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 Go (1.6) (judge verdict: Wrong Answer)

package main

import (
	"bufio"
	"fmt"
	"os"
	"strconv"
	"strings"
)

var q uint64 = 1000000007

func main() {
	stdin := bufio.NewScanner(os.Stdin)
	stdin.Scan()
	in0 := stdin.Text()
	stdin.Scan()
	in1 := stdin.Text()
	out, _ := do(in0, in1)
	fmt.Println(out)
}

func do(in0, in1 string) (string, error) {
	s := strings.Split(in1, " ")
	A := make([]uint64, 0, len(s))
	for i := range s {
		num, _ := strconv.ParseUint(s[i], 10, 64)
		A = append(A, num)
	}

	var n uint64 = 0
	for i := 0; i < len(A)-1; i++ {
		for j := i + 1; j < len(A); j++ {
			n = n + ((A[i] ^ A[j]) % q)
		}
	}
	return strconv.FormatUint(n%q, 10), nil
}