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 Perl (v5.18.2) (judge verdict: Wrong Answer)

use v5.18; # strict say state
use warnings;
use List::Util qw(reduce first max min sum0);

chomp (my $n = <STDIN>);
chomp (my @a = split / /, <STDIN>);
sub bitset {
  my $x = sprintf "%060b", shift;
  return $x;
}
my (@b, @c);
for my $i (0..($n-1)) {
  $b[$i] = [split(//, bitset($a[$i]))];
  for my $j (0..59) {
    $c[$j] += $b[$i][$j];
  }
}
say @c;
@c = map {($n-$_)*$_} @c;
say @c;
my $ans = 0;
for my $i (0..60) {
  $ans += 2 ** (59-$i) * $c[$i];
  $ans %= 1e9+7;
}
say $ans;