﻿ AGC035 A - XOR Circle - Atcoder

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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 $x_1, x_2, ..., x_n$ 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 $c_1, c_2, ...c_m$ 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:

$N$
$a_1$ $a_2$ $\ldots$ $a_{N}$


### 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.