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)

#[test]
fn test_solve() {
    assert_eq!(solve("3\n1 2 3\n"), "6\n");
    assert_eq!(solve("10\n3 1 4 1 5 9 2 6 5 3\n"), "237\n");
    assert_eq!(
        solve("10\n3 14 159 2653 58979 323846 2643383 27950288 419716939 9375105820\n"),
        "103715602\n"
    );
}

fn solve(src: &str) -> String {
    let mut sc = Scanner::from_str(src);

    let n: usize = sc.read();
    let a: Vec<Vec<bool>> = (0..n)
        .map(|_| {
            let a: usize = sc.read();
            (0..61).map(|i| a & (1 << i) != 0).collect()
        })
        .collect();
    
    let mut s = Finite(0);
    for i in 0..61 {
        let one = Finite(a.iter().filter(|&a| a[i]).count() as u64);
        let zro = Finite(n as u64) - one;
        s = s + one * zro * Finite(1<<i);
    }
    format!("{}\n", s)
}
const MOD: u64 = 1_000_000_007;
#[derive(Copy, Clone, PartialEq, Eq, Debug)]
struct Finite(u64);
impl std::fmt::Display for Finite {
    fn fmt(&self, f: &mut std::fmt::Formatter) -> std::fmt::Result {
        write!(f, "{}", self.0)
    }
}
impl std::ops::Sub for Finite {
    type Output = Self;
    fn sub(self, rhs: Self) -> Self {
        Finite((self.0 + MOD - rhs.0) % MOD)
    }
}
impl std::ops::Mul for Finite {
    type Output = Self;
    fn mul(self, rhs: Self) -> Self {
        Finite(self.0 * rhs.0 % MOD)
    }
}
impl std::ops::Add for Finite {
    type Output = Self;
    fn add(self, rhs: Self) -> Self {
        Finite((self.0 + rhs.0) % MOD)
    }
}

fn main() {
    let mut buf = String::new();
    use std::io;
    use std::io::{Read, Write};
    io::stdin().read_to_string(&mut buf).unwrap();
    io::stdout().write_all(solve(&buf).as_bytes()).unwrap();
}

struct Scanner<'a>(std::str::SplitWhitespace<'a>);
impl<'a> Scanner<'a> {
    fn from_str(src: &str) -> Scanner {
        Scanner(src.split_whitespace())
    }
    fn get(&mut self) -> &str {
        self.0.next().unwrap()
    }
    fn read<T: std::str::FromStr>(&mut self) -> T {
        self.get().parse().ok().unwrap()
    }
}