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 PHP7 (7.0.15) (judge verdict: Accepted)

<?php

$mod7 = (pow(10, 9) + 7);

$N = trim(fgets(STDIN));
$A = explode(' ', trim(fgets(STDIN)));

$cnt = [];
for ($i = 0; $i < 60; $i++) {

    $cnt[$i] = 0;
}

foreach ($A as $outerKey => $item) {

    for ($i = 0; $i < 60; $i++) {

        $cnt[$i] += $item >> $i & 1;
    }
}
$res = 0;
for ($i = 0; $i < 60; $i++) {

    $tmp = ($cnt[$i] * ($N - $cnt[$i])) % $mod7;
    $tmp2 = (1 << $i) % $mod7;
    $tmp = ($tmp * $tmp2) % $mod7;
    $res = ($res + $tmp) % $mod7;
}

echo $res . PHP_EOL;