import math



class 					snake_case__       :



   def __init__(				self   :   int			,	A__   :   str   )							->     int:




         '''simple docstring'''




         snake_case_     :			Tuple       =       len(A__   )
         snake_case_     :			Union[str, Any]       =       [0] * (
             4 * self.N
         )  # approximate the overall size of segment tree with array N
         self.build(1			,	0			,	self.N - 1   )



   def 					UpperCAmelCase__       (				self   :   Optional[Any]			,	A__   :   Tuple   )							->     Optional[int]:




         '''simple docstring'''




         return idx * 2



   def 					UpperCAmelCase__       (				self   :   Union[str, Any]			,	A__   :   List[str]   )							->     Dict:




         '''simple docstring'''




         return idx * 2 + 1



   def 					UpperCAmelCase__       (				self   :   str			,	A__   :   Any			,	A__   :   Optional[int]			,	A__   :   Tuple   )							->     List[str]:  # noqa: E741




         '''simple docstring'''




         if l == r:
               snake_case_     :			str       =       A[l]
         else:
               snake_case_     :			List[str]       =       (l + r) // 2
               self.build(self.left(A__   )			,	A__			,	A__   )
               self.build(self.right(A__   )			,	mid + 1			,	A__   )
               snake_case_     :			Union[str, Any]       =       max(self.st[self.left(A__   )]			,	self.st[self.right(A__   )]   )



   def 					UpperCAmelCase__       (				self   :   Optional[Any]			,	A__   :   List[str]			,	A__   :   Union[str, Any]			,	A__   :   str   )							->     int:




         '''simple docstring'''




         return self.update_recursive(1			,	0			,	self.N - 1			,	a - 1			,	b - 1			,	A__   )



   def 					UpperCAmelCase__       (				self   :   Optional[int]			,	A__   :   Optional[Any]			,	A__   :   List[str]			,	A__   :   Optional[Any]			,	A__   :   Union[str, Any]			,	A__   :   List[Any]			,	A__   :   str   )							->     Any:  # noqa: E741




         '''simple docstring'''




         if r < a or l > b:
               return True
         if l == r:
               snake_case_     :			List[str]       =       val
               return True
         snake_case_     :			Dict       =       (l + r) // 2
         self.update_recursive(self.left(A__   )			,	A__			,	A__			,	A__			,	A__			,	A__   )
         self.update_recursive(self.right(A__   )			,	mid + 1			,	A__			,	A__			,	A__			,	A__   )
         snake_case_     :			Tuple       =       max(self.st[self.left(A__   )]			,	self.st[self.right(A__   )]   )
         return True



   def 					UpperCAmelCase__       (				self   :   Optional[int]			,	A__   :   List[Any]			,	A__   :   Optional[Any]   )							->     str:




         '''simple docstring'''




         return self.query_recursive(1			,	0			,	self.N - 1			,	a - 1			,	b - 1   )



   def 					UpperCAmelCase__       (				self   :   Union[str, Any]			,	A__   :   Any			,	A__   :   int			,	A__   :   Tuple			,	A__   :   Tuple			,	A__   :   Dict   )							->     str:  # noqa: E741




         '''simple docstring'''




         if r < a or l > b:
               return -math.inf
         if l >= a and r <= b:
               return self.st[idx]
         snake_case_     :			Dict       =       (l + r) // 2
         snake_case_     :			Optional[Any]       =       self.query_recursive(self.left(A__   )			,	A__			,	A__			,	A__			,	A__   )
         snake_case_     :			Any       =       self.query_recursive(self.right(A__   )			,	mid + 1			,	A__			,	A__			,	A__   )
         return max(A__			,	A__   )



   def 					UpperCAmelCase__       (				self   :   Dict   )							->     Optional[Any]:




         '''simple docstring'''




         snake_case_     :			int       =       []
         for i in range(1			,	N + 1   ):
               show_list += [self.query(A__			,	A__   )]
         print(A__   )


if __name__ == "__main__":
     UpperCAmelCase							=       [1, 2, -4, 7, 3, -5, 6, 1_1, -2_0, 9, 1_4, 1_5, 5, 2, -8]
     UpperCAmelCase							=       1_5
     UpperCAmelCase							=       SegmentTree(A)
     print(segt.query(4, 6))
     print(segt.query(7, 1_1))
     print(segt.query(7, 1_2))
     segt.update(1, 3, 1_1_1)
     print(segt.query(1, 1_5))
     segt.update(7, 8, 2_3_5)
     segt.show_data()




import os
import unittest

from transformers import is_torch_available
from transformers.testing_utils import require_sentencepiece, require_tokenizers, require_torch, slow, torch_device


if is_torch_available():
     import torch

     from transformers import GPTaLMHeadModel



@require_torch
@require_sentencepiece
@require_tokenizers
class 					snake_case__       (				unittest.TestCase							):



   @slow
   @unittest.skip("Model is not available."   )
   def 					UpperCAmelCase__       (				self   :   Dict   )							->     Optional[Any]:




         '''simple docstring'''




         snake_case_     :			str       =       "nvidia/megatron-gpt2-345m/"
         if "MYDIR" in os.environ:
               snake_case_     :			int       =       os.path.join(os.environ["MYDIR"]			,	A__   )
         snake_case_     :			str       =       GPTaLMHeadModel.from_pretrained(A__   )
         model.to(A__   )
         model.half()

         snake_case_     :			Optional[int]       =       torch.tensor(
             [[1_01, 71_10, 10_05, 10_56, 20_23, 1_13_33, 1_74_13, 10_29, 1_02]]			,	device=A__			,	dtype=torch.long			,	)

         with torch.no_grad():
               snake_case_     :			Union[str, Any]       =       model(A__   ).logits

         snake_case_     :			List[str]       =       torch.Size((1, 9, 5_02_57)   )
         self.assertEqual(output.shape			,	A__   )

         snake_case_     :			Dict       =       torch.tensor(
             [
                 4.9414,
                 -0.2920,
                 -1.2148,
                 -4.0273,
                 -0.5161,
                 -5.2109,
                 -1.2412,
                 -1.8301,
                 -1.7734,
                 -4.7148,
                 -0.2317,
                 -1.0811,
                 -2.1777,
                 0.4141,
                 -3.7969,
                 -4.0586,
                 -2.5332,
                 -3.3809,
                 4.3867,
             ]			,	device=A__			,	dtype=torch.half			,	)

         for i in range(19   ):
               snake_case_  ,snake_case_     :			Dict       =       8 * i // 17, 27_92 * i  # along the diagonal
               snake_case_  ,snake_case_     :			Any       =       output[0, r, c], expected_diag[i]
               snake_case_     :			Dict       =       f"row={r} col={c} computed={computed} expected={expected}"
               self.assertAlmostEqual(A__			,	A__			,	delta=1E-4			,	msg=A__   )



