Problem:
Score : 400 points

Problem Statement

We have N integers. The i-th integer is A_i.

Find \sum_{i=1}^{N-1}\sum_{j=i+1}^{N} (A_i \mbox{ XOR } A_j), modulo (10^9+7).

What is \mbox{ XOR }?

The XOR of integers A and B, A \mbox{ XOR } B, is defined as follows:

When A \mbox{ XOR } B is written in base two, the digit in the 2^k's place (k \geq 0) is 1 if either A or B, but not both, has 1 in the 2^k's place, and 0 otherwise.

For example, 3 \mbox{ XOR } 5 = 6. (In base two: 011 \mbox{ XOR } 101 = 110.)

Constraints

2 \leq N \leq 3 \times 10^5

0 \leq A_i < 2^{60}

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
A_1 A_2 ... A_N

Output

Print the value \sum_{i=1}^{N-1}\sum_{j=i+1}^{N} (A_i \mbox{ XOR } A_j), modulo (10^9+7).

Sample Input 1

3
1 2 3

Sample Output 1

6

We have (1\mbox{ XOR } 2)+(1\mbox{ XOR } 3)+(2\mbox{ XOR } 3)=3+2+1=6.

Sample Input 2

10
3 1 4 1 5 9 2 6 5 3

Sample Output 2

237

Sample Input 3

10
3 14 159 2653 58979 323846 2643383 27950288 419716939 9375105820

Sample Output 3

103715602

Print the sum modulo (10^9+7).

Solution in C++14 (GCC 5.4.1) (judge verdict: Time Limit Exceeded)

#include <bits/stdc++.h>
#define rep(i,n) for(int i=0;i<n;i++)
#define repr(i,n) for(int i=n-1;i>=0;i--)
#define MAX(a,b) a=a>b?a:b
#define MIN(a,b) a=a>b?a:b
#define REP(i,x,n) for(int i=x;i<n;i++)
#define REPR(i,x,n) for(int i=n-1;i>=x;i--)
#define F first
#define S second
using namespace std;
typedef long long ll;
typedef pair<int, int> P;
const ll MOD =1000000007;//1e9 + 7;



int main(){
	int n;
    cin>>n;
    ll s[1010101];
    ll ma=0;
    rep(i,n){
        cin>>s[i];
        rep(j,i){
            ma=(ma+(s[j]^s[i]))%MOD;
        }
        
        
    }
    cout<<ma<<endl;

}