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Your job is to write a function/program \$F\$ that takes a positive integer \$n\$ and generates a code fragment \$F(n)\$. The outputted code fragments must have the following properties:

• \$F(n)\$ as a program must output the number \$n\$.
• \$F(a)+\!\!\!+\,F(b)\$ as a program (where \$+\!\!+\$ means concatenation) must output \$a+b\$ if \$a≥b\$, \$b−a\$ otherwise.
• This must extend to any number of code fragments emitted by your program in the way that \$b−a\$ cases take precedence (think of an arithmetic expression with +s and -s, but the two sides of -s are flipped and it has higher precedence than +).
  • You do not need to consider the cases where three consecutive input numbers are strictly increasing (the equivalent arithmetic expression has two consecutive -s).

Your job is to write a function/program \$F\$ that takes a positive integer \$n\$ and generates a code fragment \$F(n)\$ (not necessarily in the same language). The outputted code fragments must have the following properties:

• \$F(n)\$ as a full program must output the number \$n\$.
• \$F(a)+\!\!\!+\,F(b)\$ as a program (where \$+\!\!+\$ means concatenation) must output \$a+b\$ if \$a≥b\$, \$b−a\$ otherwise.
• This must extend to any number of code fragments emitted by your program in the way that \$b−a\$ cases take precedence (think of an arithmetic expression with +s and -s, but the two sides of -s are flipped and it has higher precedence than +).
  • You do not need to consider the cases where three consecutive input numbers are strictly increasing (the equivalent arithmetic expression has two consecutive -s).

• \$F(n)\$ as a program must output the number \$n\$.
• \$F(a)+\!\!\!+F(b)\$ as a program (where \$+\!\!+\$ means concatenation) must output \$a+b\$ if \$a≥b\$, \$b−a\$ otherwise.
• This must extend to any number of code fragments emitted by your program in the way that \$b−a\$ cases take precedence (think of an arithmetic expression with +s and -s, but the two sides of -s are flipped and it has higher precedence than +).
  • You do not need to consider the cases where three consecutive input numbers are strictly increasing (the equivalent arithmetic expression has two consecutive -s).

• \$F(n)\$ as a program must output the number \$n\$.
• \$F(a)+\!\!\!+\,F(b)\$ as a program (where \$+\!\!+\$ means concatenation) must output \$a+b\$ if \$a≥b\$, \$b−a\$ otherwise.
• This must extend to any number of code fragments emitted by your program in the way that \$b−a\$ cases take precedence (think of an arithmetic expression with +s and -s, but the two sides of -s are flipped and it has higher precedence than +).
  • You do not need to consider the cases where three consecutive input numbers are strictly increasing (the equivalent arithmetic expression has two consecutive -s).