Catherine received an array of integers as a gift for March 8. Eventually she grew bored with it, and she started calculated various useless characteristics for it. She succeeded to do it for each one she came up with. But when she came up with another one — xor of all pairwise sums of elements in the array, she realized that she couldn't compute it for a very large array, thus she asked for your help. Can you do it? Formally, you need to compute

$$$ (a_1 + a_2) ⊕ (a_1 + a_3) ⊕ … ⊕ (a_1 + a_n) \\\ ⊕ (a_2 + a_3) ⊕ … ⊕ (a_2 + a_n) \\\ … \\\ ⊕ (a_{n-1} + a_n) \\\ $$$

Here x ⊕ y is a bitwise XOR operation (i.e. x ^ y in many modern programming languages). You can read about it in Wikipedia: <https://en.wikipedia.org/wiki/Exclusive_or#Bitwise_operation>.

Input

The first line contains a single integer n (2 ≤ n ≤ 400 000) — the number of integers in the array.

The second line contains integers a_1, a_2, …, a_n (1 ≤ a_i ≤ 10^7).

Output

Print a single integer — xor of all pairwise sums of integers in the given array.

Examples

Input


2
1 2


Output


3

Input


3
1 2 3


Output


2

Note

In the first sample case there is only one sum 1 + 2 = 3.

In the second sample case there are three sums: 1 + 2 = 3, 1 + 3 = 4, 2 + 3 = 5. In binary they are represented as 011_2 ⊕ 100_2 ⊕ 101_2 = 010_2, thus the answer is 2.

⊕ is the bitwise xor operation. To define x ⊕ y, consider binary representations of integers x and y. We put the i-th bit of the result to be 1 when exactly one of the i-th bits of x and y is 1. Otherwise, the i-th bit of the result is put to be 0. For example, 0101_2   ⊕   0011_2 = 0110_2.
//  package Quarantine;

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

public class Present {
    static class Reader
    {
        final private int BUFFER_SIZE = 1 << 16;
        private DataInputStream din;
        private byte[] buffer;
        private int bufferPointer, bytesRead;

        public Reader()
        {
            din = new DataInputStream(System.in);
            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }

        public Reader(String file_name) throws IOException
        {
            din = new DataInputStream(new FileInputStream(file_name));
            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }

        public String readLine() throws IOException
        {
            byte[] buf = new byte[64]; // line length
            int cnt = 0, c;
            while ((c = read()) != -1)
            {
                if (c == '\n')
                    break;
                buf[cnt++] = (byte) c;
            }
            return new String(buf, 0, cnt);
        }

        public int nextInt() throws IOException
        {
            int ret = 0;
            byte c = read();
            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)
                c = read();
            do
            {
                ret = ret * 10 + c - '0';
            }  while ((c = read()) >= '0' && c <= '9');

            if (neg)
                return -ret;
            return ret;
        }

        public long nextLong() throws IOException
        {
            long ret = 0;
            byte c = read();
            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)
                c = read();
            do {
                ret = ret * 10 + c - '0';
            }
            while ((c = read()) >= '0' && c <= '9');
            if (neg)
                return -ret;
            return ret;
        }

        public double nextDouble() throws IOException
        {
            double ret = 0, div = 1;
            byte c = read();
            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)
                c = read();

            do {
                ret = ret * 10 + c - '0';
            }
            while ((c = read()) >= '0' && c <= '9');

            if (c == '.')
            {
                while ((c = read()) >= '0' && c <= '9')
                {
                    ret += (c - '0') / (div *= 10);
                }
            }

            if (neg)
                return -ret;
            return ret;
        }

        private void fillBuffer() throws IOException
        {
            bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE);
            if (bytesRead == -1)
                buffer[0] = -1;
        }

        private byte read() throws IOException
        {
            if (bufferPointer == bytesRead)
                fillBuffer();
            return buffer[bufferPointer++];
        }

        public void close() throws IOException
        {
            if (din == null)
                return;
            din.close();
        }
    }
    public static void main(String[] args)throws IOException {
        Reader s=new Reader();
        int n=s.nextInt();
        int a[]=new int[n+1];
        for(int i=1;i<=n;i++){
            a[i]=s.nextInt();
        }
        int ans=0;
        for(int i=0;i<=25;i++){
            int b[]=getArray(a,i);
            Arrays.sort(b);
            long count=getCount(b,n,i);
//            System.out.println(count);
            if(count%2!=0){
                ans|=1<<i;
            }
        }
        System.out.println(ans);
    }
    public static int[] getArray(int a[],int k){
        int b[]=new int[a.length];
        int t=1<<(k+1);
        for(int i=1;i<a.length;i++){
            b[i]=a[i]%t;
        }
        return b;
    }
    public static long getCount(int b[],int n,int k){
        long ans=0;
        int left1=1<<k;
        int right1=1<<(k+1);
        int left2=(1 << k) + (1 << (k + 1));
        int right2=(1 << (k + 2)) - 1;
        for(int i=1;i<=n;i++){
            int rc=getInd(b,i,n,left1);
            int lc=getInd(b,i,n,right1);
            if(lc>=rc)
            ans+=lc-rc;
            if(k!=0) {
                rc = getInd(b, i, n, left2);
                lc = getInd(b, i, n, right2);
                if(lc>=rc)
                ans += lc - rc;
            }
        }
        return ans;
    }
    public static int getInd(int a[],int ind,int n,int reqd){
        int num=a[ind];
        int low=ind+1;
        int high=n;
        int ans=n+1;
        while(low<=high){
            int mid=(low+high)>>1;
            if(a[mid]+num>=reqd){
                ans=mid;
                high=mid-1;
            }
            else{
                low=mid+1;
            }
        }
        return ans;
    }
}
