Problem:
Score : 300 points

Problem Statement

Snuke has N hats. The i-th hat has an integer a_i written on it.

There are N camels standing in a circle.
Snuke will put one of his hats on each of these camels.

If there exists a way to distribute the hats to the camels such that the following condition is satisfied for every camel, print Yes; otherwise, print No.

The bitwise XOR of the numbers written on the hats on both adjacent camels is equal to the number on the hat on itself.

What is XOR?

The bitwise XOR x_1 \oplus x_2 \oplus \ldots \oplus x_n of n non-negative integers x_1, x_2, \ldots, x_n is defined as follows:

- When x_1 \oplus x_2 \oplus \ldots \oplus x_n is written in base two, the digit in the 2^k's place (k \geq 0) is 1 if the number of integers among x_1, x_2, \ldots, x_n whose binary representations have 1 in the 2^k's place is odd, and 0 if that count is even.

For example, 3 \oplus 5 = 6.

Constraints

All values in input are integers.

3 \leq N \leq 10^{5}

0 \leq a_i \leq 10^{9}

Input

Input is given from Standard Input in the following format:

N
a_1 a_2 \ldots a_{N}

Output

Print the answer.

Sample Input 1

3
1 2 3

Sample Output 1

Yes

If we put the hats with 1, 2, and 3 in this order, clockwise, the condition will be satisfied for every camel, so the answer is Yes.

Sample Input 2

4
1 2 4 8

Sample Output 2

No

There is no such way to distribute the hats; the answer is No.

Solution in C# (Mono 4.6.2.0) (judge verdict: Runtime Error)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace AtCorder
{
	public class Program
	{
		const long MOD = 1000000007;
		static void Main(string[] args)
		{
			Scanner cin = new Scanner();
			long n = cin.Long();
			long[] a = new long[n];
			for (int i = 0; i < n; i++) {
				a[i] = cin.Long();
			}

			long[] nums = new long[100001];
			for (int i = 0; i < n; i++) {
				nums[a[i]]++;
			}

			var av = nums
				.Select((x, index) => new Tuple<long, long>(index, x))
				.Where(x => x.Item2 > 0)
				.ToList();
			if (av.Count == 1) {
				if (av[0].Item1 == 0) {
					Console.WriteLine("Yes");
				} else {
					Console.WriteLine("No");
				}
			} else if (av.Count == 2) {
				if (av[0].Item2 == av[1].Item2 * 2) {
					if (av[1].Item1 == 0 && ((av[0].Item1 ^ av[0].Item1) == 0)) {
						Console.WriteLine("Yes");
					} else {
						Console.WriteLine("No");
					}
				} else if (av[0].Item2 * 2 == av[1].Item2) {
					if (av[0].Item1 == 0 && ((av[1].Item1 ^ av[1].Item1) == 0)) {
						Console.WriteLine("Yes");
					} else {
						Console.WriteLine("No");
					}
				} else {
					Console.WriteLine("No");
				}
			} else if (av.Count == 3) {
				if (av[0].Item2 == av[1].Item2
					&& av[1].Item2 == av[2].Item2
					&& ((av[0].Item1 ^ av[1].Item1 ^ av[2].Item1) == 0)) {
					Console.WriteLine("Yes");
				} else {
					Console.WriteLine("No");
				}
			} else {
				Console.WriteLine("No");
			}
		}
	}

	public class Scanner
	{
		private readonly char[] delimiter_ = new char[] { ' ' };
		private string[] buf_;
		private int index_;
		
		public Scanner()
		{
			buf_ = new string[0];
			index_ = 0;
		}

		public string Next()
		{
			if (index_ < buf_.Length) {
				return buf_[index_++];
			}

			string st = Console.ReadLine();
			while (st == "") {
				st = Console.ReadLine();
			}

			buf_ = st.Split(delimiter_, StringSplitOptions.RemoveEmptyEntries);
			if (buf_.Length == 0) {
				return Next();
			}

			index_ = 0;
			return buf_[index_++];
		}

		public int Int()
		{
			return int.Parse(Next());
		}
		public int[] ArrayInt(int N, int add = 0)
		{
			int[] Array = new int[N];
			for (int i = 0; i < N; i++) {
				Array[i] = Int() + add;
			}
			return Array;
		}

		public long Long()
		{
			return long.Parse(Next());
		}

		public long[] ArrayLong(int N, long add = 0)
		{
			long[] Array = new long[N];
			for (int i = 0; i < N; i++) {
				Array[i] = Long() + add;
			}
			return Array;
		}

		public double Double()
		{
			return double.Parse(Next());
		}

		public double[] ArrayDouble(int N, double add = 0)
		{
			double[] Array = new double[N];
			for (int i = 0; i < N; i++) {
				Array[i] = Double() + add;
			}
			return Array;
		}
	}
}