1368_D. AND, OR and square sum
Gottfried learned about binary number representation. He then came up with this task and presented it to you.

You are given a collection of n non-negative integers a_1, …, a_n. You are allowed to perform the following operation: choose two distinct indices 1 ≤ i, j ≤ n. If before the operation a_i = x, a_j = y, then after the operation a_i = x~AND~y, a_j = x~OR~y, where AND and OR are bitwise AND and OR respectively (refer to the Notes section for formal description). The operation may be performed any number of times (possibly zero).

After all operations are done, compute ∑_{i=1}^n a_i^2 — the sum of squares of all a_i. What is the largest sum of squares you can achieve?

Input

The first line contains a single integer n (1 ≤ n ≤ 2 ⋅ 10^5).

The second line contains n integers a_1, …, a_n (0 ≤ a_i < 2^{20}).

Output

Print a single integer — the largest possible sum of squares that can be achieved after several (possibly zero) operations.

Examples

Input


1
123


Output


15129


Input


3
1 3 5


Output


51


Input


2
349525 699050


Output


1099509530625

Note

In the first sample no operation can be made, thus the answer is 123^2.

In the second sample we can obtain the collection 1, 1, 7, and 1^2 + 1^2 + 7^2 = 51.

If x and y are represented in binary with equal number of bits (possibly with leading zeros), then each bit of x~AND~y is set to 1 if and only if both corresponding bits of x and y are set to 1. Similarly, each bit of x~OR~y is set to 1 if and only if at least one of the corresponding bits of x and y are set to 1. For example, x = 3 and y = 5 are represented as 011_2 and 101_2 (highest bit first). Then, x~AND~y = 001_2 = 1, and x~OR~y = 111_2 = 7.
```python
from sys import stdin
input = stdin.readline
n = int(input())
a = [*map(lambda x: bin(int(x))[:1:-1], input().split())]
c1 = len(max(a, key=len))
a = [x + '0' * (c1 - len(x)) for x in a]
b = [sum(c[i] == '1' for c in a) for i in range(c1)]
c2 = max(b)
ans = 0
for i in range(c2):
	num = ''
	for i in range(c1):
		if b[i] != 0:
			b[i] -= 1
			num += '1'
		else:
			num += '0'
	ans += int(num[::-1], 2) ** 2
print(ans)
```