Write a problem, input, output, algorithm, comments and design a python program. The purpose of this assignment is to practice the use of Python input/output, modules and selectioncontrol structures to develop a solution to the given problem. Your solution will consist of two parts:(i) your name, university id, section number and your program design (written as comments at thebeginning of your program by defining the problem statement, input/output data and the algorithm inpseudocode), (ii) The corresponding Python program.Problem DefinitionThe factorial of a number n (written n!) is the number times the factorial of itself minus one; and thefactorial of 1 is, by definition, equals to 1. For example, the factorial of 2 is 2*1! = 2*1, and the factorialof 3 is 3*2! = 3*2*1=6, and so on. Implementing this definition using a computer program is relativelyslow, instead Sterling's formula is used as an approximation of the factorial for large values. Sterling'sformula is defined as follows:n! = e-nn" V2 πηThe exp(x) function in the math module gives the value of e raised to the power of xWrite a Python program that:1. Requests the user to enter 5 integer values of n greater than 10. It should check:a. if all entered values are greater than 10, then your program should:• output the message: "Thanks for entering 5 valid numbers greater than 10"calculate their factorial using sterling's formulaallow the users to enter one of the following format types, which should be used toprint the factorials of the numbersDefault representationScientific representation with default precisionNon Scientific representation with 2 decimal precisionsDSvalidate the format type:> if the format type is "Default representation", then it shouldV display the results in a tabular format using "Default representation" asshown in Figurel.else if the format type is "Scientific representation with default precision",then it shouldV display the results in a tabular format using "Scientific representation withdefault precision" as shown in Figure2.> else if the format type is "Non Scientific representation", then it shouldV display the results in a tabular format using "Non Scientific representationwith 2 decimal precisions" as shown in Figure3.otherwise, your program should display the following message as shown inFigure4:"You entered an invalid format type"b. otherwise, your program should output the following message:"Sorry you entered wrong numbers ====> BYE" Figurel shows a sample run of the program with valid numbers and Default representation formattype. Figure2 shows a sample run of the program with valid numbers and Scientific representationformat type. Figure3 shows a sample run of the program with valid numbers and Non Scientificrepresentation format type. Figure4 shows a sample run of an invalid format type and Figure5 showsa sample run of the program with invalid numbers.O Console 1/A DO Console 1/ADPlease enter 5 integer numbers greater than 10: 11 12 13 14 15Thanks for entering 5 valid numbers greater than 10Please enter 5 integer numbers greater than 10: 11 12 13 14 15Thanks for entering 5 valid numbers greater than 10Please Enter the format type:Please Enter the format type:Defalut representationScientific representation and default precisionNon Scientific representation and 2 decimal precisionDefalut representationScientific representation and default precisionNon Scientific representation and 2 decimal precisionNOutput format:Output format:Default representationScientific representationPrecision - default:NumSterling ValueNumSterling Value======3.961563e+07111213141539615625475687486618723947511121314154.756875e+086.187239e+098.666100e+101.300431e•12866610017401300430722199In (2): |Figurel: Sample run of the program with validnumbers and Default representation format type.In [24):Figure2: Sample run of the program with validnumbers and Scientific representation format type.O Cansole 1/A OO Console 1/APlease enter 5 integer numbers greater than 10: 11 12 13 14 15Thanks for entering 5 valid numbers greater than 10In [21]: runfile('C:/zuhoor_Hard disk/Zuhoor 2020/COMP2101/PythonCOMP2101_Spring2021/H\s/H2/H«2 Sample Solution SP2021_zuhoor.py', wdir='C:/zuhoor_Hard disk/Zuhoor 2820/COMP2101/Python COMP2101_Spring2021/Hls/HN2" )Please Enter the format type:Defalut representationScientific representation and default precisionNon Scientific representation and 2 decimal precisionDPlease enter 5 integer numbers greater than 10: 11 12 13 14 15Thanks for entering 5 valid numbers greater than 10InOutput format:Please Enter the format type:Non-Scientific representationPrecision = 2:Defalut represeScientific representation and default precisionNon Scientific representation and 2 decimal precisionDNumSterling Value111213141539615625.05k9475687486.476187239475.1986661001740. 601300430722199.47You entered an invalid format typeIn [22]:**.. .. ..Figure3: Sample run of the program with validnumbers and Non Scientific representation format format type.Figure4: Sample run of the program with invalidtype.

import mathfrom decimal import Decimalprint("Please enter 5 integer numbers greater than…

Problem Definition The factorial of a number n (written n!) is the number times the factorial of itself minus one; and the factorial of 1 is, by definition, equals to 1. For example, the factorial of 2 is 2*1! = 2*1, and the factorial of 3 is 3*2! = 3*2*1 =6, and so on. Implementing this definition using a computer program is relatively slow, instead Sterling's formula is used as an approximation of the factorial for large values. Sterling's formula is defined as follows: n! = e-n n" V2 n n The exp(x) function in the math module gives the value ofe raised to the power of x Write a Python program that: 1. Requests the user to enter 5 integer values of n greater than 10. It should check: a. if all entered values are greater than 10, then your program should: output the message: "Thanks for entering 5 valid numbers greater than 10" calculate their factorial using sterling's formula allow the users to enter one of the following format types, which should be used to print the factorials of the numbers Default representation Scientific representation with default precision Non Scientific representation with 2 decimal precisions S N validate the format type: > if the format type is "Default representation", then it should v display the results in a tabular format using "Default representation" as shown in Figurel. > else if the format type is "Scientific representation with default precision", then it should V display the results in a tabular format using “Scientific representation with default precision" as shown in Figure2. > else if the format type is "Non Scientific representation", then it should V display the results in a tabular format using "Non Scientific representation with 2 decimal precisions" as shown in Figure3. otherwise, your program should display the following message as shown in Figure4: "You entered an invalid format type" b. otherwise, your program should output the following message: "Sorry you entered wrong numbers === ==> BYE"