x) throws RuntimeException {
		if (ls.size() == 0)
			return -1;
		if (ls.get(0) instanceof Integer) {
			return ~Collections.binarySearch(ls, x, (t1, t2) -> ((Integer) t1).compareTo((Integer) t2) < 0 ? 1 : -1);
		} else if (ls.get(0) instanceof Long) {
			return ~Collections.binarySearch(ls, x, (t1, t2) -> ((Long) t1).compareTo((Long) t2) < 0 ? 1 : -1);
		} else if (ls.get(0) instanceof Double) {
			return ~Collections.binarySearch(ls, x, (t1, t2) -> ((Double) t1).compareTo((Double) t2) < 0 ? 1 : -1);
		} else {
			System.err.println(
					String.format("%s:数値でないリストを二分探索しています。", Thread.currentThread().getStackTrace()[1].getMethodName()));
			throw new RuntimeException();
		}
	}

	static <T> int rlowerBound(List<T> ls, T x) {
		if (ls.size() == 0)
			return -1;
		if (ls.get(0) instanceof Integer) {
			return ~Collections.binarySearch(ls, x, (t1, t2) -> ((Integer) t1).compareTo((Integer) t2) <= 0 ? 1 : -1);
		} else if (ls.get(0) instanceof Long) {
			return ~Collections.binarySearch(ls, x, (t1, t2) -> ((Long) t1).compareTo((Long) t2) <= 0 ? 1 : -1);
		} else if (ls.get(0) instanceof Double) {
			return ~Collections.binarySearch(ls, x, (t1, t2) -> ((Double) t1).compareTo((Double) t2) <= 0 ? 1 : -1);
		} else {
			System.err.println(
					String.format("%s:数値でないリストを二分探索しています。", Thread.currentThread().getStackTrace()[1].getMethodName()));
			throw new RuntimeException();
		}
	}

	static int[] concat(int x, int arr[]) {
		int ret[] = new int[arr.length + 1];
		System.arraycopy(arr, 0, ret, 1, ret.length - 1);
		ret[0] = x;
		return ret;
	}

	static int[] concat(int arr[], int x) {
		int ret[] = new int[arr.length + 1];
		System.arraycopy(arr, 0, ret, 0, ret.length - 1);
		ret[ret.length - 1] = x;
		return ret;
	}

	static long[] concat(long x, long arr[]) {
		long ret[] = new long[arr.length + 1];
		System.arraycopy(arr, 0, ret, 1, ret.length - 1);
		ret[0] = x;
		return ret;
	}

	static long[] concat(long arr[], long x) {
		long ret[] = new long[arr.length + 1];
		System.arraycopy(arr, 0, ret, 0, ret.length - 1);
		ret[ret.length - 1] = x;
		return ret;
	}

	static int max(int x, int y) {
		return Math.max(x, y);
	}

	static int min(int x, int y) {
		return Math.min(x, y);
	}

	static int max(int x, int y, int z) {
		x = Math.max(x, y);
		x = Math.max(x, z);
		return x;
	}

	static int min(int x, int y, int z) {
		x = Math.min(x, y);
		x = Math.min(x, z);
		return x;
	}

	static long max(long x, long y) {
		return Math.max(x, y);
	}

	static long min(long x, long y) {
		return Math.min(x, y);
	}

	static long max(long x, long y, long z) {
		x = Math.max(x, y);
		x = Math.max(x, z);
		return x;
	}

	static long min(long x, long y, long z) {
		x = Math.min(x, y);
		x = Math.min(x, z);
		return x;
	}

	static double max(double x, double y) {
		return Math.max(x, y);
	}

	static double min(double x, double y) {
		return Math.min(x, y);
	}

	static double max(double x, double y, double z) {
		x = Math.max(x, y);
		x = Math.max(x, z);
		return x;
	}

	static double min(double x, double y, double z) {
		x = Math.min(x, y);
		x = Math.min(x, z);
		return x;
	}

	static void sort(int[] ar) {
		Arrays.sort(ar);
	}

	static void sort(long[] ar) {
		Arrays.sort(ar);
	}

	static void sort(double[] ar) {
		Arrays.sort(ar);
	}

	static void rsort(int[] ar) {
		Arrays.sort(ar);
		int len = ar.length;
		for (int i = 0; i < len / 2; i++) {
			int tmp = ar[i];
			ar[i] = ar[len - 1 - i];
			ar[len - 1 - i] = tmp;
		}
	}

	static void rsort(long[] ar) {
		Arrays.sort(ar);
		int len = ar.length;
		for (int i = 0; i < len / 2; i++) {
			long tmp = ar[i];
			ar[i] = ar[len - 1 - i];
			ar[len - 1 - i] = tmp;
		}
	}

	static void rsort(double[] ar) {
		Arrays.sort(ar);
		int len = ar.length;
		for (int i = 0; i < len / 2; i++) {
			double tmp = ar[i];
			ar[i] = ar[len - 1 - i];
			ar[len - 1 - i] = tmp;
		}
	}

	static void fill(int arr[], int x) {
		Arrays.fill(arr, x);
	}

	static void fill(long arr[], long x) {
		Arrays.fill(arr, x);
	}

	static void fill(double arr[], double x) {
		Arrays.fill(arr, x);
	}

	static void fill(int arr[][], int x) {
		for (int i = 0; i < arr.length; i++)
			Arrays.fill(arr[i], x);
	}

	static void fill(long arr[][], long x) {
		for (int i = 0; i < arr.length; i++)
			Arrays.fill(arr[i], x);
	}

	static void fill(double arr[][], double x) {
		for (int i = 0; i < arr.length; i++)
			Arrays.fill(arr[i], x);
	}

	//MOD culc
	static long plus(long x, long y) {
		long res = (x + y) % mod;
		return res < 0 ? res + mod : res;
	}

	static long sub(long x, long y) {
		long res = (x - y) % mod;
		return res < 0 ? res + mod : res;
	}

	static long mul(long x, long y) {
		long res = (x * y) % mod;
		return res < 0 ? res + mod : res;
	}

	static long div(long x, long y) {
		long res = x * pow(y, mod - 2) % mod;
		return res < 0 ? res + mod : res;
	}

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

	public static void main(String[] args) throws Exception {
		is = INPUT.isEmpty() ? System.in : new ByteArrayInputStream(INPUT.getBytes());
		out = new PrintWriter(System.out);
		solve();
		out.flush();
	}

	//input
	private static byte[] inbuf = new byte[1024];
	static int lenbuf = 0, ptrbuf = 0;

	private static 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 static boolean isSpaceChar(int c) {
		return !(c >= 33 && c <= 126);
	}

	private static int skip() {
		int b;
		while ((b = readByte()) != -1 && isSpaceChar(b))
			;
		return b;
	}

	@SuppressWarnings("unused")
	private static double nd() {
		return Double.parseDouble(ns());
	}

	@SuppressWarnings("unused")
	private static char nc() {
		return (char) skip();
	}

	private static String ns() {
		int b = skip();
		StringBuilder sb = new StringBuilder();
		while (!(isSpaceChar(b))) {
			sb.appendCodePoint(b);
			b = readByte();
		}
		return sb.toString();
	}

	private static char[] ns(int n) {
		char[] buf = new char[n];
		int b = skip(), p = 0;
		while (p < n && !(isSpaceChar(b))) {
			buf[p++] = (char) b;
			b = readByte();
		}
		return n == p ? buf : Arrays.copyOf(buf, p);
	}

	@SuppressWarnings("unused")
	private static char[][] nm(int n, int m) {
		char[][] map = new char[n][];
		for (int i = 0; i < n; i++)
			map[i] = ns(m);
		return map;
	}

	@SuppressWarnings("unused")
	private static int[] na(int n) {
		int[] a = new int[n];
		for (int i = 0; i < n; i++)
			a[i] = ni();
		return a;
	}

	private static 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();
		}
	}

	@SuppressWarnings("unused")
	private static long nl() {
		long num = 0;
		int 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();
		}
	}

}
