Problem:
Score: 600 points

Problem Statement

We have N non-negative integers: A_1, A_2, ..., A_N.

Consider painting at least one and at most N-1 integers among them in red, and painting the rest in blue.

Let the beauty of the painting be the \mbox{XOR} of the integers painted in red, plus the \mbox{XOR} of the integers painted in blue.

Find the maximum possible beauty of the painting.

What is \mbox{XOR}?

The bitwise \mbox{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.

2 \leq N \leq 10^5

0 \leq A_i < 2^{60}\ (1 \leq i \leq N)

Input

Input is given from Standard Input in the following format:

N
A_1 A_2 ... A_N

Output

Print the maximum possible beauty of the painting.

Sample Input 1

3
3 6 5

Sample Output 1

12

If we paint 3, 6, 5 in blue, red, blue, respectively, the beauty will be (6) + (3 \oplus 5) = 12.

There is no way to paint the integers resulting in greater beauty than 12, so the answer is 12.

Sample Input 2

4
23 36 66 65

Sample Output 2

188

Sample Input 3

20
1008288677408720767 539403903321871999 1044301017184589821 215886900497862655 504277496111605629 972104334925272829 792625803473366909 972333547668684797 467386965442856573 755861732751878143 1151846447448561405 467257771752201853 683930041385277311 432010719984459389 319104378117934975 611451291444233983 647509226592964607 251832107792119421 827811265410084479 864032478037725181

Sample Output 3

2012721721873704572

A_i and the answer may not fit into a 32-bit integer type.

Solution in C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <iostream>
#include <vector>
#include <map>
#include <set>
#include <string>
#include <utility>
#include <algorithm>
#include <cstdio>
#include <iomanip>
#include <queue>
#include <deque>
#include <stack>
#include <fstream>
#include <cmath>
#include <random>
#include <complex>
#include <functional>
#include <bitset>
#include <sstream>
#include <cassert>
#include <time.h>

#define ll int64_t
#define Rep(i, n) for (ll i = 0; i < n; i++)
using namespace std;
typedef vector<ll> vec;
typedef vector<vec> mat;

const ll inf = 1LL << 60;

template<class T> inline void chmin(T& a, T b) {
    if (a > b) {
        a = b;
    }
}
template<class T> inline void chmax(T& a, T b) {
    if (a < b) {
        a = b;
    }
}
void printvec (vec &v) {
    Rep (i, (ll)v.size()) {
        cout << v[i] << " \n"[i+1 == (ll)v.size()];
    }
}

int main(){
    cin.tie(0);
    ios::sync_with_stdio(false);

    ll N;
    cin >> N;
    vec A(N);
    Rep (i, N) {
        cin >> A[i];
    }

    ll ans = 0;
    Rep (i, 60) {
        ll cnt = 0;
        Rep (j, N) {
            if ((A[j] >> i) & 1) {
                cnt++;
            }
        }

        if (cnt % 2 == 1) {
            // cout << "i=" << i << "\n";
            ans += (1LL << i);
            Rep (j, N) {
                A[j] &= ~(1LL << i);
            }
        }
    }

    // printvec(A);

    vec basis;
    for (ll e : A) {
        for (ll b : basis) {
            chmin(e, e ^ b);
        }
        if (e) {
            basis.push_back(e);
        }
    }
    
    sort(basis.begin(), basis.end());

    ll n = basis.size();
    Rep (i, n) {
        Rep (j, n) {
            if (i == j) continue;
            chmin(basis[j], basis[j] ^ basis[i]);
        }
    }

    // printvec(basis);

    ll tmp = 0;
    for (ll e : basis) {
        tmp = tmp ^ e;
    }

    ans += 2 * tmp;
    cout << ans << "\n";

    // for (ll i = n-1; i >= 0; i--) {
    //     ans += 2 * basis[i];
    //     for (ll digit = 59; digit >= 0; digit--) {
    //         if (basis[i] >> digit & 1) {
    //             for (ll j = i-1; j >= 0; j--) {
    //                 if (basis[j] >> digit & 1) basis[j] = 0;
    //             }
    //         }
    //     }
    // }

    // cout << ans << "\n";

}