cf424c 亦或交换律 模循环节 亦或前缀和

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 p₁, p₂, ...,p_n. Lets write down some magic formulas:

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

The expression  means applying the bitwisexor (excluding "OR") operation to integersx 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 sequencep, calculate the value of Q.

Input

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

Output

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

Sample test(s)

Input

31 2 3

Output

3

1--n mod 1--n

#include<iostream>#include<cstdio>#include<cmath>#include<algorithm>#include<cstring>#include<queue>using namespace std;long long esum[1000005];int main(){   int n;   while(~scanf("%d",&n))   {       long long ans=0;       for(int i=0;i<n;i++)       {           long long tp;           scanf("%lld",&tp);           ans^=tp;       }       esum[0]=0;       esum[1]=1;       for(int i=2;i<=n;i++)       {           esum[i]=i^esum[i-1];       }       for(int i=2;i<=n;i++)       {           int num=n/i;           int res=n%i;           if(num%2==1)            ans^=esum[i-1];           ans^=esum[res];       }       printf("%lld\n",ans);   }}