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 Python (3.4.3) (judge verdict: Time Limit Exceeded)

import sys
import math
from collections import defaultdict

sys.setrecursionlimit(10**7)
def input():
    return sys.stdin.readline()[:-1]

mod = 10**9 + 7

def I(): return int(input())
def II(): return map(int, input().split())
def III(): return list(map(int, input().split()))
def Line(N):
    read_all = [tuple(map(int, input().split())) for _ in range(N)]
    return map(list,zip(*read_all))

#################

import numpy as np

def F2_GaussJordan(A, is_extended = False):
    rank = 0
    for col in range(len(A[0])):
        if (is_extended and col == len(A[0])-1):
            break
        pivot = -1
        for row in range(rank,len(A)):
            if A[row][col]:
                pivot = row
                break
        if pivot == -1: 
            continue
        A[[pivot,rank]] = A[[rank,pivot]]
        for row in range(len(A)):
            if (row != rank and A[row][col]):
                A[row] ^= A[rank]
        rank += 1
    return A

N = I()
A = III()

xor = 0
for i in range(N):
    xor ^= A[i]
xor = format(xor,'b').zfill(60)

use_digit = []
ans = 0
for j in range(60)[::-1]:
    if xor[60-j-1] == '1':
        ans += 2**j
    else:
        use_digit.append(j)

a = np.zeros((N,len(use_digit)), dtype=int)
for i in range(N):
    binary = format(A[i], 'b').zfill(60)
    k = 0
    for j in use_digit:
        if binary[60-j-1] == '1':
            a[i][k] = 1
        else:
            a[i][k] = 0
        k += 1

g = F2_GaussJordan(a,False)

s = np.zeros(len(use_digit),dtype=int)
for i in range(N):
    for j in range(len(use_digit)):
        if g[i][j]==1:
            s ^= g[i]
            break

for k in range(len(s)):
    ans += s[k]*2**(use_digit[k]+1)

print(ans)