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

public class Main implements Runnable {
		
	public void solve() throws IOException {
		//http://codeforces.com/blog/entry/11917#comment-167054
            int N = nextInt();
            int answer = 0;
            for(int i = 0; i < N; i++) answer = answer ^ nextInt();
            
            for(int k = 1; k <= N; k++){
                int repeat = N / k; //times
                int remains = N % k;
                if(repeat % 2 == 1) answer = answer ^ getXOR(k-1);
                answer = answer ^ getXOR(remains);
            }
            
            out.println(answer);
	}
        
        private int getXOR(int n){
            if(n%4 == 0) return n;
            else if(n%4 == 1) return 1;
            else if(n%4 == 2) return n + 1;
            else if(n%4 == 3) return 0;
            
            //it could also be done by taking XOR 0^1^2^3^...n and storing it in array [preprocess]
            return -1;
        }

	
	
	
	
	
	
	
	
	
	
	
	
	
	
	
	
	
	
	//-----------------------------------------------------------
	public static void main(String[] args) {
		new Main().run();
	}

        public void debug(Object... arr){
            System.out.println(Arrays.deepToString(arr));
        }

        public void print1Int(int[] a){
                for(int i = 0; i < a.length; i++)
                        System.out.print(a[i] + " ");
                System.out.println();
        }
        
        public void print2Int(int[][] a){
                for(int i = 0; i < a.length; i++){
                        for(int j = 0; j < a[0].length; j++){
                                System.out.print(a[i][j] + " ");
                        }
                        System.out.println();
                }
        }
        
	public void run() {
		try {
			in = new BufferedReader(new InputStreamReader(System.in));
                        out = new PrintWriter(System.out);
			tok = null;
			solve();
			in.close();
                        out.close();
		} catch (IOException e) {
			System.exit(0);
		}
	}

	public String nextToken() throws IOException {
		while (tok == null || !tok.hasMoreTokens()) {
			tok = new StringTokenizer(in.readLine());
		}
		return tok.nextToken();
	}

	public int nextInt() throws IOException {
		return Integer.parseInt(nextToken());
	}

	public long nextLong() throws IOException {
		return Long.parseLong(nextToken());
	}

	public double nextDouble() throws IOException {
		return Double.parseDouble(nextToken());
	}
        PrintWriter out;
	BufferedReader in;
	StringTokenizer tok;
}