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 Julia (0.5.0) (judge verdict: Time Limit Exceeded)

parseInt(x) = parse(Int, x)
parseMap(x::Array{SubString{String},1}) = map(parseInt, x)

function GaussJordan(a::Array{Int,2},n,m)
	for i in 1:n
		for j in 1:m
			f = 0
			for k in i:n
				if a[k,j] != 0
					tmp = a[i,:]
					a[i,:] = a[k,:].%2
					if i!=k
						a[k,:] = tmp
					end
					for l in k+1:n
						x = lcm(a[l,j],a[i,j])
						if x > 0
							a[l,:] = mod.(div(x,a[l,j])*a[l,:]-div(x,a[i,j])*a[i,:],2)
						end
					end
					f = 1
					break
				end
			end
			if f == 1
				break
			end
		end
	end
	for i in 1:n
		j = 0
		for q in 1:m
			if a[n-i+1,q] != 0
				j = q
				break
			end
		end
		if j>0
			for k in i+1:n
				x = lcm(a[n-i+1,j],a[n-k+1,j])
				if x>0
					a[n-k+1,:] = mod.(div(x,a[n-i+1,j])*a[n-i+1,:]-div(x,a[n-k+1,j])*a[n-k+1,:],2)
				end
			end
		end
	end
	a
end


function main()
	n = readline() |> parseInt
	a = readline() |> split |> parseMap
	o = 0
	for i in 1:n
		o = o$a[i]
	end
	x = zeros(Int,60)
	r = 0
	while r<60
		if (o>>r)%2==1
			x[60-r] = 1
		end
		r += 1
	end
	g = zeros(Int,n,60)
	for i in 1:n
		for j in 1:60
			if x[j] == 0
				g[i,j] = (a[i]>>(60-j))%2
			end
		end
	end
	g=GaussJordan(g,n,60)
	y = zeros(Int,60)
	for i in 1:n
		for j in 1:60
			y[j] = y[j]$g[i,j]
		end
	end
	z = 0
	for i in 0:59
		z += y[i+1]*(2^(60-i))
		z += x[i+1]*(2^(59-i))
	end
	println(z)
end

main()