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++14 (GCC 5.4.1) (judge verdict: Accepted)

#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef pair<ll,ll>pi;
const int MAXN=200005;
const int MOD=1000000007;
#define FOR(i,a,b) for(int i=(a);i<=(b);i++)
#define DEC(i,a,b) for(int i=(a);i>=(b);i--)
#define fst first
#define snd second
#define pb push_back
#define all(v) (v).begin(),(v).end()
#define sz(v) ((int)(v).size())
#define db(x) cerr<<#x<<" = "<<x<<"\n"
#define LOW(v,x) (lower_bound(all(v),(x))-(v).begin())

int N;
int A[MAXN];
map<int,int>cnt;
void imp(){cout<<"No\n";exit(0);}

int32_t main(){
	ios_base::sync_with_stdio(false);
	cin.tie(0);
	
	cin>>N;
	FOR(i,0,N-1)cin>>A[i];
	FOR(i,0,N-1)cnt[A[i]]++;
	if(sz(cnt)>3)imp();
	if(N%3==0){
		if(sz(cnt)==1){
			if(cnt.begin()->fst!=0)imp();
		}
		else if(sz(cnt)==2){
			if(cnt.begin()->fst!=0)imp();
			if(cnt.begin()->snd!=N/3)imp();
		}
		else if(sz(cnt)==3){
			int x=0;
			for(auto i:cnt)x^=i.fst;
			if(x!=0)imp();
			for(auto i:cnt)if(i.snd!=N/3)imp();
		}
	}
	else{
		if(sz(cnt)>1)imp();
		if(cnt.begin()->fst!=0)imp();
	}
	cout<<"Yes\n";
}
/*
5
0 011001010110110110100111110011010111111111111000101011100101001
7 011001010110110110100111110011010111111111111000101011100101001
62 011001010110110110100111110011010111111111111000101011100101001
63 011001010110110110100111110011010111111111111000101011100101001
-1 011001010110110110100111110011010111111111111000101011100101001
*/