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 Rust (1.15.1) (judge verdict: Wrong Answer)

const NOD: u64 = 1000000000 + 7;

fn read_vec<T: std::str::FromStr>() -> Vec<T>
{
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).ok();
    s.trim().split_whitespace()
        .map(|e| e.parse().ok().unwrap()).collect()
}

fn xor_series(src :&Vec<u64>, idx: usize, n: usize) -> u64
{
    let mut ret :u64 = 0;
    for i in (idx+1)..n {
        ret += {src[idx] ^ src[i]};
    }
    ret % NOD
}

fn main() {
    let mut n = String::new();
    std::io::stdin().read_line(&mut n).ok();
    let n :usize = n.trim().parse().ok().unwrap();

    let src :Vec<u64> = read_vec();
    //let mut xor :Vec<u32> = Vec::with_capacity(n);
    let mut xor_sum :u64 = 0;
    for i in 0..(n-1) {
        //xor.push(xor_series(&src, i, n);
        xor_sum += xor_series(&src, i, n);
    }
    println!("{}", xor_sum % NOD);
}