While playing yet another strategy game, Mans has recruited $n$ Swedish heroes, whose powers which can be represented as an array $a$.

Unfortunately, not all of those mighty heroes were created as capable as he wanted, so that he decided to do something about it. In order to accomplish his goal, he can pick two consecutive heroes, with powers $a_i$ and $a_{i+1}$, remove them and insert a hero with power $-(a_i+a_{i+1})$ back in the same position. 

For example if the array contains the elements $[5, 6, 7, 8]$, he can pick $6$ and $7$ and get $[5, -(6+7), 8] = [5, -13, 8]$.

After he will perform this operation $n-1$ times, Mans will end up having only one hero. He wants his power to be as big as possible. What's the largest possible power he can achieve?


-----Input-----

The first line contains a single integer $n$ ($1 \le n \le 200000$).

The second line contains $n$ integers $a_1, a_2, \ldots, a_n$ ($-10^9 \le a_i \le 10^9$) — powers of the heroes.


-----Output-----

Print the largest possible power he can achieve after $n-1$ operations.


-----Examples-----
Input
4
5 6 7 8

Output
26

Input
5
4 -5 9 -2 1

Output
15



-----Note-----

Suitable list of operations for the first sample:

$[5, 6, 7, 8] \rightarrow [-11, 7, 8] \rightarrow [-11, -15] \rightarrow [26]$

Difficulty: VERY_HARD
Tags: Dynamic programming

Implementation

Complete search
Skill types: Dynamic programming

Complete search

Starter code:

Solutions:
(N, x, y, z, v, w) = (input(), -9000000000.0, -9000000000.0, -9000000000.0, 0, 1)
for A in map(int, input().split()):
	(x, y, z, v, w) = (max(z + A, y - A), max(x + A, z - A), max(y + A, x - A, v - w * A), v + w * A, -w)
print([v, y][N > '1'])


n = int(input())
a = list(map(int, input().split()))
if n == 1:
	print(a[0])
	exit()
inf = 1002003004005006007
dp = [[[-inf, -inf, -inf] for _ in range(2)] for _ in range(n + 1)]
dp[0][0][0] = 0
for i in range(n):
	for j in range(2):
		for k in range(3):
			dp[i + 1][j][(k + 1) % 3] = max(dp[i + 1][j][(k + 1) % 3], dp[i][j][k] + a[i])
			dp[i + 1][j][(k - 1) % 3] = max(dp[i + 1][j][(k - 1) % 3], dp[i][j][k] - a[i])
	if i + 1 < n:
		for k in range(3):
			dp[i + 2][1][(k + 2) % 3] = max(dp[i + 2][1][(k + 2) % 3], dp[i][0][k] + a[i] + a[i + 1])
			dp[i + 2][1][(k - 2) % 3] = max(dp[i + 2][1][(k - 2) % 3], dp[i][0][k] - a[i] - a[i + 1])
ans = dp[n][1][1]
print(ans)


n = int(input())
a = list(map(int, input().split()))
INF = 10 ** 20
DP = [-INF] * 12
DP[1] = a[0]
DP[5] = -a[0]
for elem in a[1:]:
	newDP = []
	newDP.append(DP[5] + elem)
	newDP.append(DP[3] + elem)
	newDP.append(DP[4] + elem)
	newDP.append(DP[1] - elem)
	newDP.append(DP[2] - elem)
	newDP.append(DP[0] - elem)
	newDP.append(max(DP[2] + elem, DP[8] + elem, DP[11] + elem))
	newDP.append(max(DP[0] + elem, DP[6] + elem, DP[9] + elem))
	newDP.append(max(DP[1] + elem, DP[7] + elem, DP[10] + elem))
	newDP.append(max(DP[4] - elem, DP[7] - elem, DP[10] - elem))
	newDP.append(max(DP[5] - elem, DP[8] - elem, DP[11] - elem))
	newDP.append(max(DP[3] - elem, DP[6] - elem, DP[9] - elem))
	DP = newDP
if n == 1:
	print(a[0])
else:
	print(max(DP[7], DP[10]))


from sys import stdin
input = stdin.readline

def solve():
	n = int(input())
	a = list(map(int, input().split()))
	if n == 1:
		print(max(a[0], -a[0]))
		return
	NINF = -10 ** 15
	dp = [[[[NINF] * 2 for i in range(2)] for j in range(3)] for k in range(n)]
	dp[0][n % 3][0][1] = a[0]
	dp[0][(n + 1) % 3][0][0] = -a[0]
	for i in range(n - 1):
		for j in range(3):
			for k in range(2):
				for l in range(2):
					if dp[i][j][k][l] > NINF:
						dp[i + 1][j][k or l == 1][1] = max(dp[i + 1][j][k or l == 1][1], dp[i][j][k][l] + a[i + 1])
						dp[i + 1][(j + 1) % 3][k or l == 0][0] = max(dp[i + 1][(j + 1) % 3][k or l == 0][0], dp[i][j][k][l] - a[i + 1])
	print(max(dp[n - 1][1][1][1], dp[n - 1][1][1][0]))

def __starting_point():
	solve()
__starting_point()


n = int(input())
a = [int(i) for i in input().split()]
if n == 1:
	print(a[0])
else:
	dp = [dict(), dict()]
	dp[0][0, 0, 0] = a[0]
	dp[0][1, 0, 1] = -a[0]
	for i in range(1, n):
		_i = i & 1
		dp[_i].clear()
		for j in range(3):
			dp[_i][j, 0, 0] = dp[1 - _i].get((j, 0, 1), -200000000000000.0 - 5) + a[i]
			dp[_i][j, 0, 1] = dp[1 - _i].get(((j + 2) % 3, 0, 0), -200000000000000.0 - 5) - a[i]
			dp[_i][j, 1, 0] = max(dp[1 - _i].get((j, 0, 0), -200000000000000.0 - 5) + a[i], dp[1 - _i].get((j, 1, 0), -200000000000000.0 - 5) + a[i], dp[1 - _i].get((j, 1, 1), -200000000000000.0 - 5) + a[i])
			dp[_i][j, 1, 1] = max(dp[1 - _i].get(((j + 2) % 3, 0, 1), -200000000000000.0 - 5) - a[i], dp[1 - _i].get(((j + 2) % 3, 1, 0), -200000000000000.0 - 5) - a[i], dp[1 - _i].get(((j + 2) % 3, 1, 1), -200000000000000.0 - 5) - a[i])
	print(max(dp[n - 1 & 1][(3 - (n + 2) % 3) % 3, 1, 0], dp[n - 1 & 1][(3 - (n + 2) % 3) % 3, 1, 1]))


N = int(input())
(a, b, c, d, e) = (float('-inf'), float('-inf'), float('-inf'), 0, 1)
for x in map(int, input().split()):
	(a, b, c, d, e) = (max(c + x, b - x), max(a + x, c - x), max(b + x, a - x, d - e * x), d + e * x, -e)
print([d, b][N > 1])


from heapq import nsmallest
from math import inf as _inf
import sys as _sys

def main():
	(n,) = _read_ints()
	a = tuple(_read_ints())
	result = find_max_power_can_make(a)
	print(result)

def _read_line():
	result = _sys.stdin.readline()
	assert result[-1] == '\n'
	return result[:-1]

def _read_ints():
	return map(int, _read_line().split())

def find_max_power_can_make(heroes_powers):
	heroes_powers = tuple(heroes_powers)
	assert heroes_powers
	abs_powers_sum = sum(map(abs, heroes_powers))
	if len(heroes_powers) <= 9:
		return _compute_using_brute_force(heroes_powers)
	zeros_n = heroes_powers.count(0)
	if zeros_n >= 2:
		return abs_powers_sum
	assert zeros_n <= 1
	n = len(heroes_powers)
	if n % 3 == 1 % 3:
		can_invert_mod_3 = 0
	elif n % 3 == 2 % 3:
		can_invert_mod_3 = 2
	else:
		assert n % 3 == 3 % 3
		can_invert_mod_3 = 1
	result = -_inf
	for is_zero_positive in (False, True):
		if zeros_n == 0 or is_zero_positive:
			signs = [1 if x >= 0 else -1 for x in heroes_powers]
		else:
			signs = [1 if x > 0 else -1 for x in heroes_powers]
		negative_n = signs.count(-1)
		have_pair_of_same = any((signs[i] == signs[i + 1] for i in range(len(signs) - 1)))
		is_trivial = not (not have_pair_of_same and negative_n % 3 == can_invert_mod_3)
		if is_trivial:
			if negative_n % 3 == can_invert_mod_3:
				result = max(result, abs_powers_sum)
				continue
			negative_to_inverse_1 = negative_n
			while negative_to_inverse_1 % 3 != can_invert_mod_3:
				negative_to_inverse_1 -= 1
			negative_to_inverse_2 = negative_to_inverse_1 + 3
		else:
			negative_to_inverse_1 = negative_n - 3
			negative_to_inverse_2 = negative_n + 3
			min_pos = max(heroes_powers, key=lambda x: (x >= 0 if is_zero_positive else x > 0, -abs(x)))
			max_neg = max(heroes_powers, key=lambda x: (x < 0 if is_zero_positive else x <= 0, x))
			result = max(result, abs_powers_sum - 2 * abs(min_pos) - 2 * abs(max_neg))
		if negative_to_inverse_1 >= 0:
			negative_to_remain_n = negative_n - negative_to_inverse_1
			assert negative_to_remain_n > 0
			negative_powers = tuple(filter(lambda x: x < 0 if is_zero_positive else x <= 0, heroes_powers))
			if negative_to_remain_n <= len(negative_powers):
				negative_to_remain = nsmallest(negative_to_remain_n, negative_powers, key=abs)
				result = max(result, abs_powers_sum - 2 * abs(sum(negative_to_remain)))
		if negative_to_inverse_2 <= n:
			positive_to_inverse_n = negative_to_inverse_2 - negative_n
			assert positive_to_inverse_n > 0
			positive_powers = tuple(filter(lambda x: x >= 0 if is_zero_positive else x > 0, heroes_powers))
			if positive_to_inverse_n <= len(positive_powers):
				positive_to_inverse = nsmallest(positive_to_inverse_n, positive_powers, key=abs)
				result = max(result, abs_powers_sum - 2 * sum(positive_to_inverse))
	return result

def _compute_using_brute_force(seq):
	n = len(seq)
	if n == 1:
		return seq[0]
	return max((_compute_using_brute_force(seq[:i] + (-(seq[i] + seq[i + 1]),) + seq[i + 2:]) for i in range(n - 1)))

def __starting_point():
	main()
__starting_point()