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: Time Limit Exceeded)

package main

import (
	"fmt"
	"math"
)

func main() {
	var n int
	fmt.Scan(&n)
	an := make([]int64, n)
	for i := 0; i < n; i++ {
		fmt.Scan(&an[i])
	}

	mod := int64(math.Pow(10, 9) + 7)
	var ans int64
	for d := 0; d <= 60; d++ {
		var count0 int64
		var count1 int64
		for _, a := range an {
			if (a>>uint(d))&1 == 1 {
				count1++
			} else {
				count0++
			}
		}

		keta := (1 << uint(d)) % mod
		count := (count0 * count1) * keta % mod
		ans += count
		ans %= mod
	}

	fmt.Println(ans)
}