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 Java8 (OpenJDK 1.8.0) (judge verdict: Runtime Error)

import java.io.*;
import java.util.*;

public class Main {
	public static void main(String[] args) throws IOException {
		try (BufferedReader in =
new BufferedReader(new InputStreamReader(System.in))) {
			
String line;
line = in.readLine();

int n = Integer.parseInt(line);

int[][] sayTable = new int[n][];
for (int i = 0; i < n; ++i) {
line = in.readLine();
int a = Integer.parseInt(line);
sayTable[i] = new int[a];
for (int j = 0; j < a; ++j) {
line = in.readLine();
String[] params = line.split(" ");
	int x = Integer.parseInt(params[0]) - 1;
	int y = Integer.parseInt(params[1]);
		sayTable[i][x] = y + 1;
	}
}
int maxHonest = search(sayTable, new int[n], 0);
System.out.println(maxHonest);
}
	}

	public static int search(
int[][] sayTable, int[] honest, int i) {

		if (i >= sayTable.length) {
			return (int) Arrays.stream(honest)
.filter(say -> say == 2)
.count();
		}

		int[] sayArray = sayTable[i];

		int count = 0;
		if (checkHonest(honest, sayArray)) {
	int[] copyHonest = Arrays.copyOf(honest, honest.length);
	setHonest(copyHonest, sayArray);
int c = search(sayTable, copyHonest, i + 1);
count = Math.max(c, count);
	}
		if (checkUnkind(honest, sayArray)) {
		int[] copyHonest = Arrays.copyOf(honest, honest.length);
setUnkind(copyHonest, sayArray);
int c = search(sayTable, copyHonest, i + 1);
count = Math.max(c, count);
	}
return count;
}



	public static boolean checkHonest(int[] honest, int[] sayArray) {
		for (int i = 0; i < sayArray.length; ++i) {
			int say = sayArray[i];
			if (say <= 0) {
				continue;
			}
			int h = honest[i];
			if (h != 0 || h != say) {
return false;				
			}
		}
return true;
	}

	public static boolean checkUnkind(int[] honest, int[] sayArray) {
		for (int i = 0; i < sayArray.length; ++i) {
			int say = sayArray[i];
			if (say <= 0) {
				continue;
			}
			int h = honest[i];
			if (h != 0 || h == say) {
return false;				
			}
		}
return true;
	}

public static void setHonest(int[] honest, int[] sayArray) {
		for (int i = 0; i < sayArray.length; ++i) {
			int say = sayArray[i];
			if (say == 1) {
				honest[i] = 1;
			} else if (say == 2) {
				honest[i] = 2;
			}
		}
	}

	public static void setUnkind(int[] honest, int[] sayArray) {
		for (int i = 0; i < sayArray.length; ++i) {
			int say = sayArray[i];
			if (say == 1) {
				honest[i] = 2;
			} else if (say == 2) {
				honest[i] = 1;
			}
		}
	}
}