【cf424C】Magic Formulas

2014年4月26日9770

People in the Tomskaya region like magic formulas very much. You can see some of them below.

Imagine you are given a sequence of positive integer numbers p1p2, …, pn. Lets write down some magic formulas:

Here, “mod” means the operation of taking the residue after dividing.

The expression  means applying the bitwise xor (excluding “OR”) operation to integers x and y. The given operation exists in all modern programming languages. For example, in languages C++ and Java it is represented by “^“, in Pascal — by “xor”.

People in the Tomskaya region like magic formulas very much, but they don’t like to calculate them! Therefore you are given the sequence p, calculate the value of Q.

Input

The first line of the input contains the only integer n (1 ≤ n ≤ 106). The next line contains n integers: p1, p2, …, pn (0 ≤ pi ≤ 2·109).

Output

The only line of output should contain a single integer — the value of Q.

Sample test(s)
input

output

题解

首先通过交换律可得出变为ans=p1^p2^p3^…pn

然后ans^1-n这一段分别^1-n