title: Maximum Sum Subarray Removing One Element
signature: def maximum_sum_subarray_removing_one_element(arr, n):
test_code: import array
  import bisect
  import collections
  import datetime
  import functools
  import heapq
  import itertools
  import math
  import queue
  import re
  import string
  import sys
  from typing import Any, Dict, List, Optional, Set
  
  
  # SOLUTION CODE
  # ============================================
  PLACEHOLDER_CODE_BODY
  
  # TESTING CODE 
  # ============================================
  def validate_solution(actual, expected):
      return actual == expected
  
  def driver(arr, n, expected):
      try:
          if validate_solution(PLACEHOLDER_FN_NAME(
              arr, n),
              expected
          ):
              return "PASSED"
          return "FAILED"
      except Exception as exception_obj:
          return type(exception_obj).__name__
      
  if __name__ == "__main__":
      result = driver([2, 8, 14, 17, 19, 35, 38, 45, 50, 53, 55, 70, 82, 88, 92, 96], 13, 488)
      print(f"TEST-0...{result}")
  
      result = driver([-64, -56, -80, -82, 72, 62, -8, 48, -96, 34, 64, -38, -60, 80, 4, -64, -62, 34, 94, -16, 38, 62, -84, 48, 42, -40], 22, 344)
      print(f"TEST-1...{result}")
  
      result = driver([0, 0, 0, 0, 1, 1, 1], 6, 2)
      print(f"TEST-2...{result}")
  
      result = driver([3, 7, 50, 53, 72, 14, 18, 74, 27, 65, 41, 20, 54, 17, 87, 40, 63, 15, 47], 11, 424)
      print(f"TEST-3...{result}")
  
      result = driver([-96, -96, -94, -80, -74, -74, -74, -74, -70, -64, -60, -58, -52, -52, -44, -42, -40, -38, -36, -34, -30, -14, -12, -8, -2, 6, 12, 16, 24, 24, 48, 48, 66, 76, 76, 84, 90], 32, 178)
      print(f"TEST-4...{result}")
  
      result = driver([1, 1, 0, 1, 1, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0], 8, 7)
      print(f"TEST-5...{result}")
  
      result = driver([4, 4, 5, 9, 11, 13, 13, 15, 16, 21, 23, 25, 27, 30, 31, 35, 35, 43, 43, 47, 49, 50, 52, 54, 55, 55, 57, 57, 57, 59, 62, 64, 66, 68, 69, 71, 73, 76, 80, 84, 88, 88, 90, 90, 97, 97, 99], 34, 1255)
      print(f"TEST-6...{result}")
  
      result = driver([-86, -60, 4, 14, 6, -6, -50, 46, -50, -62, -56, 16, -76, 90, 40, 2, 36, 48, -26, 34, 78, 84, 2, -54, 94, 60, -26, 60, 84, 2, -98, 2, -74], 25, 482)
      print(f"TEST-7...{result}")
  
      result = driver([0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1], 9, 1)
      print(f"TEST-8...{result}")
  
      result = driver([36, 99, 27, 8, 90, 74, 67, 77, 49, 23, 43, 25, 68, 56, 85, 6], 12, 646)
      print(f"TEST-9...{result}")
  
      sys.exit(0)
source_py: def maximum_sum_subarray_removing_one_element(arr, n):
      fw = [0 for k in range(n)]
      bw = [0 for k in range(n)]
      (cur_max, max_so_far) = (arr[0], arr[0])
      for i in range(n):
          cur_max = max(arr[i], (cur_max + arr[i]))
          max_so_far = max(max_so_far, cur_max)
          fw[i] = cur_max
      cur_max = max_so_far = bw[(n - 1)] = arr[(n - 1)]
      i = (n - 2)
      while (i >= 0):
          cur_max = max(arr[i], (cur_max + arr[i]))
          max_so_far = max(max_so_far, cur_max)
          bw[i] = cur_max
          i -= 1
      fans = max_so_far
      for i in range(1, (n - 1)):
          fans = max(fans, (fw[(i - 1)] + bw[(i + 1)]))
      return fans
source_cpp: int maximum_sum_subarray_removing_one_element(vector<int> arr, int n) {
    int fw [ n ], bw [ n ];
    int cur_max = arr [ 0 ], max_so_far = arr [ 0 ];
    fw [ 0 ] = arr [ 0 ];
    for ( int i = 1;
    i < n;
    i ++ ) {
      cur_max = max ( arr [ i ], cur_max + arr [ i ] );
      max_so_far = max ( max_so_far, cur_max );
      fw [ i ] = cur_max;
    }
    cur_max = max_so_far = bw [ n - 1 ] = arr [ n - 1 ];
    for ( int i = n - 2;
    i >= 0;
    i -- ) {
      cur_max = max ( arr [ i ], cur_max + arr [ i ] );
      max_so_far = max ( max_so_far, cur_max );
      bw [ i ] = cur_max;
    }
    int fans = max_so_far;
    for ( int i = 1;
    i < n - 1;
    i ++ ) fans = max ( fans, fw [ i - 1 ] + bw [ i + 1 ] );
    return fans;
  }