People in the Tomskaya region like magic formulas very much. You can see some of them below.

Imagine you are given a sequence of positive integer numbers p1, p2, ..., pn. Lets write down some magic formulas:

<image><image>

Here, "mod" means the operation of taking the residue after dividing.

The expression <image> means applying the bitwise xor (excluding "OR") operation to integers x and y. The given operation exists in all modern programming languages. For example, in languages C++ and Java it is represented by "^", in Pascal — by "xor".

People in the Tomskaya region like magic formulas very much, but they don't like to calculate them! Therefore you are given the sequence p, calculate the value of Q.

Input

The first line of the input contains the only integer n (1 ≤ n ≤ 106). The next line contains n integers: p1, p2, ..., pn (0 ≤ pi ≤ 2·109).

Output

The only line of output should contain a single integer — the value of Q.

Examples

Input

3
1 2 3


Output

3
import java.io.*;
import java.util.*;
import java.math.*;

/**
 * Depeche Mode - Black Celebration.
 * 
 * @author Gorokhov Nikita (wackloner@gmail.com)
 */

public class C implements Runnable {
	
	private void solve() {
		int n = readInt(), q = 0;
		for (int i = 0; i < n; i++)
			q ^= readInt();
		int[] xor = new int[n + 1];
		for (int i = 1; i <= n; i++)
			xor[i] = xor[i - 1] ^ i;
		for (int mod = 2; mod <= n; mod++) {
			int cnt = n / mod, go = n - cnt * mod;
			if ((cnt & 1) == 1) {
				if (go + 1 < mod)
					q ^= xor[mod - 1] ^ xor[go];
			} else {
				q ^= xor[go];
			}
		}
		println(q);
	}
	
	public static void main(String[] args) {
		new C().run();
	}
	
	public void run() {
		solve();
		writer.close();
	}
	
	void halt() {
		writer.close();
		System.exit(0);
	}
	
	PrintWriter writer = new PrintWriter(System.out);
	
	void print(Object... objects) {
		for (int i = 0; i < objects.length; i++) {
			if (i != 0)
				writer.print(' ');
			writer.print(objects[i]);
		}
	}
	
	void println(Object... objects) {
		print(objects);
		writer.println();
	}
	
	void printArray(int[] array) {
		for (int i = 0; i < array.length; i++) {
			if (i != 0) writer.print(' ');
			writer.print(array[i]);
		}
		writer.println();
	}
	
	void printArray(long[] array) {
		for (int i = 0; i < array.length; i++) {
			if (i != 0) writer.print(' ');
			writer.print(array[i]);
		}
		writer.println();
	}
	
	void printMatrix(int[][] matrix) {
		for (int i = 0; i < matrix.length; i++)
			printArray(matrix[i]);
	}
	
	void printMatrix(long[][] matrix) {
		for (int i = 0; i < matrix.length; i++)
			printArray(matrix[i]);
	}
	
	/**
	 * Pure Egor's code is straight ahead.
	 */
	
	InputStream stream = System.in;
	byte[] buf = new byte[1024];
	int curChar, numChars;
	
	int readInt() {
		int c = read();
		while (isWhitespace(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 (!isWhitespace(c));
		return res * sgn;
	}
	
	long readLong() {
		int c = read();
		while (isWhitespace(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 (!isWhitespace(c));
		return res * sgn;
	}
	
	double readDouble() {
		int c = read();
		while (isWhitespace(c))
			c = read();
		int sgn = 1;
		if (c == '-') {
			sgn = -1;
			c = read();
		}
		double res = 0;
		while (!isWhitespace(c) && c != '.') {
			if (c == 'e' || c == 'E')
				return res * Math.pow(10, readInt());
			if (c < '0' || c > '9')
				throw new InputMismatchException();
			res *= 10;
			res += c - '0';
			c = read();
		}
		if (c == '.') {
			c = read();
			double m = 1;
			while (!isWhitespace(c)) {
				if (c == 'e' || c == 'E')
					return res * Math.pow(10, readInt());
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				m /= 10;
				res += (c - '0') * m;
				c = read();
			}
		}
		return res * sgn;
	}
	
	BigInteger readBigInteger() {
		try {
			return new BigInteger(readString());
		} catch (NumberFormatException e) {
			throw new InputMismatchException();
		}
	}
	
	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++];
	}
	
	String readString() {
		int c = read();
		while (isWhitespace(c))
			c = read();
		StringBuilder res = new StringBuilder();
		do {
			if (Character.isValidCodePoint(c))
				res.appendCodePoint(c);
			c = read();
		} while (!isWhitespace(c));
		return res.toString();
	}
	
	String readLine() {
		StringBuilder buf = new StringBuilder();
		int c = read();
		while (c != '\n' && c != -1) {
			if (c != '\r')
				buf.appendCodePoint(c);
			c = read();
		}
		return buf.toString();
	}
	
	boolean isWhitespace(int c) {
		return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
	}
}