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 Pascal (FPC 2.6.2) (judge verdict: Accepted)

const p = 1000000007;
var
  a: array [1..300000] of int64;
  n, i, j, s, ans: longint;
function add(x, y: longint): longint; inline;
begin
  inc(x, y);
  if x >= p then dec(x, p);
  exit(x);
end;
function mul(x, y: longint): longint; inline;
begin
  exit(int64(x) * y mod p);
end;
begin
  read(n);
  for i := 1 to n do read(a[i]);
  for i := 0 to 59 do
  begin
    s := 0;
    for j := 1 to n do inc(s, (a[j] shr i) and 1);
    ans := add(ans, mul(mul(s, n - s), int64(1) shl i mod p));
  end;
  writeln(ans);
end.