Problem: 2062C - Cirno and Operations
Language: python

Solution 1 (runtime: 140 ms):
mod = 1e9 + 7


def binpow(a, n):
    res = 1
    while n != 0:
        print(bin(n))
        if n & 1:
            res = res * a % mod
        a = a * a % mod
        n >>= 1
    return res


def resheto(n):
    # n = int(input())
    primes = [int(a) for a in range(n + 1)]
    primes[1] = 0

    i = 2
    while i <= n:
        j = i + i
        while j <= n:
            primes[j] = 0
            j += i

        i += 1
    primes = [i for i in primes if i != 0]
    return primes


def delit(x):
    arr = []
    for i in range(2, int(x ** 0.5) + 1):
        if x % i == 0:
            arr.append(i)
            arr.append(x // i)
    return sorted(arr)


# n, k = 100000, 1
# arr = [10000] * 99999
# arr.append(-1)


def xfind(arr, x):
    r = len(arr) - 1
    l = 0
    while l <= r:
        mid = (l + r) // 2

        if arr[mid] == x:
            return True

        elif arr[mid] < x:
            l = mid + 1

        elif arr[mid] > x:
            r = mid - 1

    return False



from math import ceil
import bisect

from decimal import Decimal, getcontext

getcontext().prec = 15
#
# resh = resheto(10**6)

# def s(arr):
#     s = 0
#     for i in range(len(arr)):
#         mn = 1000000
#         for j in range(i, len(arr)):
#             mn = min(mn, arr[j])
#             s += mn
#     print(s)


from bisect import bisect_left, bisect_right

# def bs_l(a, x, lo=0, hi=None):
#     if hi is None: hi = len(a)
#     pos = bisect_left(a, x, lo, hi)
#     return pos if pos != hi and a[pos] == x else -1
#
# def bs_r(a, x, lo=0, hi=None):
#     if hi is None: hi = len(a)
#     pos = bisect_right(a, x, lo, hi)
#     return pos if pos != hi and a[pos] == x else -1

def pref_sum(arr):
    pref_sum_arr = [0] * len(arr)
    pref_sum_arr[0] = arr[0]
    for i in range(1, len(arr)):
        pref_sum_arr[i] = pref_sum_arr[i-1] + arr[i]
    return pref_sum_arr


def fibonacci(n):
    if n < 2:
        return n
    pp = 0
    p = 1
    for i in range(n - 1):
        pp, p = p, pp + p
    return p


import math
def fibonacci_binet(n):
    sqrt5 = math.sqrt(5)
    phi = (1 + sqrt5) / 2
    psi = (1 - sqrt5) / 2
    return round((phi**n - psi**n) / sqrt5)


from math import ceil
from bisect import bisect_left, bisect_right
from math import gcd, factorial
from decimal import Decimal
getcontext().prec = 4


def new_arr(arr):
    x = []
    for i in range(len(arr) - 1):
        x.append(arr[i+1] - arr[i])
    return x

def solve():
    n = int(input())
    arr = [int(a) for a in input().split()]
    ans = sum(arr)
    
    while len(arr) > 1:
        rev_arr = new_arr(arr[::-1])
        arr = new_arr(arr)
        ans = max(ans, sum(arr), sum(rev_arr))
        
    print(ans)


def main():
    t = int(input())
    for _ in range(t):
        # if _ == 152:
        #     n, k = map(int, input().split())
        #     s = input()
        #     print(s)
        # else:
        solve()


main()



Solution 2 (runtime: 234 ms):
'''
Observations:

- After a reversal, you must replace the sequence with its difference sequence as otherwise nothing has been done to the sum.
- The different sequence replacement reduces the length of the sequence by 1 so we can only do it a fixed number of times.

Therefore, if we brute-force:
Options are:
1. Nothing (current sum)
2. Reverse + difference
3. Difference
'''

from math import inf
from functools import lru_cache

def get_difference_sequence(path):
    return [path[i] - path[i - 1] for i in range(1, len(path))]

@lru_cache(None)
def backtrack(length, path):
    if length == 0:
        return -inf
    
    # Convert tuple back to list for processing
    path = list(path)
    
    # Reverse + Difference
    reverse_path = path[::-1]
    diff_path = get_difference_sequence(reverse_path)
    curr = sum(diff_path)
    ans = max(curr, backtrack(length - 1, tuple(diff_path)))
    
    # Difference only
    diff_path = get_difference_sequence(path)
    curr = sum(diff_path)
    
    return max(ans, curr, backtrack(length - 1, tuple(diff_path)))

t = int(input())

while t > 0:
    n = int(input())
    a = tuple(map(int, input().split()))
    s = sum(a)
    
    if n == 1:
        print(s)
    else:
        print(max(s, backtrack(n, a)))
    
    t -= 1