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 PHP (5.6.30) (judge verdict: Wrong Answer)

<?php 
// A Simple PHP program to compute 
// sum of bitwise OR of all pairs 

// Returns sum of bitwise OR 
// of all pairs 
function pairORSum($arr, $n) 
{ 
	
	// Initialize result 
	$ans = 0; 

	// Consider all pairs 
	// (arr[i], arr[j) such that 
	// i < j 
	for ( $i = 0; $i < $n; $i++) 
		for ( $j = $i + 1; $j < $n; $j++) 
			$ans += $arr[$i] ^ $arr[$j]; 

	return $ans; 
} 

	// Driver Code 
	$arr = array( 5, 9, 7, 6 ); 
	$n = count($arr); 
	echo pairORSum($arr, $n) ; 

// This code is contributed by anuj_67. 
?>